Percentages
Calculators, worked examples and guides — from basic percentage of a number through to reverse percentages and compound interest.
Learning about Percentages
The key idea: percent means "out of 100." That's literally all it is. 35% = 35 out of every 100 = 0.35 as a decimal. Everything else follows from that.
Type 1 — Finding a percentage of a number
"What is 35% of 260?"
Step 1: 260 ÷ 100 = 2.6 (find 1%)
Step 2: 2.6 × 35 = 91 (multiply by the percentage)
Shortcut: 260 × 0.35 = 91
Type 2 — Percentage change
"A jacket costs £80. It's reduced to £60. What is the percentage decrease?"
Step 1: Change = 80 − 60 = 20
Step 2: 20 ÷ 80 = 0.25
Step 3: 0.25 × 100 = 25% decrease
Formula: (new − original) ÷ original × 100
Type 3 — Reverse percentage
"After a 20% discount, a TV costs £320. What was the original price?"
Step 1: £320 is 80% of the original (100% − 20% = 80%)
Step 2: 1% = 320 ÷ 80 = 4
Step 3: 100% = 4 × 100 = £400
Shortcut: 320 ÷ 0.8 = £400
Percentage Formula Sheet & Rules
Need a printable revision sheet? Access percentage increase and decrease multipliers, reverse percentages, simple and compound interest, depreciation, and profit margins with step-by-step worked examples and custom print export.
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Percentage Questions Answered
What is a percentage?
A percentage is a number expressed as a fraction of 100. The word "percent" means "out of one hundred." So 35% means 35 out of every 100, or 0.35 as a decimal.
How do I find a percentage of a number?
Divide the number by 100, then multiply by the percentage. To find 35% of 260: 260 ÷ 100 × 35 = 91. Or multiply directly: 260 × 0.35 = 91.
How do I calculate percentage change?
Use the formula: percentage change = (new value − original value) ÷ original value × 100. A positive result is an increase; negative is a decrease.
What is a reverse percentage?
A reverse percentage works backwards from the result of a percentage change to find the original value. If a price after a 20% discount is £320, divide by 0.8 to get the original: £320 ÷ 0.8 = £400.
What is the difference between percentage and percentile?
A percentage is a proportion out of 100. A percentile describes where a value sits within a distribution — scoring in the 90th percentile means you scored higher than 90% of people, not that you scored 90%.