Percentages. They appear everywhere — sale signs, tax forms, nutritional labels, exam results, interest rates, news headlines. And yet a surprising number of adults quietly struggle with them. If you've ever stared at a "20% off" sign and had to reach for your phone, or nodded along to a "15% increase" in a meeting without quite working out what it means, this guide is for you. No maths degree required.
What Is a Percentage?
A percentage is simply a way of expressing a number as a fraction of 100. "Per cent" literally means "per hundred" in Latin. So 25% means 25 out of every 100, or 0.25 as a decimal, or 1/4 as a fraction. All three are saying exactly the same thing.
Our percentage calculator handles all the common percentage calculations in one place — but understanding the formulas helps you do quick mental estimates and catch errors when they appear.
Formula 1: Finding X% of a Number
"What is 15% of £80?" This is the most basic percentage calculation.
Answer = (Percentage ÷ 100) × Number
15% of £80 = (15 ÷ 100) × 80 = 0.15 × 80 = £12
Mental shortcut: 10% is always easy to find (just divide by 10). Then adjust. 10% of £80 = £8. Half of 10% = 5% = £4. Add them together: 15% = £12. Done.
Formula 2: What Percentage Is X of Y?
"My score was 42 out of 60. What percentage is that?"
Percentage = (Part ÷ Whole) × 100
42 ÷ 60 × 100 = 70%
This formula is useful for exam marks, survey results, conversion rates, and any time you want to express a ratio as a percentage.
Formula 3: Percentage Increase
"My salary went from £28,000 to £31,500. What's the percentage increase?"
% Increase = ((New − Old) ÷ Old) × 100
= ((31,500 − 28,000) ÷ 28,000) × 100 = (3,500 ÷ 28,000) × 100 = 12.5%
Our discount calculator uses this same logic in reverse — great for checking whether that "40% off" claim on a product is actually what it seems.
Formula 4: Percentage Decrease
"A product dropped from £120 to £90. What's the percentage decrease?"
% Decrease = ((Old − New) ÷ Old) × 100
= ((120 − 90) ÷ 120) × 100 = (30 ÷ 120) × 100 = 25%
Note: percentage increase and decrease are always calculated relative to the original (old) value. A common mistake is to use the new value as the denominator, which gives a different (and wrong) answer.
Formula 5: Finding the Original Value After a Percentage Change
"A price including 20% VAT is £84. What was the price before VAT?"
Original = Current Value ÷ (1 + Percentage/100)
= £84 ÷ 1.20 = £70
This reversal formula is especially useful for VAT calculations, discounts, and any time you need to "undo" a percentage change.
Percentage Points vs Percentages: A Critical Distinction
This confusion trips up even intelligent people. If interest rates rise from 2% to 5%, they have risen by 3 percentage points — not 3%. The percentage increase is actually (5−2) ÷ 2 × 100 = 150%. Politicians and journalists frequently exploit this ambiguity. A "50% reduction in crime" (percentage) sounds better than "crime fell from 4% to 2% of incidents" (percentage points). Read carefully.
Quick Mental Maths Tips
- To find 1%: divide by 100
- To find 10%: divide by 10
- To find 50%: divide by 2
- To find 25%: divide by 4
- To find 75%: find 25% and multiply by 3
- To find 5%: find 10% and halve it
- X% of Y = Y% of X (surprisingly useful: 8% of 25 = 25% of 8 = 2)
Percentages are one of the most practically useful areas of maths you'll encounter in everyday life. A few minutes spent really understanding these formulas pays dividends forever.
Further reading: Khan Academy has excellent free lessons on percentages, from basic to advanced. Learn more percentages at Khan Academy.