Percentage Change Calculator
Find the percentage increase or decrease between any two numbers, plus the raw difference.
The formula
80 → 100: (100 − 80) ÷ 80 × 100 = +25% (increase). Reverse, 100 → 80: (80 − 100) ÷ 100 × 100 = −20%.
Overnight low temperature moves from −10°C to 5°C. Using the absolute value of the old number in the denominator: (5 − (−10)) ÷ |−10| × 100 = 15 ÷ 10 × 100 = +150%.
Without taking the absolute value, dividing by −10 directly would flip the sign of the whole result to −150% — technically implying a decrease — even though the temperature clearly rose. That's exactly why the formula uses |Old|, not Old, in the denominator.
The asymmetry that trips people up
A 25% gain and a 25% loss don't cancel out, because each percentage is taken from a different base. This matters most with money: a stock that drops 50% must then rise 100% just to break even, not 50%. That's why average returns can mislead and why CAGR exists. For directionless comparisons (like the difference between two measurements with no clear "before"), percentage difference — dividing by the average — is the right tool instead. For money-specific change, see the discount and ROI calculators.
Percentage change quick reference
| Change | Multiplier to apply to old value |
|---|---|
| +10% | × 1.10 |
| +25% | × 1.25 |
| +50% | × 1.50 |
| +100% | × 2.00 |
| −10% | × 0.90 |
| −25% | × 0.75 |
| −50% | × 0.50 |
Converting a percentage change to a multiplier is often faster than running the full formula when you just need the resulting value — multiply the old value by (1 + the change as a decimal) for an increase, or (1 − the change) for a decrease.
Common percentage change mistakes
- Dividing by the new value instead of the old. The denominator is always the starting value, not the ending one — swapping them silently changes the answer.
- Forgetting the absolute value with a negative starting number. As the temperature example above shows, dividing by a negative Old value directly can flip the sign of the whole result.
- Assuming a reversed percentage undoes the original change. A 25% increase followed by a 25% decrease lands below the starting point, because the decrease is calculated on the new, larger base.
Frequently asked questions
How do I calculate percentage change?
(New − Old) ÷ Old × 100. 80 → 100 = +25%.
Why isn't a 25% increase reversed by a 25% decrease?
The base changes — 80 up 25% is 100, but 100 down 25% is 75.
What is percentage difference?
Absolute difference ÷ the average of the two values — for comparisons with no clear starting point.
How do I calculate percentage change when the starting value is negative?
Divide by the absolute value of the old number. −10°C to 5°C is 15 ÷ |−10| × 100 = +150%, not a negative number.
How can I estimate percentage change quickly without a calculator?
Find 10% of the old value (move the decimal one place), then see how many of those chunks fit the difference. 200 → 230 is about 1.5 chunks of 20, or ~15%.
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Last reviewed: September 2026.