Calculate percentages with step-by-step explanations. Choose Learn Mode for interactive quizzes or Quick Mode for instant answers. Perfect for homework, exams, shopping discounts, tips, and more.
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What is X% of Y?
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A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred”. Percentages are everywhere in everyday life — from exam scores and shopping discounts to interest rates and statistics.
25% means 25 out of 100, or 25/100, or 0.25 as a decimal. To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100.
Percentages let you compare quantities on a common scale. “80 out of 120” is harder to compare with “45 out of 60” — but 66.7% vs 75% is immediately clear.
50% = half, 25% = quarter, 10% = tenth, 33.3% = third, 75% = three-quarters. Memorising these makes mental maths much faster.
Everything you need for percentage calculations, from simple “what is X% of Y?” to reverse percentages and step-by-step learning.
Find percentage of a number, what percentage X is of Y, percentage change, increase/decrease by percentage, and reverse percentage — all in one tool.
Interactive step-by-step quizzes that break each problem into multiple choice questions. Practice like a game — perfect for exam revision.
Every calculation shows detailed workings with LaTeX-rendered formulas, explanations at each step, and the final boxed answer.
Built-in formula reference, fraction/decimal/percentage conversion table, mental maths shortcuts, and real-world application examples.
Calculation history persists across sessions (saved locally). Copy questions, answers, or share links with one click.
Pre-loaded examples for each calculation type. Click any example to instantly load it and see how the calculator works.
The six core percentage formulas you need to know. Each formula is used by a different mode in the calculator above.
(X ÷ 100) × Y
Y × (X/100)
Example: 15% of 200 = 0.15 × 200 = 30
(X ÷ Y) × 100
(Part ÷ Whole) × 100
Example: 30 is what % of 200? = 15%
((New − Old) ÷ Old) × 100
Change ÷ Original × 100
Example: 80 → 100 = +25% increase
Value × (1 + X/100)
Multiplier = 1 + X/100
Example: 100 + 20% = 100 × 1.20 = 120
Value × (1 − X/100)
Multiplier = 1 − X/100
Example: 100 − 25% = 100 × 0.75 = 75
Result ÷ (X/100)
Result ÷ Multiplier
Example: 30 is 15% of what? = 200
Key equivalents you should memorise. These come up constantly in GCSE and everyday maths.
| Fraction | Decimal | Percentage | Quick Trick |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half — divide by 2 |
| 1/3 | 0.333... | 33.3% | Third — divide by 3 |
| 1/4 | 0.25 | 25% | Quarter — divide by 4 |
| 1/5 | 0.2 | 20% | Fifth — divide by 5 |
| 1/8 | 0.125 | 12.5% | Eighth — half of a quarter |
| 1/10 | 0.1 | 10% | Tenth — divide by 10 |
| 2/3 | 0.666... | 66.7% | Two thirds |
| 3/4 | 0.75 | 75% | Three quarters — ÷4, ×3 |
| 4/5 | 0.8 | 80% | Four fifths — ÷5, ×4 |
| 7/8 | 0.875 | 87.5% | 100% − 12.5% |
Divide the fraction, then multiply by 100
3/4 = 0.75 × 100 = 75%
Divide by 100 (move decimal 2 left)
45% = 45 ÷ 100 = 0.45
Multiply by 100 (move decimal 2 right)
0.35 = 0.35 × 100 = 35%
Percentage change is one of the most tested topics at GCSE. Here are the key concepts and common pitfalls.
% Change = ((New − Old) ÷ Old) × 100
Always divide by the original (old) value. Positive result = increase, negative = decrease.
20% increase → multiply by 1.20
15% decrease → multiply by 0.85
7.5% increase → multiply by 1.075
33% decrease → multiply by 0.67
A 50% increase followed by a 50% decrease does NOT return to the original value!
100 → +50% → 150 → −50% → 75 (not 100)
The decrease uses the new (larger) value as its base.
For multiple percentage changes, multiply the multipliers together:
+10% then +20% = 1.10 × 1.20 = 1.32 (32% total increase)
Not 30% — the second increase applies to the already-increased value.
Percentages are used everywhere. Here are the most common real-world scenarios.
30% off £80: £80 × 0.70 = £56. Use "Decrease by %" in the calculator.
Use: Decrease by %Add VAT: price × 1.20. Remove VAT (reverse): price ÷ 1.20. £120 inc. VAT = £100 before VAT.
Use: Increase / Reverse %15% tip on £45 bill: £45 × 0.15 = £6.75. Total = £51.75. Split between 2: £25.88 each.
Use: Find %3% pay rise on £28,000: £28,000 × 1.03 = £28,840. That is an extra £840 per year.
Use: Increase by %72 out of 90: (72 ÷ 90) × 100 = 80%. Grade boundaries are set as percentages.
Use: What % of?Was £250, now £199. Change: ((199−250) ÷ 250) × 100 = −20.4% decrease.
Use: % ChangeThese shortcuts help you estimate percentages quickly without a calculator — useful for exams and everyday life.
X% of Y = Y% of X
8% of 25 = 25% of 8 = 2
4% of 75 = 75% of 4 = 3
If one way is hard, flip it around! This works because multiplication is commutative.
Break complex percentages into simple ones and add/subtract:
15% = 10% + 5%
35% = 25% + 10%
17.5% = 10% + 5% + 2.5%
90% = 100% − 10%
Percentage questions appear on every GCSE maths paper. Here are the key topics and how to tackle them.
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 15% of 200: divide 15 by 100 to get 0.15, then 0.15 × 200 = 30.
Subtract the old value from the new, divide by the old value, multiply by 100. Always divide by the ORIGINAL value. Positive = increase, negative = decrease.
Finding the original number when you know the result and the percentage. If the sale price is £60 after a 20% discount, divide by 0.80 to find the original price: £75.
Use "Decrease by %" — multiply the price by (1 − discount/100). For 30% off £80: £80 × 0.70 = £56. The multiplier for 30% off is 0.70.
UK VAT is 20%. Add VAT: multiply by 1.20. Remove VAT: divide by 1.20. For example, £120 with VAT ÷ 1.20 = £100 before VAT.
Because the decrease applies to the larger (increased) value. 100 + 50% = 150. Then 150 − 50% = 75, not 100. The base changes between operations.
Converting percentage changes into a single multiplication. 20% increase → ×1.20, 15% decrease → ×0.85. For successive changes, multiply multipliers: ×1.10 × ×1.20 = ×1.32.
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 = 37.5%. Or multiply the fraction by 100: (3/8) × 100 = 37.5%.
10% = ÷10, 5% = half of 10%, 1% = ÷100, 25% = ÷4. Combine: 15% = 10% + 5%. The flip trick: X% of Y = Y% of X (e.g., 8% of 25 = 25% of 8 = 2).
For compound changes (like compound interest), use the increase/decrease calculator multiple times, or calculate the compound multiplier: e.g., 5% for 3 years = 1.05³ = 1.1576 (15.76% total).
Yes! It covers all GCSE percentage topics including the multiplier method, reverse percentages, and successive changes. Learn Mode provides gamified step-by-step practice with multiple choice questions.
A negative percentage change means a decrease. For example, −25% means the value went down by a quarter. In "percentage change" mode, negative indicates the new value is smaller than the old.
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