Percentage Calculator
Six everyday percentage questions, all on one page. Type your numbers into any card and the answer and its formula update as you type.
Percent of a number
20
25 ÷ 100 × 80 = 20
What percent
25%
20 ÷ 80 × 100 = 25%
Percentage change
50% increase
(75 − 50) ÷ |50| × 100 = 50%
Find the whole
80
20 ÷ (25 ÷ 100) = 80
Increase or decrease by a percentage
230
200 × (1 + 15 ÷ 100) = 230
Percentage difference
66.6666666667%
|10 − 20| ÷ ((10 + 20) ÷ 2) × 100 = 66.6666666667%
A percentage is a number out of 100, so 25% means 25 ÷ 100 = 0.25. Almost every percentage question is one of the six cards above, and each one is just a rearrangement of the same relationship: part = percent ÷ 100 × whole.
Percentage change compares a new value with an old one and divides by the old value, so it depends on direction: going from 50 to 75 is a 50% increase, but going from 75 back to 50 is a 33.33% decrease. Percentage difference compares two values with no starting point, so it divides by their average and gives the same answer either way round.
A change from 0 has no percentage, because you can't divide by zero. The calculator tells you so instead of showing infinity.
Which card should I use?
Percent of a number
A 15% tip on a 40 bill: what is 15% of 40? Answer: 6.
What percent
You scored 42 out of 50: 42 is what percent of 50? Answer: 84%.
Percentage change
A price went from 80 to 100. That is a 25% increase.
Find the whole
You paid a 30 deposit, which was 20% of the price. The full price was 150.
Increase or decrease
Add 20% VAT to 250 (300), or take 30% off 250 in a sale (175).
Percentage difference
Compare two quotes of 90 and 110 with no clear 'before': 20% different.
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 25% of 80 = 25 ÷ 100 × 80 = 20.
What is the difference between percentage change and percentage difference?
Percentage change measures a move from an old value to a new one and divides by the old value. Percentage difference compares two values on equal terms and divides by their average, so the order does not matter.
Why can't I work out a percentage change from 0?
The formula divides by the starting value, and dividing by zero is undefined. Any increase from 0 would be an infinite percentage, so the calculator shows a message instead.
If a price goes up 10% and then down 10%, is it back where it started?
No. 100 up 10% is 110, and 110 down 10% is 99. The second 10% is taken from a bigger number, so you end up 1% lower.
