Percentage Calculator
Three types of percentage problem — percentage of a number, percentage change, and reverse percentages — with full step-by-step working shown.
Step by step calculations
Enter values in the calculator to see the step by step calculations.
Percentage Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Understanding percentages
The key idea: "percent" means "out of 100". So 35% simply means 35 out of every 100 — a fraction with 100 on the bottom. Once you see percentages as fractions and decimals in disguise, every percentage calculation becomes straightforward arithmetic.
This calculator handles three types: finding a percentage of a number, calculating percentage change, and working backwards with reverse percentages.
Finding a percentage of a number
"What is 15% of 240?"
Method: divide by 100, then multiply
240 ÷ 100 = 2.4 (1%)
2.4 × 15 = 36
Shortcut: convert to a decimal multiplier — 15% = 0.15, so 240 × 0.15 = 36
Percentage change
"A price goes from £80 to £92. What's the percentage increase?"
Change = 92 − 80 = 12
12 ÷ 80 × 100 = 15% increase
Always divide by the original value — the starting point, not the new one
Reverse percentage
"After a 20% discount, a coat costs £72. What was the original price?"
£72 = 80% of the original (100% − 20%)
1% = 72 ÷ 80 = 0.90
100% = 0.90 × 100 = £90
Never just add the % back on — that gives the wrong answer
Percentages
What is a percentage?
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum — meaning "out of a hundred". When you see 35%, it means 35 out of every 100.
Percentages appear in everyday life constantly: VAT is charged at 20%, exam scores are reported out of 100, interest rates are expressed as annual percentages, and sale discounts are shown as percentage reductions. Understanding which value is the base — the one that represents 100% — is the key to solving almost every percentage problem correctly.
Percentages
The three types of percentage problem
Find % of a number
When you'd use this: VAT on a purchase, discounts, tips, exam marks, percentage of a budget
Example: 20% of £85
→ (20 ÷ 100) × 85 = £17
Percentage change
When you'd use this: Price rises, salary increases, comparing before and after, growth rates
Example: £80 → £100
→ ((100 − 80) ÷ 80) × 100 = 25% increase
Find the original
When you'd use this: Working backwards from a sale price, finding the pre-VAT amount, reverse calculations
Example: £64 after 20% off
→ 64 ÷ 0.8 = £80
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Common mistakes to avoid
✗ "From £80 to £100 — the difference is £20, so I divide by £100"
The original value is always the base — the thing you're measuring change from.
✓ Always divide by the original value: 20 ÷ 80 × 100 = 25%
✗ "The price is £64 after 20% off, so the original must be £64 + 20% = £76.80"
Adding 20% of the discounted price is not the same as restoring the original 20%.
✓ Divide by the remaining percentage: £64 ÷ 0.8 = £80
✗ "Interest rates went from 2% to 3% — that's a 1% increase"
The rate increased by 1 percentage point, but the percentage change is 50%.
✓ Say "1 percentage point" when comparing two percentages directly
✗ "You can't have 150% of something"
If a value doubles, that's a 100% increase. Tripling is a 200% increase.
✓ Percentages above 100% are valid — the calculator handles them correctly
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