Calculator to Find Percentage

Finding a percentage sounds simple until you're staring at two numbers and can't remember which one to divide by. Was 45 out of 60 a good score? How much is 15% of a £240 bill? A jacket costs £42 after 30% off, so what was it before? Each of these is a slightly different calculation, and mixing them up gives the wrong answer.

Our Calculator to Find Percentage handles all of them. Pick what you want to find, enter two numbers and it shows the answer with the working. This guide explains each calculation in plain English, with examples you can check by hand.

The five things you can find

1. What percentage is X of Y?

Use this when you have a part and a total, and want the part as a percentage. Test scores, shares of a budget and how much of a target you've reached all work this way.

Percentage = X ÷ Y × 100

Divide the part by the total, then multiply by 100. The total always goes on the bottom.

2. What is X% of Y?

Use this to find a share of an amount: a tip, a deposit, a discount or a commission.

X% of Y = Y × X ÷ 100

3. X is Y% of what number?

This is the reverse calculation. You know a part and what percentage it represents, and want the whole. For example, if £9,000 is a 10% deposit, what's the full price?

Whole = X ÷ Y × 100

So £9,000 ÷ 10 × 100 = £90,000.

4. Add X% to a number

Use this for price rises, pay rises or adding a percentage such as VAT.

New amount = Y × (1 + X ÷ 100)

Adding 20% to £50 is £50 × 1.2 = £60.

5. Take X% off a number

Use this for discounts and reductions.

New amount = Y × (1 − X ÷ 100)

Taking 30% off £60 is £60 × 0.7 = £42.

How to use the calculator (Calculator to Find Percentage)

1. Choose what you want to find from the list.
2. Enter X. Depending on the option, this is the part or the percentage.
3. Enter Y. This is the total, the amount, or the percentage when you're finding the whole.

The answer updates as you type, with the working shown underneath so you can follow it or copy it into a spreadsheet.

A worked example

With the calculator's default settings, you scored 45 out of a possible 60:

• 45 ÷ 60 = 0.75
• 0.75 × 100 = 75%

Now try the other options with the same kind of numbers:

• 15% of 240 = 240 × 15 ÷ 100 = 36
• 36 is 15% of what? = 36 ÷ 15 × 100 = 240
• Add 15% to 240 = 240 × 1.15 = 276
• Take 15% off 240 = 240 × 0.85 = 204

Notice how the first two are the reverse of each other. Once you know any two of the part, the whole and the percentage, you can always find the third.

Everyday examples

• Exam and test marks. 52 out of 80 is 52 ÷ 80 × 100 = 65%.
• Household budgets. If your rent is £950 of a £2,500 monthly take-home pay, it takes 38% of your income. Our Salary Calculator shows your take-home pay after tax.
• Tips and service charges. 12.5% of a £64 restaurant bill is £8.
• Deposits. A 10% deposit on a £250,000 home is £25,000.
• Savings goals. If you've saved £1,800 towards £2,400, you're 75% of the way there.
• Sales. A "40% off" label on a £35 item means you pay £35 × 0.6 = £21.

Finding the original number after a percentage change

This is where most mistakes happen. If a price has already had a percentage added or taken off, you can't reverse it by applying the same percentage the other way.

Before a percentage was added: divide by (1 + the percentage as a decimal). A price of £120 including 20% VAT was £120 ÷ 1.2 = £100 before VAT, not £96. The standard VAT rate in the UK is 20%, and our VAT Calculator does this for you.

Before a percentage was taken off: divide by (1 − the percentage as a decimal). If a jacket costs £42 after 30% off, the original price was £42 ÷ 0.7 = £60.

You can also use option 3 in the calculator. A sale price of £42 is 70% of the original, so "42 is 70% of what number?" gives £60.

Mental maths shortcuts

• 10%: move the decimal point one place to the left. 10% of £340 is £34.
• 5%: halve 10%. 5% of £340 is £17.
• 1%: move the decimal point two places. 1% of £340 is £3.40.
• 20%: double 10%. 25%: divide by 4. 50%: halve it.
• Build the rest from those. 15% is 10% plus 5%. 35% is 25% plus 10%.
• Swap the numbers if it's easier. 4% of 75 is the same as 75% of 4, which is 3.

Common mistakes

Dividing by the wrong number

When finding what percentage X is of Y, the total goes on the bottom. 15 out of 60 is 15 ÷ 60 = 25%, while 60 ÷ 15 gives 400%, which clearly isn't a score out of 60.

Adding percentages one after another

Two 10% rises aren't a 20% rise. £100 rises to £110, then 10% of £110 takes it to £121, which is 21% more than you started with. Price inflation, published monthly by the ONS, compounds in the same way over the years.

Mixing up percentages and percentage points

Going from 20% to 25% is a rise of 5 percentage points, but a 25% increase in the rate itself. For changes between two numbers, use the Percent Change Calculator.