How to Calculate Percentages: Formulas, Examples and the Most Common Mistakes

September 29, 2026

Percent means "per hundred": 15% is 15 parts in every 100. Almost every everyday calculation fits one of four questions. Here is the formula for each, examples and the traps that confuse people most.

1. What is X% of a number?

Number × X ÷ 100. What is 15% of 200? 200 × 15 ÷ 100 = 30.

Mental shortcut: 10% is the number with the decimal point moved one place left (10% of 200 = 20), 5% is half of that (10), so 15% = 20 + 10 = 30.

2. What percentage is one number of another?

Part ÷ total × 100. 45 is what percent of 180? 45 ÷ 180 × 100 = 25%.

3. Increases and discounts

To apply an increase of X%, multiply by (1 + X/100); for a discount, by (1 − X/100).

20% off 250: 250 × 0.80 = 200 (a saving of 50).
An 8% rise on 1,500: 1,500 × 1.08 = 1,620.

4. Percentage change

(New value − old value) ÷ old value × 100. A price went from 80 to 100: (100 − 80) ÷ 80 × 100 = +25%.

The most common traps

Up and down by the same percentage does not get you back

From 80 to 100 is +25%, but from 100 to 80 is −20%: the base changed. Likewise, a 10% rise followed by a 10% discount leaves the price 1% lower (1.10 × 0.90 = 0.99).

Successive percentages do not add up

Two 10% discounts in a row are not 20%: they are 0.9 × 0.9 = 0.81, that is 19%.

A percentage point is not a percentage

If an interest rate goes from 10% to 12%, it rose by 2 percentage points – but by 20% in relative terms.

Percentages with the rule of three

Any of these can also be solved with the rule of three: if 100% is 180, what is 25%? See the rule of three guide.

Do the maths

The percentage calculator answers the five most common questions – X% of a number, what percentage it is, change, discount and splitting a tip – and shows the working.

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