How to calculate a percentage (and percentage change)

To find X% of Y, multiply Y by X, then divide by 100. In other words: result = (Y × X) ÷ 100. So 20% of 150 is (150 × 20) ÷ 100 = 30.

You can also think of 20% as 0.20. Multiplying 150 × 0.20 gives the same 30. That form is handy on a phone calculator when you already know the decimal.

This is the method behind discounts (“20% off”), commission, exam scores, and “what is 15% of my bill?” questions. If you only need this one step, enter the percentage and the original amount in the Percentage Calculator and read the first result.

Percentage change compares a new value with an original: ((new − original) ÷ original) × 100. A rise from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25%. A fall from 100 to 80 is ((80 − 100) ÷ 100) × 100 = −20%.

Notice the two answers are not the same. Going up 25% and then down 20% can land you back near the start, but the percentages are measured from different bases. Always divide by the original figure for that comparison, not the new one.

To apply an increase, multiply by (1 + rate). A 20% rise on £100 is £100 × 1.20 = £120. To apply a decrease, multiply by (1 − rate). A 20% fall on £100 is £100 × 0.80 = £80.

A reverse percentage asks: if this amount already includes a percentage change, what was it before? Divide the current amount by (1 + rate) for an increase, or by (1 − rate) for a decrease.

Example: a price is £120 after a 20% increase. Original = 120 ÷ 1.20 = £100. Example: a sale price is £80 after 20% off. Original = 80 ÷ 0.80 = £100.

This is the same idea as removing VAT from a gross price. If you specifically need UK VAT at 20%, the VAT Calculator is labelled for add/remove tax rather than a generic reverse percentage.

People often add 20% by multiplying by 20 instead of 1.20, or they divide a change by the new number instead of the old one. Another trap is treating “20% of” and “20% more than” as the same thing — they are not.

For shopping, check whether a discount is off the marked price or stacked with another offer. For tax, use the rate that actually applies (standard, reduced, or zero), not a round number you assumed.

Use the Percentage Calculator for planning and checking homework-style questions. Confirm important money decisions with a receipt, contract, or professional when the number matters.