What Can This Calculator Do?
Percentages appear constantly in daily life: a shop showing "30% off", a bank quoting "3.5% interest", a teacher returning a "78% test score", or a pay packet showing a "5% raise". All of these are different types of percentage problem — and each requires a slightly different formula.
This calculator covers all five common cases in one place. You don't need to remember any formula — just choose the mode that matches your question and enter your numbers.
The 4 Core Formulas (and How to Apply Them)
1 Finding X% of Y
Use this when you know the percentage and the total, and want the actual amount. The most common example: calculating a discount or a tip.
Question: A coat costs £120. It's 25% off. How much do you save?
Answer: £120 × (25 ÷ 100) = £120 × 0.25 = £30 saving
2 Increasing or decreasing by X%
Used for salary raises, price changes, VAT additions, and discount prices. The multiplier approach is faster than finding the percentage and then adding/subtracting.
Question: Your salary is £32,000 and you get a 7% raise. What's your new salary?
Answer: £32,000 × 1.07 = £34,240
💡 Mental shortcut: For a 10% increase, simply move the decimal point one place right. 10% of £85 = £8.50. For 20%, double it: £17. For 5%, halve the 10% result: £4.25.
3 What percentage is X of Y?
Used for exam grades, survey responses, or understanding a part relative to a whole. If you scored 36 out of 50, this tells you that's 72%.
Question: A class of 28 students has 17 girls. What percentage is that?
Answer: (17 ÷ 28) × 100 = 60.71%
4 Percentage change (from → to)
Tells you how much something changed, expressed as a percentage of the original value. Used for price rises, stock movements, weight loss/gain, or any before-and-after comparison.
Question: A house was worth £240,000 in 2020 and is now worth £285,000. How much has it risen?
Answer: ((285,000 − 240,000) ÷ 240,000) × 100 = (45,000 ÷ 240,000) × 100 = +18.75%
⚠️ Common mistake — percentage points vs. percentages: If interest rates rise from 2% to 5%, that's a 3 percentage point increase — but it's actually a 150% increase in the rate itself. The two measures are not the same.
Real-World Use Cases
🛒 Shopping & Sales
A 30% off sale on a £75 jacket: use X% of Y → £75 × 0.30 = £22.50 discount, leaving a sale price of £52.50. For stacked discounts (e.g., 20% off then an extra 10% at checkout), apply them sequentially: £100 → £80 → £72 — not £70, since the second 10% is taken off the already-discounted price.
💰 Tax & Finance
UK Income Tax uses percentage brackets: 20% on earnings between £12,571–£50,270, then 40% above that. If you earn £55,000, only £4,730 is taxed at 40% — not the full salary. For VAT at 20%, adding it means multiplying by 1.20; removing it means dividing by 1.20 (not subtracting 20%).
📊 Data & Statistics
In surveys, "62% of 1,200 respondents agreed" means 744 people. In business, a conversion rate improvement from 2.1% to 2.6% is a 23.8% relative increase (not 0.5% — that's the percentage point difference).
🏋️ Health & Fitness
If you weigh 90kg and want to lose 8%, your target weight is 90 × 0.92 = 82.8kg. To track progress, if you've lost 5kg from 90kg: (5 ÷ 90) × 100 = 5.56% body weight lost.
Quick Reference: Common Percentages as Fractions & Decimals
Memorise a few of these and you'll be able to do most percentage calculations in your head.
| Percentage | Fraction | Decimal | Mental maths trick |
|---|---|---|---|
| 1% | 1/100 | 0.01 | Divide by 100 (move decimal 2 left) |
| 5% | 1/20 | 0.05 | Half of 10% |
| 10% | 1/10 | 0.10 | Divide by 10 (move decimal 1 left) |
| 12.5% | 1/8 | 0.125 | Divide by 8 |
| 20% | 1/5 | 0.20 | Divide by 5, or 10% × 2 |
| 25% | 1/4 | 0.25 | Divide by 4, or halve twice |
| 33.3% | 1/3 | 0.333… | Divide by 3 |
| 50% | 1/2 | 0.50 | Divide by 2 (halve it) |
| 75% | 3/4 | 0.75 | Three-quarters — subtract 25% from 100% |
| 100% | 1/1 | 1.00 | The whole amount |
| 150% | 3/2 | 1.50 | One and a half times the value |
| 200% | 2/1 | 2.00 | Double the value |
Percentage Calculator FAQ
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This calculator and its explanations are maintained by The Online Calculator editorial team. All formulas follow standard mathematical conventions. Last reviewed: April 2026. Found an error? Let us know.