Percentage Change Formula Explained, With Examples
Every percentage change result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
% change = (new − old) ÷ |old| × 100.
What each input means
- Old value: the value you enter in the calculator.
- New value: the value you enter in the calculator.
Example
For example, with these inputs:
- Old value: 80
- New value: 100
the calculator returns:
- Change: 25.00%
- Difference: 20
How the result changes
The table keeps the other inputs at their example values and changes old value.
| Old value | Change | Difference |
|---|---|---|
| 80 | 25.00% | 20 |
| 40 | 150.00% | 60 |
| 60 | 66.67% | 40 |
| 100 | 0.00% | 0 |
| 120 | -16.67% | -20 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
Related calculations
- Percentage Difference Calculator: Compares two values relative to their average.
- Average (Mean) Calculator: Finds the arithmetic mean of a list.
- Median Calculator: Finds the middle value of a list.
- Mode Calculator: Finds the most frequent value(s).
Use the Percentage Change Calculator to plug in your own numbers.
Run your own numbers: Percentage Change Calculator