Relative change puts a change in context. A rise of 5 kg is dramatic for a 10 kg dog and trivial for a 500 kg cow. Scientists and economists use relative change (or its percentage form) to compare changes of quantities with very different sizes.
How to use the Relative Change Calculator
- Initial value (xᵢ)
- Final value (x_f)
- Every result field is editable: type into Relative change (%) and Final value (x_f) plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
Subtract the initial value from the final value and divide by the absolute value of the initial value. Multiply by 100 for the percentage version.
Inputs explained
| Field | What to enter |
|---|---|
| Initial value (xᵢ) | A number |
| Final value (x_f) | A number |
What each result means
- Relative change = ([Final value (x_f)] – [Initial value (xᵢ)])÷abs([Initial value (xᵢ)])
- Relative change (%) = ([Final value (x_f)] – [Initial value (xᵢ)])÷abs([Initial value (xᵢ)])×100
- Absolute change = [Final value (x_f)] – [Initial value (xᵢ)]
Example values
How the main result changes when Final value changes and everything else stays at the example values above:
| Final value (x_f) | Relative change |
|---|---|
| 7.5 | -0.4 |
| 11.25 | -0.1 |
| 15 | 0.2 |
| 18.75 | 0.5 |
| 22.5 | 0.8 |
| 30 | 1.4 |
Formula
Relative change = (x_f − xᵢ) ÷ |xᵢ|
Relative change (%) = 100 × (x_f − xᵢ) ÷ |xᵢ|
Worked example
Inputs — Initial value (xᵢ): 12.5; Final value (x_f): 15.
Results — Relative change = 0.2; Relative change (%) = 20 %; Absolute change = 2.5.
Key terms
- Relative change
- A change divided by the starting value.
Frequently asked questions
What is the difference between relative and absolute change?
Absolute change is x_f − xᵢ in the original units; relative change divides it by the starting value, so it has no units.
Why use the absolute value of xᵢ?
So the sign of the result shows the direction of change even when the initial value is negative.
What if xᵢ = 0?
Relative change is undefined.
Is relative change the same as percentage change?
Yes, apart from the factor of 100.