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Relative change
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably.
Relative change is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change (relative change expressed as a percentage) called percent error occurs in measuring situations where the reference value is the accepted or actual value (perhaps theoretically determined) and the value being compared to it is experimentally determined (by measurement).
The relative change formula is not well-behaved under many conditions. Various alternative formulas, called indicators of relative change, have been proposed in the literature. Several authors have found log change and log points to be satisfactory indicators, but these have not seen widespread use.
Given two numerical quantities, vref and v with vref some reference value, their actual change, actual difference, or absolute change is
The term absolute difference is sometimes also used even though the absolute value is not taken; the sign of Δ typically is uniform, e.g. across an increasing data series. If the relationship of the value with respect to the reference value (that is, larger or smaller) does not matter in a particular application, the absolute value may be used in place of the actual change in the above formula to produce a value for the relative change which is always non-negative. The actual difference is not usually a good way to compare the numbers, in particular because it depends on the unit of measurement. For instance, 1 m is the same as 100 cm, but the absolute difference between 2 and 1 m is 1 while the absolute difference between 200 and 100 cm is 100, giving the impression of a larger difference. But even with constant units, the relative change helps judge the importance of the respective change. For example, an increase in price of $100 of a valuable is considered big if changing from $50 to 150 but rather small when changing from $10,000 to 10,100.
We can adjust the comparison to take into account the "size" of the quantities involved, by defining, for positive values of vref :
The relative change is independent of the unit of measurement employed; for example, the relative change from 2 to 1 m is −50%, the same as for 200 to 100 cm. The relative change is not defined if the reference value (vref) is zero, and gives negative values for positive increases if vref is negative, hence it is not usually defined for negative reference values either. For example, we might want to calculate the relative change of −10 to −6. The above formula gives (−6) − (−10)/ −10 = 4/ −10 = −0.4, indicating a decrease, yet in fact the reading increased.
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Relative change AI simulator
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Relative change
In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used. The terms "change" and "difference" are used interchangeably.
Relative change is often used as a quantitative indicator of quality assurance and quality control for repeated measurements where the outcomes are expected to be the same. A special case of percent change (relative change expressed as a percentage) called percent error occurs in measuring situations where the reference value is the accepted or actual value (perhaps theoretically determined) and the value being compared to it is experimentally determined (by measurement).
The relative change formula is not well-behaved under many conditions. Various alternative formulas, called indicators of relative change, have been proposed in the literature. Several authors have found log change and log points to be satisfactory indicators, but these have not seen widespread use.
Given two numerical quantities, vref and v with vref some reference value, their actual change, actual difference, or absolute change is
The term absolute difference is sometimes also used even though the absolute value is not taken; the sign of Δ typically is uniform, e.g. across an increasing data series. If the relationship of the value with respect to the reference value (that is, larger or smaller) does not matter in a particular application, the absolute value may be used in place of the actual change in the above formula to produce a value for the relative change which is always non-negative. The actual difference is not usually a good way to compare the numbers, in particular because it depends on the unit of measurement. For instance, 1 m is the same as 100 cm, but the absolute difference between 2 and 1 m is 1 while the absolute difference between 200 and 100 cm is 100, giving the impression of a larger difference. But even with constant units, the relative change helps judge the importance of the respective change. For example, an increase in price of $100 of a valuable is considered big if changing from $50 to 150 but rather small when changing from $10,000 to 10,100.
We can adjust the comparison to take into account the "size" of the quantities involved, by defining, for positive values of vref :
The relative change is independent of the unit of measurement employed; for example, the relative change from 2 to 1 m is −50%, the same as for 200 to 100 cm. The relative change is not defined if the reference value (vref) is zero, and gives negative values for positive increases if vref is negative, hence it is not usually defined for negative reference values either. For example, we might want to calculate the relative change of −10 to −6. The above formula gives (−6) − (−10)/ −10 = 4/ −10 = −0.4, indicating a decrease, yet in fact the reading increased.