Percent Rate of Change: Formula and Examples

A percent rate of change calculator finds how much a value has increased or decreased relative to its starting value. Enter the original value and the new value; the result is the percentage change, with a positive result indicating an increase and a negative result indicating a decrease.

Formula

Percent rate of change = (new value − original value) ÷ original value × 100.

• Original value is the starting or reference amount, in any unit.
• New value is the ending amount, in the same unit.
• Percent rate of change is the signed change expressed as a percentage.
• Absolute change is the difference between the new and original values, in the original unit.

The calculator uses (new − original) / original × 100. The units cancel in the division, so the percentage does not depend on whether matching values are entered in dollars, metres, kilograms, or another unit. The original value must not be zero, because division by zero is undefined.

Worked Example

With the defaults, the original value is 100 and the new value is 125.

1. Find the difference: 125 − 100 = 25.
2. Divide by the original value: 25 ÷ 100 = 0.25.
3. Convert to a percentage: 0.25 × 100 = 25%.

The percent rate of change is 25.00%, and the absolute change is 25. These match the calculator’s two outputs.

How to Calculate It

Use the starting value as the denominator, not the ending value. The order matters too: subtract the original value from the new value. Together, these choices make the calculation measure the change against the amount you started with.

• Write down the original and new values.
• Subtract original from new to get the signed difference.
• Divide that difference by the original value.
• Multiply by 100 and attach the percent sign.

For instance, if a quantity falls from 80 to 60, the difference is 60 − 80 = −20. Then −20 ÷ 80 × 100 = −25%. The negative sign shows a decrease of 25% from the starting amount.

How to Read the Result

A positive percentage means the new value is greater than the original; a negative percentage means it is smaller. A result of 0% means there was no change. The size of the percentage describes the change relative to the original, not the number of units gained or lost.

That distinction is useful when comparing different scales. An increase of 10 units is a 10% change from 100, but only a 1% change from 1,000. Always consider both the percentage and the underlying values when the practical size of a change matters.

Percent change is not the same as a percentage-point change. If a proportion moves from 20% to 25%, it rises by 5 percentage points. Its percent rate of change is (25 − 20) ÷ 20 × 100 = 25%. The first comparison subtracts percentages directly; the second measures the difference relative to the starting percentage.

Common Mistakes and Limits

• Using the wrong denominator: Divide by the original value. Dividing by the new value answers a different question.
• Reversing the subtraction: Use new minus original so the sign correctly indicates direction.
• Mixing units: Convert measurements to the same unit before subtracting. Comparing 2 metres with 250 centimetres without conversion produces an invalid difference.
• Rounding too early: Keep the full result through the calculation, then round the final percentage to a sensible number of decimal places.
• Starting at zero: A percentage change from zero cannot be calculated by this formula. Report the absolute change or describe the movement without calling it a percent change.

The formula describes change between two values; it does not explain why the change happened or account for what occurred between the measurements. If the interval matters, state it separately—for example, “a 12% increase over three months.” The percentage alone is not a per-day, per-month, or annual rate.

Percent Change Versus Growth Rate

For a single period, “percent change” and “percent rate of change” are often used for the same calculation. For repeated periods, however, the phrase “rate” can refer to an average or compound rate, which needs additional information such as the number and length of periods.

For example, an overall change from 100 to 121 across two equal periods is 21%. The constant compound change per period is 10%, since 100 × 1.10 × 1.10 = 121. Simply dividing 21% by two gives 10.5%, which is an arithmetic average, not the compound rate. Use the measure that fits the question being asked.

Frequently Asked Questions

What is the formula for percent rate of change?
Subtract the original value from the new value, divide by the original value, and multiply by 100: (new − original) ÷ original × 100.

Can percent change be negative?
Yes. A negative result means the new value is below the original value. Its magnitude gives the percentage decrease relative to the original.

How do I calculate percent change from zero?
You cannot calculate it with the standard formula because it requires division by the original value. Give the absolute difference or explain the change in words instead.

Is percent change the same as percentage points?
No. Percentage points are the direct difference between two percentages. Percent change divides that difference by the original percentage before converting it to a percent.

How do I calculate percent change over multiple periods?
For the total change, compare the ending value with the starting value using the standard formula. For a constant compound rate across n periods, use ((ending ÷ starting)^(1/n) − 1) × 100, provided the starting and ending values are suitable for that calculation.

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in original | Original value | - | 100 | 0
in new | New value | - | 125 | 0
out rate | Percent rate of change | % | (new - original) / original * 100 | 2
out difference | Absolute change | - | new - original | 2