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Percentage Formulas and Equations

See formulas for percent of a number, percent change, percent difference, increase, decrease, discount, and percentage error.

How do the Percentage Calculator formulas work?

This formula page defines the variables used by the Percentage Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Percentage of a Number

part=p100×whole\text{part}=\frac{p}{100}\times\text{whole}

Divide the percentage by 100 and multiply by the reference whole.

What Percent Is One Number of Another?

For “What Percent Is One Number of Another?,” the Percentage Calculator formula organizes the relevant inputs, applies the documented method, and shows a result that can be compared across scenarios. The points below identify the specific considerations and assumptions users should review before relying on the estimate.

p=partwhole×100p=\frac{\text{part}}{\text{whole}}\times100

The whole must not be zero.

Percentage Change

% change=new−original∣original∣×100\%\text{ change}=\frac{\text{new}-\text{original}}{|\text{original}|}\times100

A positive result is an increase and a negative result is a decrease when the original value is nonzero.

Percentage Difference

% difference=∣V1−V2∣(∣V1∣+∣V2∣)/2×100\%\text{ difference}=\frac{|V_1-V_2|}{(|V_1|+|V_2|)/2}\times100

This symmetric formula uses the average magnitude of the two values as its reference.

Percentage Error

% error=∣observed−actual∣∣actual∣×100\%\text{ error}=\frac{|\text{observed}-\text{actual}|}{|\text{actual}|}\times100

The actual or accepted value must not be zero.

References

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