What Is a Percentage?

A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum," meaning "per hundred." When we say 35%, we mean 35 out of every 100 — or the decimal 0.35, or the fraction 35/100. Percentages are one of the most universally used mathematical concepts in everyday life — appearing in payslips, mortgage statements, tax returns, sale prices, nutritional information, and virtually every news article covering economic or health data.

Three Core Percentage Calculations

Type 1: Finding a Percentage of a Number

"What is 15% of £240?" — Convert the percentage to a decimal (divide by 100), then multiply: 15 ÷ 100 = 0.15 → 0.15 × 240 = £36. Mental maths shortcut: find 10% (move decimal left) then add 5% (half of 10%). 10% of £240 = £24; 5% = £12; 15% = £36.

Type 2: Finding What Percentage One Number Is of Another

"18 is what percentage of 72?" — Divide the part by the whole, then multiply by 100: (18 ÷ 72) × 100 = 25%. Used for: calculating exam scores as a percentage, finding what proportion of income goes to rent, determining market share.

Type 3: Finding the Whole When You Know a Part and Its Percentage

"£45 is 30% of what number?" — Divide the known part by the percentage as a decimal: 45 ÷ 0.30 = £150. Used for: working backwards from a discounted price to the original price, finding pre-tax income from an after-tax figure.

Percentage Increase and Decrease

Percentage change formula: ((New Value − Old Value) ÷ Old Value) × 100. A salary rising from £32,000 to £35,000: ((35,000 − 32,000) ÷ 32,000) × 100 = 9.375% increase. A share price falling from £8.50 to £7.20: ((7.20 − 8.50) ÷ 8.50) × 100 = −15.3% decrease.

Finding the Original Value After a Percentage Change

Common mistake: "A jacket costs £68 after a 20% discount — original price?" Many add 20% back to £68, getting £81.60. This is wrong because the 20% was calculated on the original price. Correct: the sale price represents 80% of original (100% − 20%), so: 68 ÷ 0.80 = £85. Check: 20% of £85 = £17; £85 − £17 = £68. ✓

This reverse calculation appears constantly in financial contexts — recovering the pre-VAT price from a VAT-inclusive total, finding the pre-tax salary from a net wage.

Percentage Points vs Percentages

One of the most common errors in interpreting financial news is confusing percentage points with percentages. If an interest rate rises from 2% to 3%, it has risen by 1 percentage point. But as a percentage change, it has risen by 50% (because 1 is 50% of 2). Percentage points describe absolute changes in a percentage figure. Percentages describe relative changes. The confusion arises when the two are used interchangeably.

Common Real-World Applications

VAT (UK): Standard VAT is 20%. To find the VAT-inclusive price: multiply by 1.20. To find the ex-VAT price from an inclusive price: divide by 1.20. A product costing £60 ex-VAT costs £72 including VAT.

Salary negotiations: A £2,000 rise on a £25,000 salary is 8%; on a £60,000 salary it is only 3.3%. Always express pay rises as a percentage of your current salary to evaluate their real value.

Investment returns: A 10% gain followed by a 10% loss does not return you to zero. Starting with £1,000: a 10% gain gives £1,100; a 10% loss on £1,100 gives £990. Percentage gains and losses are not symmetrical — you need an 11.1% gain to recover from a 10% loss.

Nutrition labels: The % Daily Reference Intake on food labels shows what percentage of a recommended daily intake a serving provides. A product showing 40% DRI for sodium in one serving is a significant contributor to your daily sodium budget.

Quick Mental Maths Techniques

  • 1%: move decimal two places left. 1% of £430 = £4.30
  • 10%: move decimal one place left. 10% of £430 = £43
  • 5%: find 10% then halve. 5% of £430 = £21.50
  • 25%: divide by 4. 25% of £430 = £107.50
  • 50%: divide by 2. 50% of £430 = £215
  • 75%: find 25% and multiply by 3. 75% of £430 = £322.50

Percentages in Statistics and Data

Percentages normalise comparisons between groups of different sizes. "24 people in Group A and 36 in Group B responded positively" is less informative than "60% of Group A (n=40) and 45% of Group B (n=80)" — because the latter accounts for different group sizes. When reading statistics, always ask: what is the base number? A "200% increase" sounds dramatic, but if the base is 3 people, it means 6 — which may not be significant.

Conclusion

Percentages underpin a huge proportion of the numerical information we encounter every day. Fluency with the three core calculation types, an understanding of percentage change, and awareness of the percentage points distinction will serve you in nearly every financial and professional context. Use our free Percentage Calculator for instant, accurate calculations whenever you need them.