To calculate a percentage, divide the part by the whole and multiply by 100: 42 out of 50 is 42 ÷ 50 × 100 = 84%. To find a percentage of a number, turn the percent into a decimal and multiply: 15% of 240 = 0.15 × 240 = 36. For percentage change, subtract the old value from the new one, divide by the old value and multiply by 100.
Every percentage problem is a version of one relationship, so once you can spot which number is the part, which is the whole and which is the percent, the rest is arithmetic. This guide walks through each type with real numbers, then covers the mistakes that trip people up on exams, price tags and payslips. If you just want the answer, the Percentage Calculator handles all six question types and shows the result instantly.
The one formula behind every percentage question
“Percent” means “per hundred”, so 25% is 25/100, or 0.25. Everything follows from:
Part = Percent ÷ 100 × Whole
Rearrange it depending on which number you are missing:
| You want to find | Formula | Example |
|---|---|---|
| The part (X% of Y) | Percent ÷ 100 × Whole | 15% of 240 = 0.15 × 240 = 36 |
| The percent (X is what % of Y) | Part ÷ Whole × 100 | 36 ÷ 240 × 100 = 15% |
| The whole (Y is X% of what) | Part ÷ (Percent ÷ 100) | 36 ÷ 0.15 = 240 |
| Percentage change | (New − Old) ÷ Old × 100 | 240 → 276 = 36 ÷ 240 × 100 = +15% |
A quick way to identify the whole: it usually follows the word “of” (“15% of 240”, “what percent of the class”), and in change questions it is always the starting value.
How to find a percentage of a number
Convert the percent to a decimal by dividing by 100 (move the decimal point two places left), then multiply.
- 15% → 15 ÷ 100 = 0.15
- 0.15 × 240 = 36
Worked example (tipping in the US or Canada): a 20% tip on a $65 restaurant bill is 0.20 × 65 = $13. An 18% tip is 0.18 × 65 = $11.70.
Mental math shortcuts
- 10%: move the decimal one place left. 10% of 240 = 24.
- 5%: half of 10%. 5% of 240 = 12, so 15% = 24 + 12 = 36.
- 1%: move the decimal two places left. 1% of 240 = 2.4, so 3% = 7.2.
- 25%, 50%, 75%: divide by 4, by 2, or take three quarters.
- The swap trick: X% of Y always equals Y% of X. 8% of 50 is hard; 50% of 8 is obviously 4.
How to work out what percentage one number is of another
Divide the part by the whole, then multiply by 100.
Worked example (test score): you scored 42 out of 50. 42 ÷ 50 = 0.84, and 0.84 × 100 = 84%.
Worked example (budget share): rent is $1,450 of a $4,200 monthly take-home pay. 1,450 ÷ 4,200 = 0.3452, so rent takes 34.5% of income.
If you are averaging several assignments with different weights, a simple part-over-whole calculation is not enough; the Grade Percentage Calculator handles weighted marks.
How to calculate percentage increase and decrease
Percentage change = (New value − Old value) ÷ Old value × 100
A positive answer is an increase; a negative answer is a decrease.
Worked example (pay rise): a salary rises from $52,000 to $55,120.
- Difference: 55,120 − 52,000 = 3,120
- Divide by the old value: 3,120 ÷ 52,000 = 0.06
- Multiply by 100: 6% increase
Worked example (price drop): a jacket falls from £80 to £68.
- Difference: 68 − 80 = −12
- −12 ÷ 80 = −0.15
- 15% decrease
Always divide by the starting value. Going from 40 to 50 is a 25% increase (10 ÷ 40), but going from 50 back to 40 is only a 20% decrease (10 ÷ 50). Also note that percentage change from zero is undefined: you cannot divide by 0, so “sales went from 0 to 50” has no meaningful percentage increase.
How to increase or decrease a number by a percentage
The fastest method is the multiplier: 1 + (percent ÷ 100) for an increase, 1 − (percent ÷ 100) for a decrease.
- Increase 240 by 15%: 240 × 1.15 = 276
- 25% off an $84 item: 84 × 0.75 = $63
- Add 20% UK VAT to £80: 80 × 1.20 = £96
Sales taxes are where this comes up most, and the rates differ by country:
| Country | Tax | Typical rate (2026) | Example on a 100 price |
|---|---|---|---|
| US | State and local sales tax | Varies by state and city; added at checkout | 100 × 1.0825 = 108.25 at 8.25% |
| UK | VAT | 20% standard rate, included in shelf prices | 100 × 1.20 = 120 |
| Canada | GST or HST | 5% GST; 13–15% HST in harmonized provinces | 100 × 1.13 = 113 in Ontario |
| Australia | GST | 10%, included in shelf prices | 100 × 1.10 = 110 |
Rates and exemptions change, so confirm the current figure with the official source (IRS and your state revenue department, GOV.UK, Canada.ca or the ATO). For shopping maths, the Discount Calculator shows the saving and final price together.
Two increases in a row multiply rather than add. Two 10% raises give 1.10 × 1.10 = 1.21, a 21% total rise, not 20%.
Reverse percentages: finding the original number
When you know the number after a percentage was applied, divide by the multiplier. Do not subtract the percentage from the final figure.
Worked example (removing UK VAT): a price including 20% VAT is £96. The original price is 96 ÷ 1.20 = £80. The tempting wrong answer, 96 × 0.80 = £76.80, takes 20% off the wrong base.
Worked example (original price before a sale): you paid $63 after 25% off. 63 ÷ 0.75 = $84 before the discount.
Worked example (Australian GST): a $110 price includes 10% GST. Pre-GST price = 110 ÷ 1.10 = $100, so the GST is $10, which is the same as dividing the GST-inclusive price by 11.
This “Y is X% of what number?” question is a staple of GCSE maths in the UK and comes up constantly with tax-inclusive prices. For US receipts, the Sales Tax Reverse Calculator does the same job with state rates built in.
Percentage change vs percentage difference vs percentage points
These three are often confused, and they give different answers for the same pair of numbers.
| Measure | Use when | Formula | 40 and 50 |
|---|---|---|---|
| Percentage change | One value is clearly “before” and the other “after” | (New − Old) ÷ Old × 100 | +25% (40 → 50) or −20% (50 → 40) |
| Percentage difference | Comparing two values with no direction, e.g. two stores’ prices | |A − B| ÷ ((A + B) ÷ 2) × 100 | 10 ÷ 45 × 100 = 22.22% |
| Percentage points | Comparing two percentages | New % − Old % | 40% → 50% = 10 points |
Percentage points matter in news and finance. If a mortgage rate rises from 4% to 5%, it went up by 1 percentage point, but that is a 25% increase in the rate itself ((5 − 4) ÷ 4 × 100). Both statements are true; they answer different questions.
Converting fractions and decimals to percentages
Multiply a decimal by 100 to get a percent; for a fraction, divide the top by the bottom first. 3/8 = 3 ÷ 8 = 0.375 = 37.5%.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
The Fraction Calculator accepts fractions, mixed numbers like 1 1/2, and decimals, and every result comes with its decimal and percent equivalents.
Common percentage mistakes
- Using the wrong base. Percentage change is measured against the original value, not the new one.
- Assuming ups and downs cancel out. A 50% rise followed by a 50% fall leaves you below where you started: 100 → 150 → 75, a 25% loss overall.
- Adding successive percentages. Stacked discounts or raises multiply. “20% off, then a further 10% off” is 0.80 × 0.90 = 0.72, a 28% total discount, not 30%. The Discount Calculator has a stacked-discount field for exactly this.
- Reversing a percentage by subtracting it. To remove a 20% tax, divide by 1.20; do not multiply by 0.80.
- Mixing up percent and percentage points when comparing rates, polls or test pass rates.
FAQ
How do I calculate a percentage on a calculator?
Divide the part by the whole, then multiply by 100: for 42 out of 50, type 42 ÷ 50 × 100 = 84. The % key behaves differently between calculator models, so the divide-and-multiply method is the most reliable.
How do I calculate percentage increase in Excel or Google Sheets?
With the old value in A2 and the new value in B2, enter =(B2-A2)/A2 and format the cell as a percentage. Excel and Sheets multiply by 100 for you when the cell uses percent formatting.
What is 20% of 50?
- Convert 20% to 0.20 and multiply: 0.20 × 50 = 10. You can also take 10% (5) and double it.
Can a percentage increase be more than 100%?
Yes. Doubling a number is a 100% increase (30 → 60), and tripling it is a 200% increase (30 → 90). A decrease, however, cannot exceed 100% unless the value goes below zero.
How do you work out a percentage decrease?
Subtract the new value from the old value, divide by the old value and multiply by 100. A drop from 80 to 68 is 12 ÷ 80 × 100 = 15%.
What is the difference between percent and percentage points?
Percent describes a relative change; percentage points describe the simple gap between two percentages. A rate moving from 4% to 5% rises by 1 percentage point, which is a 25% relative increase.