How to calculate a percentage increase — step by step
A percentage increase tells you by what share a value has grown. The formula is (new − old) ÷ old · 100. Worked example: from 200 to 250 is a 25% increase. This kind of percentage work belongs to Grade 6–8 and underpins interest, price rises and growth rates.
Quick answer
Percentage increase is the rise divided by the old value, times 100: (new − old) ÷ old · 100. From 200 to 250 that is (250 − 200) ÷ 200 · 100 = 25%. To grow a value by p%, add value · p ÷ 100 — or simply multiply by the factor 1.25.
At a glance
| Example | 200 → 250 |
|---|---|
| Method | (new − old) ÷ old · 100 |
| Steps | 4 |
| Result | 25% |
| Factor | +25% ⇒ · 1.25 |
| Grade level | Grade 7 (ages 12–13) |
Worked example: 200 → 250
A value grows from 200 to 250. We find the rise and compare it to the old value.
Calculate a percentage increase in four steps
These steps work for any rise from an old value to a new, larger value.
Step 1 · Start
200 → 250Old value 200, new value 250.Step 2 · Formula
(250 − 200) ÷ 200 · 100Rise divided by the old value, times 100.Step 3 · Rise
50 ÷ 200 · 100The rise is 250 − 200 = 50.Step 4 · Result
= 25%0.25 · 100 gives a 25% increase.
Why the formula works
Percent means "per hundred". You are asking: what fraction of the old value was added? That is why you divide the rise (new − old) by the old value — it gives the relative growth as a decimal. Multiplying by 100 turns it into a percent. Conversely, "plus 25%" equals multiplying by the factor 1.25, because 100% + 25% = 125% = 1.25.