Percentage Calculator
To find a percentage of a number, divide the percentage by 100 and multiply: 20% of 150 is 30 (20 ÷ 100 × 150). To find what percent one number is of another, divide and multiply by 100: 30 is 20% of 150. A change from 80 to 100 is a 25% increase, 150 increased by 20% is 180, and a price of 80 after 20% off was 100 before. Each calculator below shows the formula with your numbers.
Updated Runs in your browser: nothing you enter is uploadedHow this tool works
Exact decimal arithmetic, worked out in your browser. Commas, “$” and “%” are fine to type.
What is X% of Y?
30
20% of 150 = 20 ÷ 100 × 150 = 30
- As a decimal: 20% = 0.2, and 0.2 × 150 = 30.
- What is left: 150 − 30 = 120 (80%).
X is what percent of Y?
20%
30 ÷ 150 × 100 = 20%
- As a decimal: 30 ÷ 150 = 0.2.
- As a fraction: 30/150 = 1/5.
Percentage change from X to Y
25% increase
(100 − 80) ÷ 80 × 100 = 25%
- Up by 20, from 80 to 100.
- If 80 and 100 are themselves percentages (an interest rate, a vote share), the change is +20 percentage points: a 25% relative increase.
- Percentage difference (the gap compared with their average, 90, with no “from” and “to”): ≈ 22.2222%.
Increase or decrease a number by a percentage
180
150 × (1 + 20 ÷ 100) = 150 × 1.2 = 180
- That adds 30 (20% of 150).
- Shortcut: multiply by 1.2 to add 20%.
Reverse percentage: find the original number
100
80 ÷ (1 − 20 ÷ 100) = 80 ÷ 0.8 = 100
- Check: 100 − 20% of 100 = 80.
- Not 80 + 20% = 96: the 20% was worked out on the original, not on 80.
Percent, decimal and fraction
| Percent | Decimal | Fraction | Of 80 |
|---|---|---|---|
| 1% | 0.01 | 1/100 | 0.80 |
| 5% | 0.05 | 1/20 | 4.00 |
| 10% | 0.1 | 1/10 | 8.00 |
| 12.5% | 0.125 | 1/8 | 10.00 |
| 20% | 0.2 | 1/5 | 16.00 |
| 25% | 0.25 | 1/4 | 20.00 |
| ≈ 33.3333% | 0.333333 | about 1/3 | ≈ 26.67 |
| 50% | 0.5 | 1/2 | 40.00 |
| ≈ 66.6667% | 0.666667 | about 2/3 | ≈ 53.33 |
| 75% | 0.75 | 3/4 | 60.00 |
| 100% | 1 | 1 | 80.00 |
| 150% | 1.5 | 3/2 | 120.00 |
The increase that undoes a decrease
| After a decrease of | You need an increase of | 100 becomes | and back to 100 with |
|---|---|---|---|
| 5% | ≈ 5.26% | 95 | +5 |
| 10% | ≈ 11.11% | 90 | +10 |
| 15% | ≈ 17.65% | 85 | +15 |
| 20% | 25.00% | 80 | +20 |
| 25% | ≈ 33.33% | 75 | +25 |
| 30% | ≈ 42.86% | 70 | +30 |
| 40% | ≈ 66.67% | 60 | +40 |
| 50% | 100.00% | 50 | +50 |
| 75% | 300.00% | 25 | +75 |
| 90% | 900.00% | 10 | +90 |
Common discounts on common prices
| Price | 10% off | 15% off | 20% off | 25% off | 30% off | 50% off |
|---|---|---|---|---|---|---|
| $10 | $9.00 | $8.50 | $8.00 | $7.50 | $7.00 | $5.00 |
| $19.99 | $17.99 | $16.99 | $15.99 | $14.99 | $13.99 | $10.00 |
| $25 | $22.50 | $21.25 | $20.00 | $18.75 | $17.50 | $12.50 |
| $49.99 | $44.99 | $42.49 | $39.99 | $37.49 | $34.99 | $25.00 |
| $80 | $72.00 | $68.00 | $64.00 | $60.00 | $56.00 | $40.00 |
| $99.99 | $89.99 | $84.99 | $79.99 | $74.99 | $69.99 | $50.00 |
| $250 | $225.00 | $212.50 | $200.00 | $187.50 | $175.00 | $125.00 |
How to calculate percentages by hand
- A percentage of a number. Divide the percentage by 100 and multiply by the number: 15% of 60 is 15 ÷ 100 × 60 = 9.
- What percent one number is of another. Divide the part by the whole and multiply by 100: 9 out of 60 is 9 ÷ 60 × 100 = 15%.
- The percentage change. Subtract the old value from the new one, divide by the old value and multiply by 100: from 60 to 69 is (69 − 60) ÷ 60 × 100 = 15%.
- Add or take off a percentage. Multiply by 1 plus or minus the percentage as a decimal: 60 plus 15% is 60 × 1.15 = 69; 60 minus 15% is 60 × 0.85 = 51.
- Work back to the original. Divide by that same multiplier: 51 after 15% off was 51 ÷ 0.85 = 60. Adding 15% to 51 gives 58.65, which is wrong.
Frequently asked questions
- How do I calculate a percentage of a number?
- Divide the percentage by 100 and multiply by the number. 20% of 150 is 20 ÷ 100 × 150 = 30. Another way to see it: 20% is 0.2, so multiply 150 by 0.2.
- How do I work out the original price before a discount?
- Divide the sale price by 1 minus the discount as a decimal. If a price is 80 after 20% off, the original was 80 ÷ 0.8 = 100. Adding 20% to 80 gives 96, which is wrong, because the 20% was taken from the original price, not from the sale price. The same goes for tax: a total of 107 with 7% tax is 107 ÷ 1.07 = 100.00 before tax.
- What is the difference between percent and percentage points?
- Percentage points are the plain difference between two percentages; percent is the change relative to where you started. If an interest rate goes from 4% to 5%, it rose by 1 percentage point, which is a 25% increase in the rate. News reports mix these up often. The percentage change calculator shows both.
- Why does a 50% drop need a 100% rise to recover?
- Because each percentage is worked out on a different number. 100 falls by 50% to 50; getting back to 100 means adding 50, which is 100% of 50. The table above lists the rise that undoes each fall.
- What is the difference between percentage change and percentage difference?
- Percentage change has a direction: it compares the new value with the old one, so 80 to 100 is a 25% increase and 100 to 80 is a 20% decrease. Percentage difference compares two values with no “before” and “after” by dividing the gap by their average: 80 and 100 differ by 20 ÷ 90 × 100 ≈ 22.22% either way.
- Why does this calculator not show 0.30000000000000004?
- Most software stores numbers in binary floating point, which cannot hold 0.1 exactly, so sums like 0.1 + 0.2 come out as 0.30000000000000004. This calculator works with exact decimal fractions instead, and only rounds the final answer for display. When an answer is rounded, it is marked with ≈; choose the decimal places you want, or leave it on Auto.
- Can a percentage be more than 100%?
- Yes. 150% of 40 is 60, and a price that goes from 20 to 50 rose by 150%. What cannot happen is a decrease of more than 100% of a positive amount without going below zero, so the reverse calculator refuses a discount of 100% or more.
How it works
Every number you type is read as an exact decimal fraction (numerator and denominator as whole numbers of any size), so the arithmetic never picks up floating-point errors. The formulas are the standard ones: X% of Y = X ÷ 100 × Y; X as a percent of Y = X ÷ Y × 100; the change from A to B = (B − A) ÷ |A| × 100, measured against the size of A when A is negative; Y increased or decreased by X% = Y × (1 ± X ÷ 100); and the original before a change = the result ÷ (1 ± X ÷ 100). Percentage difference divides the gap by the average of two positive values. Only the final answer is rounded, halves away from zero; on Auto it is shown in full when it has at most six decimals, and otherwise to four, marked ≈. Thousands commas, a leading currency sign and a trailing % sign are accepted and ignored. Everything runs in your browser.
Sources
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