Percentages are everywhere — discounts, tips, interest, tax, statistics — and yet they quietly defeat a lot of capable people. The confusion almost always comes from mixing up three different questions that all use the word 'percent'. Separate them, and the whole topic collapses into one simple idea.
The core idea: percent means 'per hundred'
A percent is just a fraction with 100 on the bottom. 25% is 25/100, which is 0.25. To find a percent of a number, convert the percent to a decimal and multiply. 25% of 80 is 0.25 × 80 = 20. That single move — divide by 100, then multiply — answers most percentage questions you'll ever face.
Percentage Calculator
Handles 'percent of', increase, decrease and percentage change in one place.
Increase and decrease
- Increase: multiply by (1 + rate). A 20% raise on £50,000 is 50,000 × 1.2 = £60,000.
- Decrease: multiply by (1 − rate). A 30% discount on £80 is 80 × 0.7 = £56.
- Undo a percentage: to reverse a 20% increase, divide by 1.2 — don't subtract 20%.
A 50% drop and a 50% rise don't cancel out
Lose 50% of 100 and you have 50. Gain 50% back and you have 75, not 100 — because the second percentage is taken from a smaller base. Percentages always refer to whatever number they're applied to, and that base can change.
Percentage change
To find how much something changed in percentage terms, use (new − old) ÷ old × 100. A price rising from £40 to £50 is (50 − 40) ÷ 40 × 100 = 25%. The most common error is dividing by the new value instead of the old — always divide by where you started.
Percentage points vs percent
If a rate goes from 5% to 7%, that's a rise of 2 percentage points — but a 40% increase in relative terms. News and finance often blur the two; keeping them separate saves you from big misreadings.
Divide by 100 to get a decimal, multiply to apply it, and always know which base a percentage refers to. Get those three habits down and percentages stop being a trap.