How to Work Out Percentage

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How to Work Out Percentage

Every percentage calculation you’ll ever need, in one place. Get an instant answer and see the exact formula used, so you can work it out by hand next time too.

🧮 Instant Answer
📐 Formula Shown
🔁 4 Calculation Types
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Pick the type of percentage question you have below, enter your numbers, and get an instant answer along with the formula used to reach it.

Percentage Calculator

Four common percentage calculations in one tool

Example: what is 20% of 150?
Example: 30 is what percent of 150?
Example: from 50 to 65, what’s the percentage change?
Example: £120 is the price after a 20% increase — what was the original price?

Your Answer

Updates instantly as you change the numbers

Enter your numbers to begin
Formula will appear here
💡 Tip: The formula box shows the exact calculation used, so you can repeat it by hand or in a spreadsheet next time.

The Four Formulas Explained

Almost every percentage question you’ll come across fits into one of four patterns. Here’s how to work out each one by hand.

Working Out Percentages by Hand

The core method behind each calculation type

1

Finding X% of a Number

Divide the percentage by 100, then multiply by the number: (% ÷ 100) × number. For example, 20% of 150 is (20 ÷ 100) × 150 = 30.

2

Finding What Percent One Number Is of Another

Divide the part by the whole, then multiply by 100: (part ÷ whole) × 100. For example, 30 out of 150 is (30 ÷ 150) × 100 = 20%.

3

Percentage Increase or Decrease

Subtract the original from the new value, divide by the original, then multiply by 100: ((new − old) ÷ old) × 100. A negative result means a decrease.

4

Finding the Original Number

Divide the new value by 1 plus the percentage as a decimal for an increase, or 1 minus the percentage for a decrease: new ÷ (1 ± %). For example, £120 after a 20% increase means the original was 120 ÷ 1.20 = £100.

⚠️ Common Mistake: Don’t confuse percentage points with percent. Moving from a 20% rate to a 25% rate is a rise of 5 percentage points, but it’s a 25% relative increase in the rate itself.
Identified whether you need a value or a percentage as the answer.
Confirmed which number is the “whole” and which is the “part”.
Converted the percentage to a decimal correctly (divided by 100).
Checked the sign: increase is positive, decrease is negative.
Double-checked with a rough estimate (e.g. 10% is easy to sanity-check).
Not mixed up percentage points with a percentage change.
💡 Pro Tip: To quickly estimate 10% of any number, just move the decimal point one place to the left. Use that as a sanity check for other percentages.

Common Percentage Shortcuts

Handy mental-maths shortcuts for percentages you’ll use often.

Percentage Quick Method Example (of 240)
50%Divide by 2120
25%Divide by 460
10%Move decimal point one place left24
5%Half of 10%12
1%Move decimal point two places left2.4
20%Divide by 548

Percentage FAQ

Answers to the most frequently asked questions about working out percentages.

The basic formula is: part divided by whole, multiplied by 100. This tells you what percentage the part represents of the whole. To find a percentage of a number, rearrange this to: (percentage divided by 100) multiplied by the number.

Subtract the original number from the new number, divide the result by the original number, then multiply by 100. For example, going from 50 to 65 is an increase of 15, and 15 divided by 50 multiplied by 100 equals a 30% increase.

If a value has increased by a known percentage, divide the new value by (1 plus the percentage as a decimal). If it has decreased, divide the new value by (1 minus the percentage as a decimal). For example, if £120 is the price after a 20% increase, the original price is 120 divided by 1.20, which equals £100.

A percentage point is the simple arithmetic difference between two percentages, while percent describes a relative change. For example, moving from 20% to 25% is a rise of 5 percentage points, but it is a 25% relative increase in the underlying value.

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