Cubic centimetre

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Cubic centimetre

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cubic centimetre
A measuring cup holding 1000 cubic centimetres, that is one litre (1 L) or 1000 millilitres (1000 mL)
General information
Unit system	Prefixed SI derived unit
Unit of	volume
Symbol	cm³
Conversions
1 cm³ in ...	... is equal to ...

SI base units	10⁻⁶ m³
Imperial and U.S. customary	0.06102374 in³

A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre. The mass of one cubic centimetre of water at 3.98 °C (the temperature at which it attains its maximum density) is almost equal to one gram.

One complete cycle of a straight-four engine. The areas marked in orange represent the displaced volumes.

In internal combustion engines, "cc" refers to the total volume of its engine displacement in cubic centimetres. The displacement can be calculated using the formula

d={\pi  \over 4}\times b^{2}\times s\times n

where $d$ is engine displacement, $b$ is the bore of the cylinders, $s$ is length of the stroke and $n$ is the number of cylinders.

Conversions

1 millilitre = 1 cm³
1 litre = 1000 cm³
1 cubic inch = 16.38706 cm³.

Unicode character

[edit]

The "cubic centimetre" symbol is encoded by Unicode at code point U+33A4 ㎤ SQUARE CM CUBED.^[1]

References

[edit]

^ Unicode Consortium (2019). "The Unicode Standard 12.0 – CJK Compatibility ❰ Range: 3300—33FF ❱" (PDF). Unicode.org. Retrieved May 24, 2019.

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The cubic centimetre (symbol: cm³) is a unit of volume in the metric system, defined as the volume of a cube measuring one centimetre on each side.^[1] It is exactly equivalent to one millilitre (mL) and is commonly abbreviated as "cc" or "c.c.", with 1,000 cubic centimetres equalling one litre.^[2]^[3] In practical applications, the cubic centimetre is extensively used in medicine to quantify the volume of fluids, such as medication dosages or the size of tumours and body cavities, where its equivalence to the millilitre facilitates precise administration.^[2]^[4] Despite recommendations from standards bodies to prefer "mL" over "cc" to avoid potential misinterpretation with other abbreviations like "u" for units, the term persists in clinical settings for its familiarity.^[5] In the automotive sector, cubic centimetres measure engine displacement—the total volume swept by all pistons in the cylinders—serving as a key indicator of an engine's power potential and efficiency, particularly for smaller vehicles where displacements are often expressed in the range of 1,000 to 2,000 cm³.^[6] Although the base SI unit for volume is the cubic metre (m³), the cubic centimetre's smaller scale makes it ideal for everyday and technical measurements in fields like chemistry, engineering, and manufacturing, where it denotes capacities of solids, liquids, or gases with high precision.^[1]^[7] Its adoption reflects the metric system's emphasis on decimal-based coherence, enabling straightforward conversions such as 1 cm³ = 10⁻⁶ m³.^[1]

Definition and Fundamentals

Basic Definition

The cubic centimetre (cm³) is a unit of volume in the metric system, defined as the volume occupied by a cube with each side measuring exactly one centimetre in length.^[8] This unit represents a three-dimensional measure of space, distinct from the centimetre (cm), which is a unit of linear length measuring one-hundredth of a metre.^[9] Mathematically, the volume of such a cube is calculated as the product of its side lengths:

V = 1 \, \text{cm} \times 1 \, \text{cm} \times 1 \, \text{cm} = 1 \, \text{cm}^3.

^[8] In relation to the base SI unit of volume, one cubic centimetre is equivalent to one-millionth of a cubic metre, or

10^{-6} \, \text{m}^3

, since the centimetre is

10^{-2} \, \text{m}

and cubing this factor yields

(10^{-2})^3 = 10^{-6}

.^[9] This equivalence underscores its position as a derived unit within the coherent system of metric measurements.^[8]

Relation to the Metric System

The cubic centimetre (cm³) is a unit of volume derived from the centimetre, a decimal submultiple of the metre, which serves as the base unit of length in the metric system and the International System of Units (SI).^[9] As such, it inherits the metric system's decimal-based structure, facilitating coherent scaling across length-derived quantities like area and volume.^[8] In the hierarchy of metric volume units, 1 cm³ equals 10^{-6} m³, where the cubic metre (m³) is the coherent SI derived unit for volume, obtained by cubing the metre.^[9] The cubic centimetre also relates directly to the litre (L), a special name for the cubic decimetre (dm³), such that 1 L = 1000 cm³.^[9] The cubic centimetre is a derived SI unit, obtained by cubing the centimetre, which is formed using the SI prefix centi- on the metre. This allows it to integrate seamlessly with other SI units and prefixes within the coherent metric system.^[9]^[8] Its primary advantage lies in enabling precise measurements for volumes under 1 litre, where the equivalence of 1 cm³ to 1 millilitre (mL) supports integer-based notations that avoid the fractional exponents or decimals required when using the cubic metre directly.^[8]

Symbol and Notation

Standard Symbols and Abbreviations

The primary symbol for the cubic centimetre, as defined in the International System of Units (SI), is cm³, where the superscript 3 denotes the cube of the centimetre unit.^[10] This notation is the standard in scientific literature, technical standards, and formal documentation to precisely represent a volume equal to one centimetre raised to the third power.^[11] In non-SI or informal contexts, alternative abbreviations such as cc or ccm are occasionally used, particularly in fields like automotive engineering to denote engine displacement.^[12] For instance, vehicle specifications may refer to a 2000 cc engine, equivalent to 2000 cubic centimetres.^[13] However, both cc and ccm are deprecated in SI-compliant writing, as they can lead to confusion with other units or terms, and official guidelines explicitly advise against them in favor of cm³.^[10]^[8] Formal usage guidelines emphasize the superscript cm³ for clarity and adherence to metric standards, while discouraging ambiguous notations such as "cu cm" or similar textual expansions that may be misinterpreted in technical contexts.^[14] The symbol remains unchanged in the plural form, consistent with SI conventions for unit symbols, so both one cubic centimetre and multiple are denoted as cm³.^[10] This uniformity simplifies expressions in equations and measurements, such as V = 10 cm³ for a volume of ten cubic centimetres.^[11]

Unicode and Typographic Representation

The cubic centimetre symbol is primarily encoded in Unicode through the sequence of characters U+0063 (Latin small letter c), U+006D (Latin small letter m), and U+00B3 (superscript three), forming cm³ in environments supporting full Unicode rendering. This compositional approach aligns with standard SI unit notation, where the superscript applies to the combined prefix and unit.^[11] An alternative, compatibility-specific character exists at code point U+33A4 (square cm cubed, ㎤), derived from CJK ideographic representations but rarely used in Latin-script contexts due to its specialized glyph form.^[15] Rendering challenges arise in plain text or limited Unicode-support systems, where the superscript three (U+00B3) may fail to display correctly, often defaulting to the baseline "3" (resulting in "cm3") or causing alignment issues in fixed-width fonts.^[16] Font compatibility varies across platforms; for instance, some web browsers like older Firefox versions have exhibited incorrect superscript heights or spacing for digits 1–3, affecting legibility in technical documents.^[17] These issues are exacerbated in email clients or legacy software without robust Unicode handling, potentially leading to misinterpretation of the unit. Typographic best practices emphasize upright roman typeface for unit symbols, with no space between the prefix "c" and unit "m", and the superscript applied to the entire "cm" for powers like cm³.^[11] In LaTeX, the siunitx package provides precise typesetting via commands like \si{cm^3}, ensuring consistent spacing, font uprightness, and integration with mathematical modes. Word processors such as Microsoft Word support this through built-in superscript formatting (e.g., selecting "3" and applying superscript via the font dialog), while HTML uses the entity ³ for reliable cross-browser display.^[18] For optimal compatibility, avoid the enclosed form U+33A4 in favor of the superscript composition, as recommended for SI units in international standards.

Equivalents and Conversions

Equivalents in Other Volume Units

The cubic centimetre (cm³) is a derived unit in the metric system, directly equivalent to 1 millilitre (mL), which itself equals 0.001 litres (L).^[19] Consequently, 1000 cm³ correspond exactly to 1 L.^[19] Within the International System of Units (SI), the base volume unit is the cubic metre (m³), and 1 cm³ equals exactly 10^{-6} m³, reflecting the relationship where 1 m = 100 cm.^[1] For conversions to non-metric units commonly used in the United States, the equivalents are as follows:

Unit	Equivalent
Cubic inch (in³)	1 cm³ ≈ 0.061 in³
US fluid ounce (fl oz)	1 cm³ ≈ 0.0338 fl oz

These approximations stem from the defined inch as exactly 2.54 cm and the US fluid ounce as exactly 29.57353 mL.^[20]^[21]

Conversion Formulas

The cubic centimetre (cm³) is a derived unit in the International System of Units (SI), and conversions to other volume units typically rely on exact or well-established factors defined by international standards.^[22] To convert from cubic centimetres to cubic metres, the formula is:

V (m^3) = V (cm^3) \times 10^{-6}

This factor is exact, as 1 m³ equals 1,000,000 cm³ by definition of the metre.^[22] For conversion to litres, where 1 L is defined as 1 dm³ or exactly 1,000 cm³, the formula is:

V (L) = \frac{V (cm^3)}{1000}

This relationship is also exact within the metric system.^[22] Conversions to non-metric units, such as cubic inches, use established factors based on the defined length conversion of 1 inch = 2.54 cm (exact). The formula is:

V (in^3) = V (cm^3) \times 0.0610237

This approximate factor derives from 1 in³ ≈ 16.387064 cm³, with the value rounded for practical use.^[22] In general, conversions between volume units can be approached using dimensional analysis, which involves multiplying the original quantity by a conversion factor that equates the units numerically while canceling dimensions. For example, to convert 500 cm³ to US fluid ounces (fl oz), where 1 fl oz ≈ 29.57353 cm³, apply the factor 1 cm³ ≈ 0.033814 fl oz:

500 \, \text{cm}^3 \times 0.033814 \, \frac{\text{fl oz}}{\text{cm}^3} \approx 16.907 \, \text{fl oz}

This method ensures consistency and can be extended to other units by chaining factors as needed.^[22]

Applications and Usage

In Automotive Engineering

In automotive engineering, engine displacement refers to the total volume of all cylinders in an internal combustion engine, measured in cubic centimetres (cm³, often abbreviated as cc), representing the space swept by the pistons from bottom dead center to top dead center in one complete cycle.^[23] This measurement provides a key indicator of an engine's capacity to ingest air and fuel, influencing its overall performance characteristics.^[24] Common engine displacements vary by vehicle type and purpose; small engines in economy cars and compact vehicles typically range from 1000 to 2000 cm³, offering a balance of fuel efficiency and adequate power for urban driving.^[25] Larger passenger car engines often fall between 1500 and 3000 cm³, providing sufficient torque and horsepower for highway performance and towing in sedans and mid-size SUVs.^[26] A higher displacement generally correlates with increased power output, as it allows for greater combustion volume and thus more energy production per cycle, though modern technologies like turbocharging and direct injection can enhance efficiency in smaller engines, sometimes matching the output of larger ones.^[27] For instance, the Toyota Corolla's standard 1.8-litre engine has a displacement of 1798 cm³, contributing to its responsive acceleration and reliable everyday performance.^[28] This metric unit became prevalent following the automotive industry's shift from imperial measurements, such as cubic inches, to metric specifications in the 1980s, driven by global standardization and the rise of international manufacturing.^[29]

In Medicine and Pharmacy

In medicine and pharmacy, the cubic centimetre (cm³), often abbreviated as "cc," serves as a precise unit for measuring small volumes of liquids, particularly in drug administration and formulation. This unit is widely used for dosing oral medications, such as prescribing 5 cm³ (5 cc) of cough syrup for pediatric patients to ensure accurate intake based on body weight. The precision of cm³ allows healthcare providers to tailor dosages to individual needs, minimizing risks associated with under- or overdosing in therapeutic contexts. Syringes in medical settings are commonly marked in cubic centimetres for administering injections, with standard sizes ranging from 1 cm³ for insulin delivery to 50 cm³ for larger infusions like intravenous fluids. These markings facilitate exact measurement during procedures, such as hypodermic injections or vaccinations, where even minor deviations can affect efficacy or safety. In pharmacy compounding, cm³ is employed to measure ingredients for custom preparations, ensuring consistency in concentration for solutions like antiseptics or nutritional supplements. The cubic centimetre is interchangeable with the millilitre (mL) for most aqueous solutions in medical practice, as 1 cm³ equals 1 mL, simplifying conversions during dispensing. However, safety protocols emphasize avoiding confusion with other units, such as teaspoons or milligrams, to prevent medication errors; for instance, the Institute for Safe Medication Practices recommends expressing volumes in mL rather than cc to avoid misinterpretation as "u" for units.^[30] This standardization has been critical in high-stakes environments like hospitals, where unit mix-ups have historically led to adverse events.

In Scientific and Everyday Contexts

In scientific laboratories, particularly in chemistry and biology, the cubic centimetre (cm³) serves as a standard unit for measuring small volumes of liquids and solids during experiments. For example, pipettes calibrated to 10 cm³ enable precise transfer of reagents or samples, ensuring accuracy in procedures such as dilutions or titrations. This unit is preferred because 1 cm³ is equivalent to 1 milliliter (mL), allowing seamless integration with volumetric glassware like burettes and graduated cylinders.^[31]^[1]^[32] In everyday applications, cubic centimetres are commonly used in cooking to specify recipe portions, such as 250 cm³ of liquid equivalent to a standard cup of water or milk. Packaging for household items also relies on this unit for small containers, including 100 cm³ bottles for eye drops or essential oils, where the equivalence to milliliters simplifies labeling and consumer understanding.^[33]^[34]^[35] Beyond these, the cubic centimetre finds use in specialized fields like geology, where it measures void spaces in rock samples to determine porosity; for instance, a 1 cm³ core sample allows calculation of the fraction of empty volume relative to total bulk. In 3D printing, it quantifies the material volume needed for objects, such as converting filament density (typically 1.2 g/cm³ for common plastics) to estimate usage in cubic centimetres for precise cost and waste assessment.^[36]^[37]^[38]^[39] The cubic centimetre's primary advantage lies in its suitability for small-scale precision, as its size—equivalent to the volume of a 1 cm cube—enables detailed measurements of tiny quantities that larger units like liters would render impractical or imprecise for laboratory or daily tasks. This granularity supports applications requiring exactness, such as sample analysis or portion control, without unnecessary scaling.^[40]^[41]

History and Standardization

Origins in the Metric System

The metric system, including the cubic centimetre as a unit of volume, originated during the French Revolution as part of efforts to standardize measurements on a decimal basis. In 1795, the French National Assembly passed the law of 18 Germinal, Year III (April 7, 1795), which formally adopted the metre as the fundamental unit of length—defined as one ten-millionth of the distance from the North Pole to the equator along a meridian—and derived the centimetre as one-hundredth of the metre.^[42] The cubic centimetre was thereby established as the volume of a cube measuring one centimetre on each side, providing a coherent decimal progression from the base unit for smaller-scale measurements.^[43] This initial framework relied on provisional standards. The meridian survey was conducted from 1792 to 1798 by astronomers Jean-Baptiste Delambre and Pierre Méchain. Following its completion, the "metre des archives" was manufactured in 1799 as the first physical platinum prototype for the metre, along with the kilogram, providing the cubic centimetre with more precise formalization in the early 19th century and linking volume directly to the metre's international artifact.^[44] Early adoption in scientific contexts across Europe emphasized its utility for precise volumetric calculations, such as in chemistry; for instance, Antoine Lavoisier, a key member of the 1790 Academy of Sciences commission proposing decimal units, advocated for such a system in his chemical research on gas volumes and reactions prior to the 1795 decree.^[45] A pivotal advancement came with the Metre Convention of 1875, signed on May 20 in Paris by representatives from 17 nations, which created the International Bureau of Weights and Measures (BIPM) to preserve and distribute uniform metric prototypes worldwide.^[46] This agreement solidified the cubic centimetre's role within the international metric framework by ensuring consistent standards for length and derived volume units, facilitating cross-border scientific collaboration.^[47]

Adoption and Evolution

During the 20th century, the cubic centimetre achieved widespread adoption in automotive engineering, particularly in Europe where engine displacements began to be routinely specified in cm³ starting in the 1920s amid the growth of standardized metric manufacturing practices.^[48] In medicine, its use proliferated after World War II, as the unit—often denoted as "cc"—became a standard for dosing liquid medications and injectables, facilitated by international efforts to harmonize pharmaceutical measurements.^[49] The 11th General Conference on Weights and Measures (CGPM) in 1960 formally established the International System of Units (SI), designating the cubic metre (m³) as the base unit of volume while recognizing the cubic centimetre (cm³) as a coherent derived unit equivalent to 10^{-6} m³.^[50] Although the SI endorses the millilitre (mL) as the preferred unit for liquid volumes—where 1 mL exactly equals 1 cm³—the cm³ remains in common use for solids and precise scientific contexts.^[51] Regional variations in adoption reflect differing approaches to metrication. In the European Union, metric units including the cm³ became mandatory for economic, public health, public safety, and administrative purposes under the Units of Measurement Regulations 1995, which implemented relevant EU directives to phase out non-metric units.^[52] In contrast, the United States promotes voluntary use of the metric system through national policy, with the cm³ routinely employed in scientific research and engineering despite the prevalence of customary units elsewhere. The 2019 revision of the SI, adopted by the 26th CGPM, redefined the metre based on a fixed numerical value of the speed of light in vacuum (c = 299 792 458 m/s), thereby providing a more invariant and precise foundation for derived units like the cm³ without altering its numerical value. This update enhances the long-term stability of measurements involving the cubic centimetre, supporting ongoing global standardization.^[53]

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