Percentage Difference Calculator

Intro

Use this percentage difference calculator to compare two nonnegative values when neither is the starting value. It shows the gap as a percentage of their average, alongside the numerical gap and mean.

What this calculator does

Enter two values measured in the same units, such as two package weights, two measurements or two prices in the same currency. The result treats both values equally. Switching their order leaves the percentage difference unchanged.

For a value changing over time, use the Percentage Increase Calculator, which measures the change relative to the original value.

How it works

The percentage difference method explained by Math Is Fun uses the average of the two values as the reference:

Percentage difference = absolute(first value − second value) ÷ ((first value + second value) ÷ 2) × 100.

Here, absolute means the numerical gap is always zero or positive. Both inputs must be nonnegative in this calculator, and at least one must be above zero.

1. Find the nonnegative gap between the values.
2. Find their arithmetic mean.
3. Divide the gap by the mean and multiply by 100.

Example calculation

Suppose two items have measured values of 80 and 100.

A before-and-after increase from 80 to 100 is 25%, because it divides the gap by the original 80. Percentage difference instead divides by the mean of 90. They answer different questions.

Another example: two prices of $4 and $6 have a $2 gap and a $5 mean, giving a percentage difference of 40%.

How to use the result

A larger percentage means a larger gap relative to the average. The result does not say which value is better, whether a difference is statistically significant, or whether a measurement is accurate. The labels and context of your two values still matter.

For two equal positive values, the result is 0%. Comparing zero with a positive value gives 200% under this formula. Both zero is undefined because the mean is zero.

Assumptions and limitations

• Enter comparable quantities in the same units. The tool does not convert units or currencies.
• Negative values are outside this calculator's domain. It does not choose a convention for comparisons across zero.
• Percentage difference is separate from percentage change, percentage points and percentage error.
• Normal percentages round to two decimal places. Very small nonzero percentages use scientific notation, such as 1.000000e-6%, to avoid displaying a false zero. Small or large supporting values use scientific notation too.
• Calculation uses browser Number arithmetic. Very small values whose mean cannot be represented produce a precision error. Rescale both values by the same factor to preserve the mathematical percentage difference.
• No direction, growth rate, investment return or statistical test is inferred.

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