How to calculate percentages: the three formulas you need

What a percentage is

A percentage is a fraction out of 100. 25% means 25 out of 100, which is one quarter. To use a percentage in a calculation, turn it into a decimal by dividing by 100, so 25% is 0.25 and 8% is 0.08.

Type 1: find a percentage of a number

Multiply the number by the percentage as a decimal. 15% of 200 is 0.15 × 200 = 30.

This is how you work out a tip, a tax amount or a discount. A 20% discount on 150 takes off 0.20 × 150 = 30.

Type 2: what percent is one number of another

Divide the part by the whole and multiply by 100. If you scored 45 out of 60, then 45 ÷ 60 = 0.75, so you scored 75%.

Always put the part on top and the whole on the bottom. Swapping them gives a different answer.

Type 3: percentage change

Subtract the old value from the new value, divide by the old value and multiply by 100. A price that rises from 80 to 100 changes by (100 − 80) ÷ 80 = 0.25, which is a 25% increase.

A positive result is an increase and a negative result is a decrease. Always divide by the starting value, not the final one.

Why up 25% and down 25% do not cancel

A rise from 80 to 100 is 25%, but a fall from 100 back to 80 is only 20%, because the starting value is now different. Likewise, a 10% rise followed by a 10% fall leaves you at 99% of where you began, since 1.10 × 0.90 = 0.99.

A 50% rise followed by a 50% fall leaves you 25% down, because 1.5 × 0.5 = 0.75. This surprises many people.

Working out the original price

Suppose an item costs 48 after a 20% discount. The price you paid is 80% of the original, so divide by 0.80: 48 ÷ 0.80 = 60. The original price was 60.

For a price that includes 10% tax, divide by 1.10 to remove the tax. Taking 10% off the total instead gives the wrong answer.

Percent and percentage points

If an interest rate goes from 4% to 5%, it has risen by one percentage point, but it has risen by 25% in relative terms (1 ÷ 4). News stories often mix these up, so check which one is meant.

Quick mental tricks

• 10% is the number divided by 10. 5% is half of that, and 20% is double it.
• 1% is the number divided by 100.
• To add 15% tip, find 10%, add half of it, then add to the bill.
• 50% is half, 25% is a quarter and 75% is three quarters.

Let a calculator check you

The percentage calculator on Toolstia handles all three types plus adding and subtracting a percentage, so you can check your own working. The discount calculator and VAT and GST calculator build on the same formulas for shopping and tax.