How to work out any percentage
Nearly every percentage question is one of three sums. Learn the three and you can do most of them in your head.
Three common percentage questions in one place, pick a mode and type your numbers.
Percentages feel slippery until you notice something freeing: almost every percentage question you ever meet is one of just three sums. A percent means a part out of 100, and once you can spot which of the three you are looking at, the maths is quick. Here they are, with the shortcuts that let you do most of them without a calculator.
1. A percentage of a number
This is the most common one: what is 20% of 500? Turn the percent into a decimal by dividing by 100, then multiply. So 20% becomes 0.20, and 0.20 times 500 is 100. The mental shortcut is even faster: 10% of any number just moves the decimal one place left, so 10% of 500 is 50, and 20% is double that, 100.
2. What percent one number is of another
Here the question flips: 30 is what percent of 200? Divide the part by the whole, then multiply by 100. So 30 divided by 200 is 0.15, times 100 is 15%. Use this whenever you want to express a score, a share or a tip as a percentage.
3. Percentage change
This one trips people up the most. A price goes from 200 to 260, what is the change? Subtract the old from the new, divide by the old, then multiply by 100. So (260 minus 200) divided by 200 is 0.30, a 30% rise. The key is that the starting number is always the one you divide by.
Why does the starting number matter so much?
Because percentage change is not symmetric. Going from 200 up to 260 is a 30% rise, but coming back down from 260 to 200 is only about a 23% fall, since the base is bigger the second time. This is the single most common percentage mistake, and knowing it saves you from a lot of bad conclusions about prices and figures.
The bottom line
Decide which of the three you are doing, keep the part-over-whole idea in mind, and the rest is arithmetic. When the numbers are awkward or you just want to be sure, drop them into our percentage calculator, which handles all three modes.
Frequently asked questions
How do I work out 10% of a number quickly?
Move the decimal point one place to the left. 10% of 250 is 25. From there, 20% is double (50) and 5% is half (12.5), so you can build most percentages in your head.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 200 is 30 divided by 200, times 100, which is 15%.
Why is a percentage rise and fall not the same?
Because the starting number changes. Going 200 to 260 is a 30% rise, but 260 back to 200 is only about a 23% fall, since the second sum divides by the larger number.