How to Calculate Percentages: 7 Formulas with Worked Examples

“Per cent” means “per hundred”: 15% is 15 ÷ 100 = 0.15. Almost every percentage question in daily life follows one of seven patterns. Once you recognise the pattern, the calculation takes a single line, and you can check it with our Percentage Calculator.

1. What is X% of Y?

result = Y × X ÷ 100

Example: 18% of €2,450 = 2,450 × 0.18 = €441.

A mental shortcut: 10% is the number with the decimal point moved one place (€245), and 1% is two places (€24.50). So 18% = 10% + 8 × 1% = 245 + 196 = 441.

2. What percentage is X of Y?

percentage = X ÷ Y × 100

Example: you answered 42 of 56 questions correctly: 42 ÷ 56 × 100 = 75%.

3. Percentage change

change in % = (new − old) ÷ old × 100

Example: the rent rises from €850 to €935: (935 − 850) ÷ 850 × 100 = +10%. If it then falls from €935 back to €850, the change is (850 − 935) ÷ 935 × 100 = −9.1%.

Always divide by the old value. That is why a rise and the fall back to the start do not have the same percentage.

4. Increase or decrease by a percentage

after an increase:  new = old × (1 + X ÷ 100)
after a decrease:   new = old × (1 − X ÷ 100)

Examples: a €64 jacket reduced by 25% costs 64 × 0.75 = €48. A monthly salary of €2,800 raised by 3.5% becomes 2,800 × 1.035 = €2,898.

5. Reverse percentage: find the original value

after an increase:  original = final ÷ (1 + X ÷ 100)
after a decrease:   original = final ÷ (1 − X ÷ 100)

Example: a sale price of €51 after 15% off. The original price was 51 ÷ 0.85 = €60, not 51 plus 15% = €58.65, which is a very common mistake.

VAT: net and gross prices

VAT is the most frequent reverse-percentage problem. With Germany’s standard rate of 19%, a gross price of €119 contains a net price of 119 ÷ 1.19 = €100 and €19 of VAT. So the VAT share of a gross price is 19 ÷ 119 = 15.97%, not 19%. In Spain, where the standard rate is 21%, a gross price of €249 corresponds to 249 ÷ 1.21 = €205.79 net.

6. Stacked discounts and repeated changes

A coat is reduced by 30%, and at the checkout you get an extra 20% off. That is not 50% off:

100 × (1 − 0.30) × (1 − 0.20) = 100 × 0.70 × 0.80 = 56
total discount = 100 − 56 = 44%

The same logic applies to growth over several years. Prices that rise by 2%, 6% and 3% in three consecutive years have gone up by 1.02 × 1.06 × 1.03 = 1.1136, that is 11.4% in total, not 11%. The Discount Calculator works out the final price and the amount you save for you.

7. Percent vs. percentage points

If an interest rate goes from 2% to 3%, it rose by 1 percentage point, but by 50 percent relative to its old value. The two are mixed up all the time, and the difference can be large: a tax that goes from 10% to 12% rises by “only” 2 points, yet the tax bill grows by 20%.

Two more traps: averages and growth over time

Averaging percentages

Two classes sit the same exam. In class A, 90% of 20 students pass; in class B, 60% of 80 students pass. The overall pass rate is not (90 + 60) ÷ 2 = 75%. In total, 18 + 48 = 66 of 100 students passed, so the overall rate is 66%. Percentages that refer to groups of different sizes must be weighted by the size of each group:

overall % = (part₁ + part₂) ÷ (whole₁ + whole₂) × 100
           = (18 + 48) ÷ (20 + 80) × 100 = 66%

The same mistake appears with conversion rates, survey results and interest rates on several accounts: add up the underlying numbers first, then calculate the percentage.

Growth over many years and the rule of 72

A rate that repeats every year compounds. Prices rising by 2% a year for ten years go up by 1.02¹⁰ − 1 = 21.9%, not 20%. To estimate how long it takes for something to double, divide 72 by the yearly percentage: at 3% inflation, prices double in about 72 ÷ 3 = 24 years. The exact answer is ln 2 ÷ ln 1.03 = 23.4 years, so the shortcut is close enough for planning.

years to double ≈ 72 ÷ rate in %
exact: years = ln(2) ÷ ln(1 + rate ÷ 100)

Loans work the same way in reverse: interest is charged on the remaining balance each month. The Loan Calculator shows the monthly payment and how much of it goes to interest, year by year.

Everyday examples

For restaurant bills, the Tip Calculator also splits the total between several people.

Percentage CalculatorCalculate percentages instantly: X% of Y, what percent X is of Y, percentage change, and adding or subtracting a percentage.Open tool

How to check your answer

• Estimate first. 18% of 2,450 must be a little less than 20% of 2,500, which is 500. An answer of 4,410 or 44 is obviously wrong.
• Work backwards. If 42 out of 56 is 75%, then 56 × 0.75 must give 42 again.
• Ask “percent of what?”. A change is measured against the old value, a share against the whole.
• Use a calculator for decimals and chains. Our percentage calculator has a separate box for each of the common patterns, so you only fill in the numbers.

Tools used in this guide

• Percentage Calculator

  Calculate percentages instantly: X% of Y, what percent X is of Y, percentage change, and adding or subtracting a percentage.

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• Discount Calculator

  Work out the sale price and how much you save. Supports a second (stacked) discount and adds VAT if you need it.

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• Tip Calculator

  Calculate the tip and total for any bill and split it between several people, with quick buttons for 10, 15, 18, 20 and 25 percent.

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• Loan Calculator

  Calculate the monthly payment, total interest and yearly repayment schedule for a fixed-rate loan or mortgage.

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Frequently asked questions

How do I calculate 20% of a number?

Multiply the number by 0.2, or divide it by 5. For example, 20% of 85 is 85 × 0.2 = 17.

How do I calculate a percentage increase?

Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%.

How do I remove VAT from a price?

Divide the gross price by 1 plus the VAT rate. With 19% VAT: net = gross ÷ 1.19. Subtracting 19% from the gross price is wrong, because the VAT was calculated on the net price.

What is the difference between percent and percentage points?

Percentage points are the plain difference between two percentages (from 2% to 3% is 1 point). Percent describes the relative change (from 2% to 3% is an increase of 50%).

Can a percentage be more than 100%?

Yes, for increases and comparisons: a price that rises from €20 to €50 has gone up by 150%. A share of a whole, however, can never be more than 100%.

Sources and further reading

1. VAT rules and rates – Your Europe (European Union) (europa.eu)