Percentage Change Calculator
The percentage change between two numbers — a rise or a fall, measured against where it started.
Percentage change is (new − old) ÷ old × 100.
How the percentage change calculator works
Percentage change is (new − old) ÷ old × 100. The denominator is always the starting value, which is what makes rises and falls asymmetric: 100 up 20% is 120, but 120 down 20% is 96, not 100. A positive answer is an increase and a negative one a decrease.
Formula: X% of Y = Y × X / 100; X as % of Y = X / Y × 100; change = (B − A) / A × 100
Worked examples
| Inputs | Answer | Note |
|---|---|---|
| 200 → 250 | +25% | +25% |
| 80 → 60 | -25% | −25% |
| 50 → 150 | +200% | +200% — it tripled |
FAQFrequently asked questions
How do I calculate percentage change?
Subtract the old from the new, divide by the old, multiply by 100.
Why is a 20% rise then a 20% fall not back where it started?
Because the fall is measured against the larger number: 100 → 120 → 96.
What does a change of more than 100% mean?
The value more than doubled. Going from 50 to 150 is a 200% increase, or three times the original.
Percentage change or percentage points?
Going from 10% to 15% is 5 percentage points, but a 50% increase. Say which you mean.
Why can I not start from zero?
Because any increase from nothing is infinite in percentage terms; quote the absolute change instead.
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.