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Pie chart of populations of English native speakers

A pie chart (or a circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents. While it is named for its resemblance to a pie which has been sliced, there are variations on the way it can be presented. The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801.[1][2]

Pie charts are very widely used in the business world and the mass media.[3] However, they have been criticized,[4] and many experts recommend avoiding them,[5][6][7][8] as research has shown it is more difficult to make simple comparisons such as the size of different sections of a given pie chart, or to compare data across different pie charts. Some research has shown pie charts perform well for comparing complex combinations of sections (e.g., "A + B vs. C + D").[9] Commonly recommended alternatives to pie charts in most cases include bar charts, box plots, and dot plots.

History

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The earliest known pie chart is generally credited to William Playfair's Statistical Breviary of 1801, in which two such graphs are used.[1][2][10] Playfair presented an illustration, which contained a series of pie charts. One of those charts depicted the proportions of the Turkish Empire located in Asia, Europe and Africa before 1789. This invention was not widely used at first.[1]

Playfair thought that pie charts were in need of a third dimension to add additional information.[11]

Florence Nightingale may not have invented the pie chart, but she adapted it to make it more readable, which fostered its wide use, still today. Nightingale reconfigured the pie chart making the length of the wedges variable instead of their width. The graph, then, resembled a cock's comb.[12] She was later assumed to have created it due to the obscurity and lack of practicality of Playfair's creation.[13] Nightingale's polar area diagram,[14]: 107  or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, to illustrate seasonal sources of patient mortality in the military field hospital she managed, was published in Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army and sent to Queen Victoria in 1858. According to the historian Hugh Small, "she may have been the first to use [pie charts] for persuading people of the need for change."[12]

The French engineer Charles Joseph Minard also used pie charts, in 1858. A map of his from 1858 used pie charts to represent the cattle sent from all around France for consumption in Paris.

Early types of pie charts in the 19th century
  • Pie charts from William Playfair's "Statistical Breviary", 1801
    Pie charts from William Playfair's "Statistical Breviary", 1801
  • One of the earliest pie charts, 1801
    One of the earliest pie charts, 1801
  • Minard's map, 1858
    Minard's map, 1858
  • Polar chart by Florence Nightingale, 1858
    Polar chart by Florence Nightingale, 1858

Variants and similar charts

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In a redrawing of the perspective pie chart shown at MacWorld 2008 (top), the smaller Apple slice appears larger than the Other slice – the 2D pie chart (bottom) gives the true picture.

3D pie chart and perspective pie cake

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A 3D pie chart, or perspective pie chart, is used to give the chart a 3D look. Often used for aesthetic reasons, the third dimension does not improve the reading of the data; on the contrary, these plots are difficult to interpret because of the distorted effect of perspective associated with the third dimension. The use of superfluous dimensions not used to display the data of interest is discouraged for charts in general, not only for pie charts.[7][15]

Doughnut chart

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Information about the data as a whole in the center of a doughnut chart

A doughnut chart (also spelled donut) is a variant of the pie chart, with a blank center allowing for additional information about the data as a whole to be included. [16][17] Doughnut charts are similar to pie charts in that their aim is to illustrate proportions.[citation needed] This type of circular graph can support multiple statistics at once and it provides a better data intensity ratio to standard pie charts.[17] It does not have to contain information in the center.

Exploded pie chart

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Exploded pie chart for the example data (see below), with the largest party group exploded

A chart with one or more sectors separated from the rest of the disk is known as an exploded pie chart. This effect is used to either highlight a sector, or to highlight smaller segments of the chart with small proportions.

Polar area diagram

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Like conventional pie charts, a variable-radius pie chart has wedges whose areas represent total quantities in respective categories/groups. However, here, each radius represents an amount of that quantity per unit within that category. In this example, each wedge's area represents total CO2 emissions of all people in that category, and each radius represents emissions per person within that category.

The polar area diagram is similar to a usual pie chart, except sectors have equal angles and differ rather in how far each sector extends from the center of the circle. It is used to plot cyclic phenomena (e.g., counts of deaths by month). For example, if the counts of deaths in each month for a year are to be plotted then there will be 12 sectors (one per month) all with the same angle of 30 degrees each. The radius of each sector would be proportional to the square root of the death rate for the month, so the area of a sector represents the rate of deaths in a month. If the death rate in each month is subdivided by cause of death, it is possible to make multiple comparisons on one diagram, as is seen in the polar area diagram famously developed by Florence Nightingale.

The first known use of polar area diagrams was by André-Michel Guerry, which he called courbes circulaires (circular curves), in an 1829 paper showing seasonal and daily variation in wind direction over the year and births and deaths by hour of the day.[18] Léon Lalanne later used a polar diagram to show the frequency of wind directions around compass points in 1843. The wind rose is still used by meteorologists. Nightingale published her rose diagram in 1858. Although the name "coxcomb" has come to be associated with this type of diagram, Nightingale originally used the term to refer to the publication in which this diagram first appeared—an attention-getting book of charts and tables—rather than to this specific type of diagram.[19]

  • "Diagram of the causes of mortality in the army in the East" by Florence Nightingale
    "Diagram of the causes of mortality in the army in the East" by Florence Nightingale

Ring chart, sunburst chart, and multilevel pie chart

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See also: Radial tree
Multi-level pie chart representing disk usage in a Linux file system

A ring chart, also known as a sunburst chart or a multilevel pie chart, is used to visualize hierarchical data, depicted by concentric circles.[20] The circle in the center represents the root node, with the hierarchy moving outward from the center. A segment of the inner circle bears a hierarchical relationship to those segments of the outer circle which lie within the angular sweep of the parent segment.[21]

Spie chart

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A spie chart comparing number of students with student costs across four different schools

A variant of the polar area chart is the spie chart, designed by Dror Feitelson.[22] The design superimposes a normal pie chart with a modified polar area chart to permit the comparison of two sets of related data. The base pie chart represents the first data set in the usual way, with different slice sizes. The second set is represented by the superimposed polar area chart, using the same angles as the base, and adjusting the radii to fit the data. For example, the base pie chart could show the distribution of age and gender groups in a population, and the overlay their representation among road casualties. Age and gender groups that are especially susceptible to being involved in accidents then stand out as slices that extend beyond the original pie chart.

Square chart / Waffle chart

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Square pie chart (waffle chart), showing how smaller percentages are more easily shown than on circular charts. On the 10x10 grid, each cell represents 1%.

Square charts, also called waffle charts, are a form of pie charts that use squares instead of circles to represent percentages. Similar to basic circular pie charts, square pie charts take each percentage out of a total 100%. They are often 10 by 10 grids, where each cell represents 1%. Despite the name, circles, pictograms (such as of people), and other shapes may be used instead of squares. One major benefit to square charts is that smaller percentages, difficult to see on traditional pie charts, can be easily depicted.[23]

Example

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The following example chart is based on preliminary results of the election for the European Parliament in 2004. The table lists the number of seats allocated to each party group, along with the derived percentage of the total that they each make up. The values in the last column, the derived central angle of each sector, is found by taking that percentage of 360.

Group Seats Percent (%) Central angle (°)
EUL 39 5.3 19.2
PES 200 27.3 98.4
EFA 42 5.7 20.7
EDD 15 2.0 7.4
ELDR 67 9.2 33.0
EPP 276 37.7 135.7
UEN 27 3.7 13.3
Other 66 9.0 32.5
Total 732 99.9* 360.2*

*Because of rounding, these totals do not add up to 100 and 360.

A pie chart for the example data

The size of each central angle is proportional to the size of the corresponding quantity, here the number of seats. Since the sum of the central angles has to be 360°, the central angle for a quantity that is a fraction Q of the total is 360Q degrees. In the example, the central angle for the largest group (European People's Party (EPP)) is 135.7° because 0.377 times 360, rounded to one decimal place, equals 135.7.

Use and effectiveness

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3D pie chart showing Atmospheric air components percentage

A flaw exhibited by pie charts is that they cannot show more than a few values without separating the visual encoding (the “slices”) from the data they represent (typically percentages). When slices become too small, pie charts have to rely on colors, textures or arrows so the reader can understand them. This makes them unsuitable for use with larger amounts of data. Pie charts also take up a larger amount of space on the page compared to the more flexible bar charts, which do not need to have separate legends, and can display other values such as averages or targets at the same time.[7]

Statisticians generally regard pie charts as a poor method of displaying information, and they are uncommon in scientific literature. One reason is that it is more difficult for comparisons to be made between the size of items in a chart when area is used instead of length and when different items are shown as different shapes.[24]

Three sets of percentages, plotted as both piecharts and barcharts. Comparing the data on barcharts is generally easier.

Further, in research performed at AT&T Bell Laboratories, it was shown that comparison by angle was less accurate than comparison by length. Most subjects have difficulty ordering the slices in the pie chart by size; when an equivalent bar chart is used the comparison is much easier.[25] Similarly, comparisons between data sets are easier using the bar chart. However, if the goal is to compare a given category (a slice of the pie) with the total (the whole pie) in a single chart and the multiple is close to 25 or 50 percent, then a pie chart can often be more effective than a bar graph.[26][9]

An example of a pie chart with 18 values, with some colors repeated

In a pie chart with many section, several values may be represented with the same or similar colors, making interpretation difficult.

An example of a doughnut shape pie chart, showing the batting and run records of Indian cricket players in test matches in 2019

Several studies presented at the European Visualization Conference analyzed the relative accuracy of several pie chart formats,[27][28][23] reaching the conclusion that pie charts and doughnut charts produce similar error levels when reading them, and square pie charts provide the most accurate reading.[29]

See also

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References

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Further reading

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Pie chart

View on Grokipedia
from Grokipedia
A pie chart, also known as a , is a circular statistical graphic divided into wedge-shaped slices to represent the proportional sizes of different categories within a that collectively form a whole. Each slice's is determined by the (category value / total value) × 360°, ensuring the full circle sums to 100% or the entire . This visualization is particularly suited for nominal or categorical , where the focus is on relative shares rather than exact quantities, making it a simple tool for conveying part-to-whole relationships at a glance. The pie chart was invented by Scottish engineer and political economist William Playfair in 1801, appearing in his book Statistical Breviary, showing the proportions of the Turkish Empire located in Asia, Europe, and Africa before 1789. Playfair's innovation built on earlier circular representations but introduced the divided sectors to emphasize comparative proportions, marking a key advancement in data visualization during the Enlightenment era. Since then, pie charts have become ubiquitous in fields like business, education, and journalism for summarizing market shares, budget allocations, or demographic breakdowns. Despite their intuitive appeal, pie charts have notable limitations: they are most effective with 3 to 6 distinct categories where proportions differ markedly, as humans struggle to accurately compare angles or areas in more complex or similar-sized slices. For precise comparisons across multiple datasets or numerous categories, alternatives like bar charts are often preferred, as they align better with perceptual accuracy in judging lengths over angles. Common variants include the donut chart, which features a central hole for added labels or emphasis, and exploded pie charts, where slices are pulled outward to highlight specific segments, though 3D effects can introduce and are generally discouraged. Best practices emphasize clear labeling, high-contrast colors, and starting the largest slice at the 12 o'clock position to enhance readability without overwhelming the viewer.

Fundamentals

Definition and Purpose

A pie chart is a circular statistical graphic that divides a circle into sectors, or slices, to represent the proportional parts of a whole, where the size of each slice corresponds to the magnitude of the category it depicts. This format effectively summarizes categorical by showing how individual components contribute to an overall total, such as the distribution of expenses in a or segments of among competitors. The purpose of a pie chart lies in its ability to visually communicate relative proportions at a glance, aiding in the quick comprehension of data hierarchies without requiring precise numerical reading. It is particularly useful for datasets with a small number of categories, where the emphasis is on comparative sizes rather than absolute values. The name "pie chart" originates from its visual similarity to a pie divided into wedges, with the term first appearing in English usage during the early . As a foundational tool, the pie chart's two-dimensional circular structure, including its slices and accompanying labels, provides the essential model for subsequent variations in proportional data representation.

Components and Structure

A pie chart consists of a central that represents the total , equivalent to 100% of the whole. This circular form symbolizes unity and completeness, with the entire circumference enclosing all categories. The primary structural elements are the individual slices, also known as sectors, which divide the into wedge-shaped segments. Each slice corresponds to a specific category within the , and its size is determined by the relative proportion of that category's value to the overall sum. In a standard pie chart, these slices radiate outward from the center, creating a symmetrical layout that emphasizes the interconnected parts of the whole. Proportional representation in pie charts occurs through three interrelated visual encodings: the of each slice, its along the , and the area of the segment. The , measured in degrees, directly scales with the data value, where the full circle spans 360 degrees to match the 100% total. Arc length follows proportionally from the angle, providing a linear cue along the edge, while the area of the slice, which is the product of the angle and the square of the radius, offers a two-dimensional measure that humans often perceive intuitively. Research indicates that while angle is the intended encoding, viewers may rely more heavily on area for judgments, though all three contribute to accurate interpretation when designed properly. To enhance clarity, pie charts incorporate optional labeling elements. A title or central label at the circle's core can denote the total value or dataset summary, while peripheral labels positioned adjacent to each slice identify category names and often include percentage values or absolute figures. For charts with numerous categories, a separate —typically placed outside the circle—maps colors or patterns to each slice, avoiding clutter on the main graphic. Variations in orientation maintain the radial but may include subtle radial lines extending from the center to slice boundaries for improved boundary definition, particularly in dense charts. This setup ensures the pie chart's supports quick visual assessment of part-to-whole relationships without overwhelming the viewer.

Historical Development

Invention and Early Examples

The pie chart, originally termed a "circle graph," was invented by Scottish engineer and economist in 1801. He introduced it in his book The Statistical Breviary: Shewing, on a Principle Entirely New, the Resources of Every State and of Every Empire in , where it served to visually represent proportional data in a compact, intuitive manner. Playfair's innovation built upon his earlier graphical inventions, such as the line and bar charts from 1786, adapting radial division to emphasize part-to-whole relationships more effectively than linear formats. Playfair's inaugural pie chart illustrated the territorial divisions of the Turkish Empire prior to , dividing a circle into three sectors proportional to the land areas in , , and . Subsequent examples in the same volume included pie charts depicting the relative populations and government revenues across fifteen European nations, highlighting disparities in size and fiscal capacity. In his broader oeuvre, such as later editions of The Commercial and Political Atlas, Playfair extended the form to economic indicators, including government expenditures and debts, to compare national finances over time. These applications demonstrated the pie chart's utility for summarizing complex proportional data, influenced by earlier radial diagrams in astronomy and , though Playfair formalized the equal-angular slicing based on percentages of a whole. Although conceptual precursors existed in 18th-century divided-circle representations for logical or astronomical purposes, Playfair's version marked the first systematic use in statistical graphics. The pie chart gained initial traction in the mid-19th century, appearing in statistical atlases across Europe and the United States to visualize economic and demographic data, such as trade balances and population shares. This adoption reflected growing interest in graphical methods amid industrialization, positioning the pie chart as a staple for public and governmental reports.

Evolution in the 19th and 20th Centuries

In the , pie charts gained wider adoption beyond their initial invention, particularly in geographical and demographic visualizations. French civil engineer incorporated pie charts into his thematic maps to represent proportions of goods, , and resources, such as in his 1858 map of butcher's meats supplied to the market, where divided circles depicted the relative amounts of , , and mutton. Similarly, the introduced pie charts in its Statistical Atlas, compiled under superintendent Francis A. Walker, to illustrate demographic proportions like nativity, occupation, and wealth distribution across states, marking one of the earliest large-scale governmental uses for public reporting. By the early , pie charts integrated into business and economic reporting as graphical methods proliferated. In the , corporate annual reports began featuring pie charts to summarize financial compositions, such as sources or breakdowns, reflecting the growing emphasis on visual statistics in commerce following economic analyses. During the 1940s, amid , pie charts appeared in wartime economic charts produced by U.S. government agencies, including the , to depict allocations of resources like and labor toward military versus civilian needs, aiding public and policy communication of industrial shifts. The mid-20th century saw pie charts popularized through statistical software, enhancing accessibility for analysts. The Statistical Package for the Social Sciences (), first released in , later included pie chart generation as a feature, enabling researchers to quickly visualize categorical data in social sciences and beyond. By this era, pie charts had become a standard in textbooks and journalistic graphics, used to convey part-to-whole relationships in and media, though their prominence also invited scrutiny. Critiques of pie charts emerged prominently in the 1970s, focusing on readability limitations when depicting many slices, as empirical studies showed viewers struggled with accurate angle comparisons compared to linear formats like bar charts. In the 1980s, the advent of and tools like , launched in 1985, standardized pie chart creation with user-friendly templates and automation, further embedding them in professional and everyday data presentation despite ongoing debates.

Construction Methods

Step-by-Step Creation Process

Creating a pie chart begins with thorough preparation of the . Collect categorical data, where each category represents a distinct portion of a whole, such as market shares or survey responses, and compute the total sum of all category values to establish the baseline for proportions. This total ensures that the chart accurately reflects the relative sizes of each category without distortion. The manual construction process involves several sequential steps to ensure proportional accuracy. First, draw a using a to represent the whole, marking the center point clearly. Second, establish a starting point, typically at the vertical top of the , by drawing a line from the center outward. Third, using a protractor aligned with the center and starting , measure and mark each successive for the slices in sequence, drawing radii to connect these points and form the wedges; this step demands precision to maintain equal spacing and correct proportions. Fourth, add labels directly on or adjacent to each slice—referencing the core components like these wedges and annotations—and include a if needed to identify categories. For digital creation, software tools simplify the process while upholding proportion accuracy. In , select the prepared data range including categories and values, navigate to the Insert tab, choose from the Charts group, and select a basic pie chart type; the software automatically generates the chart based on the data sums. Similar steps apply in other applications like , where inserting a pie chart from selected data ensures slices reflect exact proportions without manual measurement. Common pitfalls in construction can undermine the chart's reliability. Unequal spacing often arises from imprecise protractor alignment during manual plotting, leading to visually skewed slices that misrepresent . Additionally, failing to verify that all slices collectively sum to 360 degrees—whether through data total errors or plotting oversights—results in incomplete or overflowing representations of the whole. To mitigate these, double-check measurements or rely on software validation features before finalizing the chart.

Mathematical Calculations

The mathematical foundation of a pie chart relies on converting categorical data values into proportional representations that fit within a full circle of 360 degrees. To begin, the proportion for each category is determined by dividing its value by the sum of all category values, often expressed as a percentage by multiplying by 100: Percentage=(category valuetotal sum)×100\text{Percentage} = \left( \frac{\text{category value}}{\text{total sum}} \right) \times 100 This step quantifies each category's share of the whole. The central angle for each slice is then calculated by scaling the proportion to the full circle: Central angle=(category valuetotal sum)×360∘\text{Central angle} = \left( \frac{\text{category value}}{\text{total sum}} \right) \times 360^\circ This ensures the slices collectively span exactly 360 degrees. For example, consider data values of 20, 30, and 50, with a total sum of 100. The percentages are 20%, 30%, and 50%, respectively. The corresponding central angles are derived as follows: (20/100)×360∘=72∘(20/100) \times 360^\circ = 72^\circ, (30/100)×360∘=108∘(30/100) \times 360^\circ = 108^\circ, and (50/100)×360∘=180∘(50/100) \times 360^\circ = 180^\circ. These angles sum to 360 degrees, confirming the representation's accuracy. To position the slices sequentially around the circle, cumulative angles are used, starting from a reference line (typically at 0 degrees). The first slice occupies from 0° to its (e.g., 0° to 72°), the second from the end of the first to the sum of the first two (e.g., 72° to 180°), and so on, with each subsequent slice beginning at the cumulative of the previous ones.

Design Principles

Labeling and Visual Best Practices

Effective labeling in pie charts ensures that viewers can quickly interpret the proportions represented by each slice without confusion or excessive cognitive effort. Direct labels placed on or adjacent to slices are preferred for charts with fewer than five categories, where values or percentages can be inscribed within larger segments for immediate readability. For smaller slices, external callouts—lines connecting the label to the segment—prevent overlap and maintain clarity. Legends are recommended to avoid cluttering the visual field, though they should be positioned nearby and use consistent color matching to facilitate association. Best practices emphasize limiting pie charts to no more than five slices to enhance comparability and reduce visual complexity, as excessive divisions hinder accurate perception of relative sizes. Prioritizing the largest slices for direct labeling while grouping minor categories into an "Other" segment preserves focus on dominant proportions without sacrificing completeness. Contrasting colors between labels and backgrounds improve legibility, and adhering to Tufte's data-ink ratio principle—maximizing ink devoted to data representation while minimizing non-essential elements—avoids decorative clutter that distracts from the core information. Accessibility considerations are integral to , requiring high-contrast text for labels to accommodate low-vision users and provision of alt-text descriptions in digital formats that detail slice proportions and categories. Guidelines recommend slice labeling over legends where possible to aid navigation, ensuring patterns or textures supplement color for differentiation in or color-deficient viewing. Common errors in pie chart labeling include overlapping text on adjacent slices, which obscures data and increases misinterpretation risk, and excessive use of absolute values instead of percentages, complicating proportion judgments since slice areas do not scale linearly with numbers. Misleading , such as unnecessary shadows, can further distort perceived sizes, violating principles of honest graphical integrity.

Color and Readability Considerations

Effective color selection in pie charts is crucial for distinguishing slices and ensuring , particularly by choosing distinct, non-adjacent hues from the to maximize perceptual separation. Complementary or that are evenly spaced around the hue help viewers differentiate categories without confusion, as adjacent shades can blend visually. A key consideration is avoiding red-green combinations, which pose challenges for individuals with deuteranomaly or protanomaly, the most common forms of deficiency affecting approximately 8% of men worldwide. Readability is enhanced by varying saturation and levels across slices, allowing differentiation even in low-contrast environments or when printed in . For compatibility, incorporating patterns, textures, or within slices provides an alternative to color reliance, maintaining clarity without chromatic cues. These factors align with (WCAG) 2.1, which recommend a minimum 3:1 for graphical elements like pie slices against their background to support users with low vision. Perceptually, pie charts leverage central for value comparison, as humans judge more accurately than slice areas, according to foundational experiments in graphical . This —where outperforms area —suggests designers should prioritize arc lengths that clearly convey proportional differences, minimizing distortions from area-based misjudgments. Practical tools like ColorBrewer offer pre-designed qualitative palettes optimized for categorical data in charts such as pies, ensuring perceptual uniformity and colorblind-friendliness through simulated testing. Accessibility compliance can be verified using WCAG evaluation tools, such as contrast checkers, to confirm that color schemes meet standards like Success Criterion 1.4.1 (Use of Color), which prohibits sole reliance on hue for conveying information.

Variants

Doughnut and Exploded Charts

A doughnut chart, also known as a ring chart, is a variant of the pie chart featuring a hollow center achieved by setting an inner radius greater than zero, while preserving the angular proportions of the segments to represent parts of a whole. This design is created by drawing two concentric circles—the outer circle defining the full radius and the inner circle creating the empty space—and filling the annular region between them with wedge-shaped sectors proportional to the data values. The angular proportions follow the same base calculations as standard pie charts, where each segment's angle is determined by the ratio of its value to the total dataset. Doughnut charts are particularly useful for displaying inner and outer proportions or simple nested data structures, such as departmental where the outer ring shows overall allocations and the center can highlight a summary metric like total expenditure. For instance, in organizational reporting, they effectively illustrate hierarchical breakdowns like distributions across divisions, allowing viewers to grasp relative contributions at a glance without overwhelming detail. An exploded pie chart modifies the standard pie by pulling one or more slices outward from along radial lines, using displacement vectors to create separation and emphasize specific segments. This effect is typically achieved by applying a or selective offset, often 10-20% of the pie's , to the chosen slices via formatting tools that adjust their position relative to . Exploded charts are ideal for highlighting outliers or key categories, such as isolating the largest in a distribution to draw attention to dominant performers.

3D and Perspective Variations

3D pie charts introduce depth by extruding the slices outward from the center, producing a cylindrical or "cake-like" appearance that simulates three-dimensionality on a two-dimensional surface. The central angles of the slices remain proportional to the underlying data values as in traditional pie charts, but the added height creates varying volumes that can mislead viewers into overemphasizing larger or front-facing segments. Perspective variations, often called perspective pie cakes, apply a tilted viewpoint—typically at an angle such as 30 degrees—to enhance the of depth and drama, a feature commonly available in presentation software like . This tilt simulates a from above and to the side, making the chart appear more dynamic, though it can integrate with exploded slices for emphasis on specific segments. A key technical challenge in these variations is foreshortening, where slices closer to the viewer (particularly those at the front) project larger on the screen due to the perspective projection, distorting perceived proportions unless adjusted through trigonometric calculations for projected angles. These 3D and perspective effects gained popularity in the 1990s with the rise of , notably 97, which introduced built-in 3D chart options to appeal to users seeking visually engaging presentations. However, visualization expert critiqued such pseudo-3D representations in his 1990 book Envisioning Information for introducing unnecessary distortions and "" that obscure rather than clarify the .

Polar Area and Spie Charts

The polar area diagram, also known as a coxcomb or rose diagram, was invented by in 1858 to visualize mortality data from the (1853–1856). In this chart type, sectors maintain equal angular widths, typically 12 equal divisions representing months or categories, while the radius of each sector is scaled such that the area is proportional to the data value—meaning the radius is the of the quantity. Nightingale employed these diagrams in her report Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the , demonstrating that preventable diseases caused far more deaths than battlefield wounds, with areas for disease mortality dwarfing those for other causes across multiple years. Unlike standard pie charts, where proportions are encoded solely by angular slice size with a fixed , polar area diagrams emphasize magnitude through varying radial extent, allowing areas to directly represent quantities while equal angles facilitate temporal or categorical comparisons. This design choice makes polar area charts particularly effective for highlighting disparities in data, as the quadratic scaling of area to radius amplifies differences visually, though it can distort perceptions if not interpreted carefully. Nightingale's original diagrams used vibrant colors— for preventable deaths, for wounds, and black for other causes—to underscore sanitary reforms, influencing and . The spie chart represents a further evolution, integrating elements of both pie and polar area diagrams by superimposing angular proportions with radial or height variations to encode two variables simultaneously. In a spie chart, slice angles reflect one metric (e.g., relative shares), while radial lengths or extruded heights represent another (e.g., absolute magnitudes), creating a 3D-like surface that conveys comparative effectiveness or safety across multiple outcomes. This variant adds curvature and depth for immersive representation, distinguishing it from flat polar areas by allowing visualization of multidimensional data, such as treatment performance in clinical studies where slice width shows efficacy rates and height indicates sample sizes. Spie charts differ from traditional pies by prioritizing dual encoding over single-proportion display, enabling better comparisons of scaled quantities, though their added complexity can challenge readability. For instance, in visualizations, spie charts have quantified treatment outcomes in network meta-analysis for clinical studies, such as comparisons of treatments across efficacy and safety outcomes.

Sunburst, Ring, and Multilevel Pies

Sunburst charts extend the pie chart concept to hierarchical data structures by arranging information in concentric rings, with the innermost ring representing the top-level categories and subsequent outer rings depicting nested subcategories through subdivided arcs. Each arc's angular extent is proportional to the relative size or value of its category, allowing viewers to discern both overall proportions and detailed breakdowns in a compact, radial format. This technique originated in the 1990s as an evolution of nested pie charts and radial treemaps, building on earlier hierarchical visualization methods like Ben Shneiderman's treemap from 1992. Ring charts function as a simpler variant of charts, focusing on single-level nesting where an inner ring or circle displays primary categories, and an immediately adjacent outer ring shows their direct subcomponents without further . This design maintains the radial proportionality of pie charts while accommodating moderate , often used when depth is limited to two layers. Multilevel pies, in contrast, extend this radially for typically 2-3 layers, treating each concentric layer as a pie chart that subdivides the arcs of the previous level, emphasizing symmetrical or asymmetrical tree-like relationships in a consolidated circular view. In construction, the process begins with the innermost circle allocated to the top-level , divided into whose are calculated proportionally to category values (e.g., = (value / total) × 360°). Subsequent levels apply recursive division: each arc from the prior ring is further partitioned based on subcategory proportions relative to its , ensuring nested segments align radially and maintain proportional integrity across rings. This recursive approach enables visualization of deep hierarchies while preserving the space-filling efficiency of circular layouts. These variants find applications in representing organizational charts, where inner rings denote departments and outer rings show teams or roles, and in analytics to map user navigation paths, with rings illustrating page categories and subpaths. For instance, charts effectively summarize complex sequences like YouTube video discovery, projecting multidimensional navigation data into hierarchical rings for pattern identification. Their popularity surged in the 2010s through the library, particularly via Mike Bostock's zoomable sunburst implementation, which facilitated interactive web-based explorations of hierarchies such as file systems.

Waffle and Square Charts

Waffle charts, also known as square charts or square pies, represent proportions of a whole using a square grid divided into equal cells, typically arranged in a 10x10 layout representing 100%, where each filled cell corresponds to 1% of the total. For instance, a category accounting for 25% of the would be depicted by filling 25 cells with a designated color, providing a discrete, countable method for visualizing parts-to-whole relationships. This format facilitates straightforward percentage estimation through simple counting rather than angular assessment. The conceptual roots of waffle and square charts trace back to early 20th-century , including the ISOTYPE system developed by in the 1920s and 1930s, which utilized repeated square tiles and icons in grid-like arrangements to convey quantitative proportions accessibly to broad audiences. Compared to traditional pie charts, waffle and square charts mitigate radial distortions by aligning elements in a Cartesian grid, enabling more accurate visual judgments of relative sizes through linear alignment and direct enumeration rather than curved slices. This grid orientation reduces perceptual biases associated with angle perception and supports better comparability across categories, particularly for percentages near 0% or 100%. Waffle charts, in particular, gained prominence in data visualization discussions during the early 2010s, building on these foundational tile methods to offer compact, engaging alternatives for proportional displays.

Applications

Common Use Cases

Pie charts are frequently employed in contexts to illustrate distributions, such as the breakdown of cloud infrastructure services among leading providers like AWS, , Google Cloud, and others, where each slice represents a provider's of total . Similarly, they are used for budget allocations, depicting how organizational funds are divided across categories like , operations, and , enabling quick visual assessments of spending priorities in financial reports. In demographics, pie charts effectively display population compositions by age groups, for instance, showing the proportions of individuals in categories such as under 18, 18-44, 45-64, and 65 and over within a national census. They are also common in election reporting to represent vote percentages, such as the share of votes received by major candidates or parties in a presidential race, providing an immediate sense of electoral outcomes. For everyday applications, pie charts summarize survey results, like the distribution of preferences for favorite foods among respondents, where slices might indicate percentages favoring items such as , burgers, or salads. In resource distribution, they visualize energy source compositions, as seen in breakdowns of U.S. by categories including , , , and renewables. In digital environments, pie charts appear in dashboards like those built with Tableau for overviewing key metrics, such as regional sales contributions to total revenue in tools. They are also integrated into journalism infographics on platforms like to convey market shares or demographic shifts succinctly to broad audiences.

Effectiveness in Data Visualization

Pie charts excel in communicating proportions when limited to a small number of categories, typically 2 to 5, where they enable users to intuitively perceive relative magnitudes and identify dominant elements, such as the largest slice, through of angular sectors. This effectiveness arises from the chart's circular structure, which encodes as parts of a unified whole, facilitating rapid assessment without requiring precise numerical reading. The cognitive fit of pie charts aligns closely with part-to-whole mental models, supporting tasks that involve judging relationships between components and the total, as outlined in cognitive fit theory, which posits that representations matching task syntax enhance comprehension and decision-making performance. Empirical studies confirm this, demonstrating that pie charts yield comparable or superior accuracy to bar charts for proportion estimation in such scenarios, particularly when comparing slices within a single chart. For instance, research on patient-reported outcomes found pie charts led to higher interpretation accuracy than bar charts for simple proportional data. Pie charts prove particularly successful in static reports and presentations, where they convey proportional information more accessibly than tables for audiences less familiar with numerical , allowing quick uptake of overall composition without delving into exact values. This advantage holds in contexts like overviews, where the visual emphasis on relative shares aids non-expert viewers in grasping key distributions at a glance. Perceptual studies indicate that pie charts support accurate estimation of proportions with low bias across varying slice sizes, reinforced by Gestalt principles of closure, where the enclosed circular form promotes holistic of the as an integrated whole, strengthening the intuitive understanding of component interrelations.

Criticisms and Alternatives

Limitations of Pie Charts

Pie charts present several perceptual challenges that limit their effectiveness in accurately conveying data. Human perception of , which is essential for interpreting slice proportions, is inherently inaccurate compared to other graphical elements like lengths or positions. In a seminal study, and McGill (1984) demonstrated that angle judgments in pie charts are approximately half as accurate as position (length) judgments in bar charts, with mean log absolute error of 2.01 for angles versus 1.04 for position, leading to frequent underestimation of acute angles and overestimation of obtuse ones. This inaccuracy is particularly pronounced when comparing small slices, where errors can be substantial due to the difficulty in discerning subtle angular differences. With three or more slices, pie charts often suffer from visual clutter, as the proximity and overlapping visual cues create a "crowded" appearance that hinders quick comprehension of relative sizes. This clutter exacerbates perceptual errors, making it challenging for viewers to isolate and compare individual segments without additional cognitive effort. Pie charts scale poorly beyond a limited number of categories, becoming ineffective for datasets with more than five slices, as additional segments amplify clutter and reduce the chart's readability. Without explicit labels or values, discerning absolute quantities from pie charts is difficult, since the format emphasizes relative proportions rather than precise magnitudes, often requiring supplementary text that defeats the purpose of visual encoding. Common misuses further compound these issues, such as the implied perceptual equality among similarly shaped slices, which can lead to misjudgments if colors or patterns are not sufficiently distinct to differentiate them.

Comparisons to Other Chart Types

Bar charts are generally preferred over pie charts for comparing proportions across multiple categories, as the linear lengths of bars enable more accurate perceptual judgments than the angles of pie slices, which are difficult to compare unless they represent obvious values like 25% or 50%. This superiority is supported by research on graphical perception, which shows that people decode bar lengths more efficiently and precisely than angular differences. For datasets with five or more categories, bar charts further excel by avoiding the crowding and estimation errors common in pies, making them the recommended choice for precise comparisons. However, a 2025 study by Andrew Hill found pie charts to be as accurate as bar charts for part-to-whole relationships, with comparable mean errors of about 1 percentage point. Treemaps offer a compelling alternative to pie charts when visualizing hierarchical or nested proportions, employing nested rectangles sized by area to represent data without the radial distortions and comparison challenges of circular layouts. Unlike pie charts, which are best suited for simple, flat part-to-whole relationships with few categories, treemaps efficiently handle complex structures by utilizing rectangular space more scalably and reducing in magnitude estimation through consistent area-based encoding. This makes treemaps particularly valuable for large or multilevel datasets where pie charts would become cluttered and ineffective. Stacked bar charts surpass pie charts in scenarios involving trends over time or across multiple groups, as they display both individual component proportions and total values in a linear format that facilitates tracking changes, while pie charts are inherently static and limited to single snapshots. For example, bars allow viewers to assess how subcategories contribute to evolving wholes, providing clearer insights into compositional shifts that pies cannot convey without multiple separate charts. Data visualization guidelines, such as those from Stephen Few, emphasize using or side-by-side bars over pies for most proportional displays to enhance readability and analytical depth.

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