Percentage Calculator

Four percentage calculators in one: find a percentage of a number, work out what percentage one number is of another, calculate a percentage change, and reverse-engineer the original value.

What is a percentage?

A percentage is a fraction expressed out of 100. The word comes from the Latin per centum, meaning 'by the hundred', and the % sign is simply shorthand for ÷ 100.

That single idea is behind every calculation on this page: 25% is 25 ÷ 100 = 0.25, so finding 25% of something means multiplying it by 0.25.

The four percentage formulas

The calculator above runs whichever of these matches the mode you pick, and shows the substituted formula underneath the answer so you can check the working.

Percentage of a number: result = value × (percent ÷ 100)
X is what percent of Y: percent = (X ÷ Y) × 100
Percentage change: change = ((new − old) ÷ old) × 100
Reverse percentage: original = value ÷ (percent ÷ 100)

How to calculate a percentage of a number

Divide the percentage by 100 to turn it into a decimal, then multiply. To find 15% of 200, take 15 ÷ 100 = 0.15 and multiply by 200 to get 30.

15% of 200 = 200 × 0.15 = 30

How to calculate percentage change

Subtract the old value from the new one, divide by the old value, then multiply by 100. The old value is always the denominator — that is the single most common mistake in percentage maths.

If a price rises from 80 to 100, the change is (100 − 80) ÷ 80 × 100 = 25%. If it falls from 100 back to 80, the change is (80 − 100) ÷ 100 × 100 = −20%. The two are not symmetrical because the starting point differs.

Change % = ((new − old) ÷ old) × 100

A rise of 25% followed by a fall of 20% returns you to where you started.

Example calculations

Question	Working	Answer
What is 20% of 250?	250 × 0.20	50
18 is what percent of 60?	(18 ÷ 60) × 100	30%
From 40 to 52 is what change?	((52 − 40) ÷ 40) × 100	+30%
75 is 15% of what number?	75 ÷ 0.15	500

Percentage points vs percent

If an interest rate moves from 4% to 6%, it has risen by 2 percentage points but by 50 percent. Both statements are correct and they describe the same move, which is why news reports carefully say 'percentage points' when comparing two percentages.

Frequently Asked Questions

How do I calculate a percentage quickly in my head?

Find 10% by moving the decimal point one place left, then scale it. For 30% of 60: 10% is 6, so 30% is 18. For 5%, halve the 10% figure.

What is the difference between percentage increase and percentage points?

Percentage points measure the plain difference between two percentages, while percentage increase measures that difference relative to the starting value. Going from 4% to 6% is +2 percentage points and +50%.

How do I reverse a percentage?

Divide rather than multiply. If 75 is 15% of a number, that number is 75 ÷ 0.15 = 500. This is how you find a pre-discount or pre-tax price.

Why is a 50% rise not cancelled by a 50% fall?

Because the second percentage is taken from a larger base. 100 raised by 50% is 150, and 150 cut by 50% is 75, not 100. You would need a 33.3% fall to get back to 100.

Can a percentage be more than 100?

Yes. Any value larger than the whole gives a percentage above 100 — a figure that triples is 300% of its original value, which is a 200% increase.