How it works
The original value is multiplied by 1 plus the percentage expressed as a decimal, so a 25% increase multiplies by 1.25.
Worked through in steps, an increase of 12% on 2.5 goes: 12 ÷ 100 = 0.12, then 1 + 0.12 = 1.12, then 2.5 × 1.12 = 2.8. Those three steps are fixed: a larger or smaller starting value changes only what is multiplied, and a percentage with a decimal point in it, such as 4.9%, goes through the same process.
The multiplier also runs backwards. Dividing 2.8 by 1.12 returns 2.5, which is the reverse-percentage mode on the main Percentage Calculator.
Formula: New value = original × (1 + percentage ÷ 100)
Examples
A price increase
80 increased by 25% is 80 × 1.25 = 100.
A small increase
200 increased by 10% is 200 × 1.10 = 220.
An increase over 100%
15 increased by 200% is 15 × 3 = 45, because the 30 added is twice the 15 you started with.
Common uses
- Estimating a salary, pension or allowance after a stated percentage rise, before the revised figure is confirmed
- Adding contingency to a quoted price, such as a 10% uplift to a builder's estimate
- Rebasing figures recorded before a price change so that earlier and later amounts can be compared
Things to keep in mind
- This calculator finds the value after an increase. To go the other way — working out what a value was before a known increase — use the reverse-percentage mode on the main Percentage Calculator instead.
- A negative percentage is not rejected: it produces the same result the Percentage Decrease Calculator would for the equivalent positive percentage, since increasing by −10% and decreasing by 10% are the same calculation.
- The percentage is measured against the value you start from, never against the result. 100 increased by 50% is 150, and increasing that 150 by 50% gives 225, because the second 50% is half of 150, not half of 100.
- A decrease and its reversal are not the same size. 100 reduced by 50% is 50, but going back from 50 to 100 is a 100% increase, so a percentage decrease cannot be undone by adding the same percentage to the result. The Percentage Decrease Calculator works on the decrease itself.
- Results are rounded to 12 significant digits. That removes floating-point noise, and it also shortens an answer that repeats: 100 increased by 33.333333333333% comes back as 133.333333333.
- Only finite numbers are accepted. Both fields take any other value, including a negative starting value, so −200 increased by 10% is −220: the increase is a share of the starting value whatever its sign.