Percentage calculator: % of, % change, increase, decrease and reverse

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Choose the type of percentage question, enter the two numbers, and the calculator gives the answer with the method. It covers the six types that come up most in school maths and everyday life: a percentage of a number, what percent one number is of another, percentage change, increasing or decreasing by a percentage, and reverse percentages (finding the original amount).

PercentageNumber

What is 15% of 80?

Working

115% means 15 out of 100, so multiply by 0.15.
20.15 × 80 = 12

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The methods

Question	Method	Example
15% of 80	$0.15 \times 80$	$12$
12 is what % of 80?	$12 \div 80 \times 100$	$15\%$
% change from 40 to 50	$(50 - 40) \div 40 \times 100$	$+25\%$
Increase 50 by 20%	$50 \times 1.2$	$60$
Decrease 50 by 20%	$50 \times 0.8$	$40$
60 after a 20% increase; original?	$60 \div 1.2$	$50$

Multipliers make it quick

A multiplier turns a percentage change into one multiplication: increase by 15% → $\times 1.15$ ; decrease by 15% → $\times 0.85$ . Multipliers also handle repeated changes: a 20% rise then a 20% fall is $1.2 \times 0.8 = 0.96$ , a 4% decrease overall, not back to where you started. For compound interest over $n$ years, use $(\text{multiplier})^n$ .

Reverse percentages

"A coat costs £60 in a 25% off sale. What was the original price?" The sale price is 75% of the original, so divide by the multiplier: $60 \div 0.75 = 80$ . The common mistake is to add 25% of £60 back on (giving £75), which is wrong because the 25% was taken off the original, not the sale price.

Percentage change vs percentage points

If a test pass rate rises from 40% to 50%, that's a rise of 10 percentage points, but a 25% increase ( $10 \div 40 = 0.25$ ). News reports often mix these up. For more practice, see the percentage change guide and the percentages topic guide.

Percentages, fractions and decimals

Percentage	Fraction	Decimal
50%	$\tfrac{1}{2}$	0.5
25%	$\tfrac{1}{4}$	0.25
20%	$\tfrac{1}{5}$	0.2
12.5%	$\tfrac{1}{8}$	0.125
10%	$\tfrac{1}{10}$	0.1

Knowing these makes mental percentages fast: 12.5% of 64 is $\tfrac{1}{8}$ of 64, which is 8. See fractions, decimals and percentages.

Frequently asked questions

How do I work out a percentage of a number?

Divide the percentage by 100 and multiply: 15% of 80 is 0.15 × 80 = 12.

How do I calculate percentage change?

(New − original) ÷ original × 100. A positive answer is an increase; a negative one is a decrease.

How do I find the original price before a discount?

Divide the sale price by the multiplier. After 25% off, the multiplier is 0.75, so the original is the sale price ÷ 0.75.

Sources

National curriculum in England: mathematics programmes of study. Department for Education.
Common Core State Standards for Mathematics. Common Core State Standards Initiative.

Percentages

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How to calculate percentage change (increase and decrease)

The formula, multipliers, reverse percentages and compound change, with worked examples.

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