How to Calculate Percentages — A Step-by-Step Guide

A percentage is a number or ratio expressed as a fraction of 100. The word comes from the Latin per centum, meaning "per hundred". So 37% simply means 37 out of every 100.

The relationships between percentages, fractions, and decimals are:

• Percentage → Decimal: divide by 100. So 45% = 0.45
• Decimal → Percentage: multiply by 100. So 0.73 = 73%
• Percentage → Fraction: write over 100, then simplify. So 25% = 25/100 = ¼
• Fraction → Percentage: divide numerator by denominator, then multiply by 100. So ⅗ = 0.6 = 60%

Being fluent in converting between these three forms makes it much easier to calculate percentages in different contexts.

Common percentages to know by heart: - 50% = ½ = 0.5 - 25% = ¼ = 0.25 - 10% = 1/10 = 0.1 - 1% = 1/100 = 0.01

There are three core types of percentage calculation. Learning how to calculate percentages means mastering all three.

Method 1: Find a percentage of a number

Question: What is 30% of 240?

Method: Multiply the number by the percentage expressed as a decimal.

30% = 0.30 0.30 × 240 = 72

So 30% of 240 is 72.

Shortcut for 10%: Move the decimal point one place left. 10% of 350 = 35. Then use this to build other percentages: 20% = 10% × 2; 5% = half of 10%; 15% = 10% + 5%.

Method 2: Express one number as a percentage of another

Question: A student scored 36 out of 48. What percentage did they score?

Method: Divide the part by the whole, then multiply by 100.

(36 ÷ 48) × 100 = 0.75 × 100 = 75%

To calculate percentages this way, make sure the two numbers use the same units.

Method 3: Calculate percentage increase or decrease

Question: A price rose from £80 to £92. What is the percentage increase?

Method: Find the change, divide by the original value, multiply by 100.

Change = 92 − 80 = 12

(12 ÷ 80) × 100 = 15%

The price increased by 15%.

For a decrease: use the same formula — the result will still be positive; just label it a decrease.

Finding the new value after a percentage change

Rather than calculate percentages in two steps, use a multiplier:

• Increase by 20%: multiply by 1.20
• Decrease by 15%: multiply by 0.85 (100% − 15% = 85% = 0.85)

Example: A salary of £32,000 increases by 5%. £32,000 × 1.05 = £33,600

Multipliers make it easy to calculate percentages in compound situations — for example, when a price increases by 10% in year 1 and 10% in year 2:

£1,000 × 1.10 × 1.10 = £1,210 (not £1,200 — because the second 10% applies to the already-increased amount).

Reverse percentages

Sometimes you know the value after a change and need to find the original. This is called a reverse percentage.

Example: A coat costs £68 after a 15% reduction. What was the original price?

£68 represents 85% of the original (100% − 15% = 85%).

Original = £68 ÷ 0.85 = £80.

Reverse percentages are a common source of errors — students who calculate percentages by adding the percentage back often get the wrong answer. Always divide by the multiplier.

For parents helping with percentages at home: calculating discounts while shopping, reading nutrition labels, and checking exam percentage scores are all concrete, motivating contexts. The For parents guide has further ideas for everyday maths practice.