Percentage Increase Calculator
Work out the percentage increase from one value to another.
Percentage increase is the rise divided by the original value: (new − old) / old × 100.
How the percentage increase calculator works
Percentage increase is the rise divided by the original value: (new − old) / old × 100. Going from 40 to 50 is a 25% increase, because the rise of 10 is a quarter of the original 40.
The original value is always the denominator, and that is where mistakes happen. Dividing by the new value instead gives 20%, which is the percentage decrease going the other way — a different question with a different answer.
Formula: X% of Y = Y × X / 100; X as % of Y = X / Y × 100; change = (B − A) / A × 100
Worked examples
| Inputs | Answer | Note |
|---|---|---|
| 40 to 50 | +25% | a 25% increase |
| Doubling | +100% | 100% |
| A fall | -20% | a 20% decrease |
FAQFrequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new, divide by the old value, multiply by 100.
What is the increase from 40 to 50?
25% — the rise of 10 over the original 40.
Why is 50 to 40 not also 25%?
Because the denominator changes. Going down, the 10 is a fifth of 50, so it is a 20% decrease.
What is a 100% increase?
A doubling.
Can an increase be more than 100%?
Yes — going from 10 to 50 is a 400% increase.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.