How to calculate percentages
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". This page brings every common percentage calculation together in one place: finding a percentage of a number, working out what percent one number is of another, percentage increase and decrease, and discounts. Each calculator shows the answer instantly, and you can open a full step-by-step solution for any result. Everything runs in your browser, so nothing is uploaded.
How Percentage works
What is a percentage?
A percentage tells you how many parts you have out of 100. The symbol is %. So 10% means 10 per hundred, which is the same as the fraction 10/100, the decimal 0.10, or "ten hundredths". To turn any percentage into a decimal you divide by 100 (25% → 0.25); to turn a decimal into a percentage you multiply by 100 (0.25 → 25%).
Two related symbols you may meet: ‰ means per mille (per thousand) and ‱ means a basis point (per ten thousand), both used in finance for very small rates.
1. What is X% of Y? (a percentage of a number)
Formula: value = (P ÷ 100) × Y. "Percent" means divide by 100, and "of" means multiply.
Worked example — 20% of 300:
- Convert the percent to a decimal: 20 ÷ 100 = 0.20.
- Multiply by the number: 0.20 × 300 = 60.
- So 20% of 300 is 60.
Mental-maths shortcuts: 10% of any number is just that number with the decimal point moved one place left (10% of 300 = 30). 1% moves it two places (1% of 300 = 3). Build other percentages from these — 20% = two lots of 10%, 5% = half of 10%, 15% = 10% + 5%.
2. X is what percent of Y? (turning a value into a percentage)
Formula: percent = (X ÷ Y) × 100. Divide the part by the whole, then multiply by 100.
Worked example — 80 is what percent of 200:
- Divide the part by the whole: 80 ÷ 200 = 0.40.
- Multiply by 100 to make it a percentage: 0.40 × 100 = 40%.
- So 80 is 40% of 200.
3. Percentage increase and decrease
Formula: change = ((New − Old) ÷ Old) × 100. A positive result is an increase; a negative result is a decrease.
Example A — a price rises from 0 to 0: (240 − 200) ÷ 200 × 100 = 40 ÷ 200 × 100 = +20% (a 20% increase).
Example B — a price falls from 0 to 0: (180 − 200) ÷ 200 × 100 = −20 ÷ 200 × 100 = −10% (a 10% decrease — the minus sign shows it went down).
The key is that the change is always measured relative to the original (old) value, not the new one.
4. Percentage discount (X% off Y)
Formula: final price = Y − (P ÷ 100 × Y). First find the discount amount, then subtract it.
Worked example — 20% off ,410: discount = 0.20 × 9,410 = 1,882; final price = 9,410 − 1,882 = ,528 (you save ,882).
Common percentages, fractions and decimals
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.10 |
| 20% | 1/5 | 0.20 |
| 25% | 1/4 | 0.25 |
| 33.33% | 1/3 | 0.3333 |
| 50% | 1/2 | 0.50 |
| 75% | 3/4 | 0.75 |
| 100% | 1/1 | 1.00 |
Where percentages are used every day
Percentages turn up constantly: shop discounts and sale prices, sales tax and VAT, tips at a restaurant, loan and savings interest, inflation, exam scores and grades, commission, and comparing data or statistics. Being able to work them out quickly helps with budgeting, shopping and any kind of financial decision.
Examples
| Input | Result |
|---|---|
20% of 250 | 50 |
15% of 80 | 12 |
7.5% of 1200 | 90 |
Common uses
- Find a percentage of a number (X% of Y)
- Work out what percent one number is of another
- Calculate a percentage increase or decrease
- Work out a sale price or discount
- Add or subtract a percentage from a value
- Check tax, tip or interest amounts
- Convert between percentages, fractions and decimals
- See a full step-by-step solution for any calculation