Percent of a number
What is % of ?
12
15 ÷ 100 × 80 = 12
What percent is it?
is what % of ?
20%
12 ÷ 60 × 100 = 20%
Percentage change
From to
+30% increase
(65 − 50) ÷ 50 × 100 = +30%
Add or take off a percentage
%
92
80 × 1.15 = 92
How do you calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12.
To find what percent one number is of another, divide the part by the whole and multiply by 100: 12 out of 60 is 12 ÷ 60 × 100 = 20%.
The formulas
Every box above is one of these. They are worth knowing because the most common percentage mistakes come from picking the wrong one, not from bad arithmetic.
- P% of X — multiply X by P ÷ 100. 20% of 250 is 250 × 0.20 = 50.
- A is what % of B — divide A by B, then multiply by 100. 45 of 180 is 45 ÷ 180 × 100 = 25%.
- % change from A to B — subtract A from B, divide by A, multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = +30%.
- X plus or minus P% — multiply X by (1 + P ÷ 100) to add, or (1 − P ÷ 100) to take off. 80 plus 15% is 80 × 1.15 = 92.
| Percent | of 20 | of 50 | of 80 | of 100 | of 250 | of 1,000 |
|---|---|---|---|---|---|---|
| 5% | 1 | 2.5 | 4 | 5 | 12.5 | 50 |
| 10% | 2 | 5 | 8 | 10 | 25 | 100 |
| 15% | 3 | 7.5 | 12 | 15 | 37.5 | 150 |
| 20% | 4 | 10 | 16 | 20 | 50 | 200 |
| 25% | 5 | 12.5 | 20 | 25 | 62.5 | 250 |
| 30% | 6 | 15 | 24 | 30 | 75 | 300 |
| 50% | 10 | 25 | 40 | 50 | 125 | 500 |
| 75% | 15 | 37.5 | 60 | 75 | 187.5 | 750 |
The base is always the starting number
A percentage change is measured against where you started, and that is why it is not symmetrical. A price that goes up 50% and then down 50% does not end where it began: 100 becomes 150, and 50% off 150 is 75. The fall is measured against the bigger number.
The same trap catches discounts and markups. A 25% markup on a $100 cost gives a $125 price — but the $25 profit is only 20% of the selling price. Markup is measured against cost; margin is measured against price. If a quote says “20% margin” and you add 20% to cost, you have quoted a 16.7% margin.
Finding the original price (reverse percentages)
If a price is $115 after 15% tax, the price before tax was not $115 minus 15%. That gives $97.75, which is wrong, because the 15% was worked out on the smaller, pre-tax number.
To reverse a percentage, divide instead of subtracting: $115 ÷ 1.15 = $100. For a discount, the same idea: something that costs $60 after 25% off was $60 ÷ 0.75 = $80 before it.
Percent versus percentage points
When the numbers being compared are themselves percentages, “up 2%” is ambiguous. An interest rate that moves from 4% to 6% has gone up by 2 percentage points, but it has increased by 50 percent — 2 is half of 4. News reports and sales pitches use whichever sounds more impressive, so it is worth checking which one is meant.
Doing it in your head
Ten percent is just moving the decimal point one place left: 10% of 340 is 34. Everything else can be built from that. 5% is half of 10%, so 17. 20% is double, so 68. 15% is 10% plus 5%: 34 + 17 = 51. For a 15% or 20% tip, that is usually all you need.
Percentages also swap: 8% of 50 is the same as 50% of 8, which is 4. When one way round looks awkward, try the other.
Common questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12. On a phone calculator you can also type 80 × 15 % on most models.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. 12 out of 60 is 12 ÷ 60 = 0.2, times 100 is 20%.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 50 to 65 is 15 ÷ 50 × 100 = a 30% increase. A negative answer is a decrease.
How do I add 15% to a price?
Multiply the price by 1.15. $80 plus 15% is $80 × 1.15 = $92. To take 15% off instead, multiply by 0.85.
How do I remove tax that is already included in a price?
Divide by 1 plus the tax rate. A $115 price including 15% tax was $115 ÷ 1.15 = $100 before tax. Subtracting 15% of $115 gives $97.75, which is wrong.