The main formulas
- X% of Y: X / 100 x Y.
- A is what percent of B: A / B x 100.
- Percentage change: (new - old) / old x 100.
- Increase by X%: value x (1 + X / 100).
- Decrease by X%: value x (1 - X / 100).
Percentage points are different
A move from 35% to 42% is a 7 percentage-point increase. Relative to 35%, it is a 20% increase. Both statements can be correct, but they answer different questions.
Common mistakes
- Using the new value instead of the old value as the denominator for percentage change.
- Calling a percentage-point change a percent change.
- Comparing rates from different time periods or populations.
- Rounding too early and then reusing the rounded number.
Percentage points versus percent change
If a rate rises from 5% to 6%, the absolute change is 1 percentage point. The relative increase is 20% because (6 - 5) / 5 = 0.20. This distinction matters in interest rates, tax rates, polling, conversion rates and price changes.
For ordinary percentage calculations, 15% of 240 is 36; 36 is 15% of 240; increasing 240 by 15% gives 276; decreasing 240 by 15% gives 204. A useful percentage calculator exposes these different intents instead of forcing users to rearrange one formula mentally.
Use the calculators
FAQ
Can percentage change start from zero?
No. The standard formula divides by the old value, so percentage change is undefined when the old value is zero.
Why do two percentage answers differ?
They usually use different denominators. Check what each number is "of".
When should I use percentage points?
Use percentage points when comparing two percentages directly, such as tax rates, interest rates, survey shares or conversion rates.
Last reviewed: 2026-05-16.