Percentage Calculator
Calculate percentages, percentage change, and percentage of totals.
BSc Physics (Hons), MEng Mechanical Engineering
Physicist and engineer focused on translating complex scientific and mathematical calculations into accessible everyday tools.
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About the Percentage Calculator
Percentages are one of the most universally useful mathematical tools in everyday life — from calculating a restaurant tip, to interpreting a test score, to understanding how much a price has changed. Despite their ubiquity, many people still trip over questions like "what is 17.5% of £340?" or "if a salary went from £32,000 to £36,800, what percentage increase is that?" This calculator handles all four common percentage calculations in one place.
The core concept is simple: "per cent" means "per hundred." So 25% means 25 out of every 100, or equivalently 0.25 as a decimal. To find 25% of a number, multiply by 0.25. To find what percentage A is of B, divide A by B and multiply by 100. To find the percentage change from A to B, subtract A from B, divide by A, and multiply by 100. That's all there is to it — the challenge is usually knowing which of these operations applies to your specific question.
Percentage change is particularly important in finance and statistics. A stock that rises from £10 to £15 has increased by 50% (because +5 is 50% of the original £10). If it then falls from £15 to £10, it has decreased by only 33.3% (because −5 is 33.3% of the new base of £15). This asymmetry explains why recovering from a loss always requires a larger percentage gain: a 50% loss requires a 100% gain to break even. Understanding this prevents common errors in investment thinking.
How it works
X% of Y: result = (X ÷ 100) × Y % Change A→B: change = ((B − A) ÷ |A|) × 100 X is what % of Y: percent = (X ÷ Y) × 100 X increased by Y%: result = X × (1 + Y ÷ 100)
Where
XThe percentage value (e.g. 25 for 25%)YThe base value the percentage applies toAStarting value in a percentage change calculationBEnding value in a percentage change calculationWorked example
Example 1 — X% of Y: What is 17.5% of £340?
17.5 ÷ 100 = 0.175
0.175 × 340 = £59.50
Example 2 — % Change: Salary went from £32,000 to £36,800
36,800 − 32,000 = 4,800 increase
4,800 ÷ 32,000 = 0.15
0.15 × 100 = 15% salary increase
Example 3 — X is what % of Y: 45 marks out of 60
45 ÷ 60 = 0.75
0.75 × 100 = 75%
Tips to improve your result
- 1.
To quickly estimate 10% of any number, move the decimal point one place to the left. Then halve that for 5%, or double it for 20%.
- 2.
A 20% discount followed by a 20% increase does NOT return you to the original price. 20% off £100 = £80, then 20% on £80 = £96. You end up lower because the percentage applies to different bases.
- 3.
To reverse a percentage increase: divide by (1 + rate). If a price is £120 including 20% VAT, the ex-VAT price is £120 ÷ 1.20 = £100. Don't subtract 20% — that gives the wrong answer (£96).
- 4.
Percentage points and percentages are different. If interest rates rise from 2% to 3%, that's 1 percentage point — but a 50% increase in the rate itself.
- 5.
For large numbers, a useful mental trick: 1% of X is always X ÷ 100. So 1% of 4,750 is 47.50. Scale from there for any other percentage.