Percentage Change, Percentage Points and Percentage Difference
Updated 17 October 2026
A pass rate that moves from 40% to 50% has gone up by 10 percentage points — and by 25%. Here is how to tell the measures apart, with the formulas and the traps to avoid.
Percentage change
Percentage change compares a new value with an original one:
percentage change = (new − original) ÷ original × 100
If a price rises from $80 to $100: (100 − 80) ÷ 80 × 100 = 25% increase. If it then falls from $100 back to $80: (80 − 100) ÷ 100 × 100 = 20% decrease. The same $20 is a different percentage because the starting point changed.
Percentage change calculator →
Percentage points
When the values being compared are already percentages, the plain difference between them is measured in percentage points. If an exam pass rate rises from 40% to 50%, it has risen by 10 percentage points — but by 25 percent, because 10 is a quarter of 40.
Both statements are true, so say which one you mean. “Up 10%” for a move from 40% to 50% is ambiguous and is a common source of lost marks in statistics, economics and science coursework.
Percentage difference
Percentage change has a direction (from one value to another). When neither value is the “original” — comparing two schools, two measurements or two products — use percentage difference, which divides by the average of the two values:
percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
For 40 and 50: 10 ÷ 45 × 100 ≈ 22.2%, whichever way round you put them. Percentage difference calculator.
Percentage error
In science practicals, percentage error compares your measurement with the accepted value: |measured − accepted| ÷ accepted × 100. Measuring g as 9.6 m/s² against an accepted 9.81 m/s² gives an error of about 2.1%. Percentage error calculator.
Three traps that catch almost everyone
1. Up then down is not back where you started
A 50% rise followed by a 50% fall leaves you at 75% of the original: 100 → 150 → 75. To undo a 50% rise you need a 33.3% fall.
2. Stacked discounts don't add up
“20% off, then an extra 10% off” is 28% off in total, not 30%: 100 × 0.8 × 0.9 = 72. The discount calculator handles a second discount for you.
3. Reversing a percentage
If a price including 15% tax is $115, the tax is not 15% of $115 ($17.25). Divide instead: 115 ÷ 1.15 = $100 before tax, so the tax is $15. The same logic finds an original price after a discount — see the original price calculator.
Quick reference
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 200 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 of 120 = 25% |
| Change from A to B | (B − A) ÷ A × 100 | 80 → 100 = +25% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 250 + 12% = 280 |
| Original before X% increase | final ÷ (1 + X ÷ 100) | 115 ÷ 1.15 = 100 |
| Original before X% discount | final ÷ (1 − X ÷ 100) | 68 ÷ 0.85 = 80 |