Percentage Calculator
Percent of a number and percentage change.
Three percentage questions, one calculator
Almost every percentage problem is one of three questions: what is X% of a number, what percentage is one number of another, and by what percentage did something change. This percentage calculator answers all three at once, so you do not have to remember which way round to divide — the commonest source of percentage mistakes.
How to use the Percentage Calculator
- For X% of a number, fill in Percentage (%) and Of (number).
- For percentage change, fill in Old Value and New Value.
- Both answers appear together and update as you type.
- A negative change means a decrease.
Formula and a worked example
Part = (p ÷ 100) × whole
Percentage = part ÷ whole × 100
Change % = (new − old) ÷ old × 100
Percentage change always divides by the old value. Dividing by the new one is the classic error, and it is why a rise from 50 to 75 is a 50% increase while the fall from 75 back to 50 is only a 33.3% decrease.
Worked example
25% of 120 is 30. Going from 80 to 100 is a 25% increase; going from 100 back to 80 is a 20% decrease — the same 20 units, different percentages, because the base changed.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply. 15% of 240 is 0.15 × 240 = 36.
How do I work out percentage increase?
Subtract the old value from the new one, divide by the old value, then multiply by 100.
Why is a 50% rise not cancelled by a 50% fall?
Because the second percentage is taken from a bigger number. 100 rises to 150, then a 50% fall takes it to 75, not back to 100.
How do I reverse a percentage?
To find the original before a p% increase, divide by (1 + p ÷ 100). After a decrease, divide by (1 − p ÷ 100).
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