Percentage Change Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The rate of change between two values is calculated as: (final value − initial value) ÷ initial value × 100. For example, going from 50 to 75 represents a 50% increase.
Explanation
The rate of change measures the size of a change between a starting state and an ending state, expressed as a percentage of the starting value. A positive result indicates an increase, a negative result a decrease. This is different from a simple percentage calculator: it compares two values against each other rather than applying a fixed rate to a single value. If instead you know a part and its percentage and are looking for the starting number, the total value from a percentage calculator answers that different question. One special case worth knowing: if the initial value is 0, the rate of change is mathematically undefined (you can't express a percentage change starting from nothing) — the calculator states this clearly rather than showing a misleading number.
Example: a change from 50 to 75
Inputs
Initial value: 50. Final value: 75.
Calculation
First calculate the difference: 75 − 50 = 25. Divide that difference by the initial value: 25 ÷ 50 = 0.5. Convert to a percentage by multiplying by 100: 0.5 × 100 = 50.
Result
The value increased by 50% between the starting and ending states.
Frequently asked questions
Why do you always divide by the initial value, not the final value?
The rate of change measures the change relative to its starting point: "how much did I move, compared to where I was?" Dividing by the final value would give a different, less intuitive measure that's rarely used in practice.
What happens if the initial value is 0?
The result is mathematically undefined: you can't express a percentage change starting from a base of zero, whatever the final value reached. The calculator shows N/A in this case rather than a misleading number.
Is a change of -100% possible?
Yes, that corresponds to a final value of 0: the entire initial value has disappeared. However, a rate of change can never go below -100% if the final value stays zero or positive.
How do I calculate the change between two percentages themselves (percentage points)?
Be careful not to confuse relative change with a difference in points: going from 10% to 15% represents +5 percentage points, but a relative change of +50% (calculated as (15-10)/10×100). This calculator gives the relative change.