Percentage Calculator
Quickly calculate X% of Y, what percentage one number is of another, or the percentage change between two values.
Examples: 200 × 15 % = 30. 500 + 10 % = 550. 200 − 10 % = 180.
Or use the standard form below
What is a percentage calculator?
A percentage calculator solves the three everyday percent problems in one place: what is X% of a number, what percent one number is of another, and the percentage change between two values. Pick the type of problem in the form, enter X and Y, and the Result appears with a sentence underneath that restates the working. The desk-calculator keypad at the top of the page handles quick sums with a % key.
"Percent" means "per hundred": the % sign stands for the number 0.01, so 25% is 25 × 0.01 = 0.25, or 25⁄100. That single idea is behind every sales-tax total, restaurant tip, store discount, test score, pay raise and investment return you will calculate.
The three types of percentage problem
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 15% of $80 = 0.15 × 80 = $12 |
| X is what percent of Y? | (X ÷ Y) × 100 | 42 out of 50 = 42 ÷ 50 × 100 = 84% |
| Percent change from X to Y | ((Y − X) ÷ |X|) × 100 | $52,000 to $55,640 = 3,640 ÷ 52,000 × 100 = +7% |
Most confusion comes from picking the wrong denominator. In "X is what percent of Y", divide by the whole (Y). In percent change, divide by the original value (X), never the new one.
Fractions, decimals and percentages that are worth memorizing
| Fraction | Decimal | Percent | Fraction | Decimal | Percent |
|---|---|---|---|---|---|
| 1⁄100 | 0.01 | 1% | 1⁄3 | 0.333… | 33.3% |
| 1⁄20 | 0.05 | 5% | 2⁄5 | 0.4 | 40% |
| 1⁄10 | 0.1 | 10% | 1⁄2 | 0.5 | 50% |
| 1⁄8 | 0.125 | 12.5% | 3⁄5 | 0.6 | 60% |
| 1⁄6 | 0.1667 | 16.7% | 2⁄3 | 0.667 | 66.7% |
| 1⁄5 | 0.2 | 20% | 3⁄4 | 0.75 | 75% |
| 1⁄4 | 0.25 | 25% | 7⁄8 | 0.875 | 87.5% |
To convert any fraction to a percent, divide top by bottom and multiply by 100. To convert a percent to a decimal, move the decimal point two places left (8.25% → 0.0825). Our fraction calculator handles the awkward ones.
Percentage points vs. percent
If a savings rate rises from 4% to 6%, it has risen by 2 percentage points — but by 50 percent (2 ÷ 4 × 100; the calculator's change mode gives "Change from 4 to 6 is 50.00%"). A "50% increase in the rate" and "a 2-point increase in the rate" describe the same change; "the rate rose 2%" is ambiguous. Use points when comparing two percentages directly.
Why a 20% drop and a 20% rise do not cancel out
Percent changes are always relative to the value at that moment. A $100 stock that falls 20% is worth $80; rising 20% from $80 adds only $16, leaving $96. The same asymmetry means a 50% loss needs a 100% gain to recover. When you chain percentage changes, multiply the factors: $100 × 0.80 × 1.20 = $96 — do not add the percentages.
Percent error and percent difference
Two related formulas come up in science and statistics classes. Percent error compares a measurement with a known true value: |measured − true| ÷ true × 100. If you measure a value as 98.6 when the true value is 100, the error is 1.4 ÷ 100 × 100 = 1.4%. Percent difference compares two values when neither is "correct", using their average as the base: |A − B| ÷ ((A + B) ÷ 2) × 100. For 48 and 52 that is 4 ÷ 50 × 100 = 8%. Use percent change (this calculator's third mode) only when one value is clearly the "before" and the other the "after".
Reverse percentages: finding the original number
If a jacket costs $45 after a 25% discount, the sale price is 75% of the original, so the original was $45 ÷ 0.75 = $60. In general, original = final ÷ (1 ± rate). This is the calculation for backing sales tax out of a receipt total, working out pre-raise salary, or finding a price before a markup — see our sales tax calculator for the tax version.
Formula
- X% of Y = (X ÷ 100) × Y
- X as a percentage of Y = (X ÷ Y) × 100
- Percentage change = ((new − old) ÷ |old|) × 100 — positive is an increase, negative a decrease
- Increase Y by X% = Y × (1 + X ÷ 100)
- Decrease Y by X% = Y × (1 − X ÷ 100)
- Original value before an X% change = final ÷ (1 ± X ÷ 100)
The calculator's three modes cover the first three lines; the last three are the same formulas rearranged, and the worked examples below show each in use.
|old| is the size of the old value without its sign. It only matters for a negative start: −50 to −25 is a rise, and the calculator shows "Change from -50 to -25 is 50.00%" rather than −50%.
Two cases have no answer: a change from 0 shows "Undefined — cannot compute % change from 0" (0 to 0 shows "No change (both values are 0)"), and "X is what % of 0" shows "Undefined — cannot work out a percentage of 0".
Worked example
What is 25% of 200?
(25 ÷ 100) × 200 = 0.25 × 200 = 50. The calculator shows "25% of 200 = 50".
30 is what percentage of 150?
(30 ÷ 150) × 100 = 0.2 × 100 = 20% — "30 is 20.00% of 150".
A stock rises from $80 to $100 — what is the percent change?
((100 − 80) ÷ 80) × 100 = 20 ÷ 80 × 100 = +25% — "Change from 80 to 100 is 25.00%". Falling back from $100 to $80 is a −20% change, not −25%, because the base is now $100: "Change from 100 to 80 is -20.00%".
Everyday examples
| Situation | Calculation | Answer |
|---|---|---|
| 20% tip on a $64.50 check | 0.20 × 64.50 | $12.90 (total $77.40) |
| 8.25% sales tax on $129.99 | 0.0825 × 129.99 | $10.72 tax; $140.71 total |
| 30% off $89.99 | 89.99 × 0.70 | $62.99 (you save $27.00) |
| Test score of 42 out of 50 | 42 ÷ 50 × 100 | 84% |
| Raise from $52,000 to $55,640 | 3,640 ÷ 52,000 × 100 | 7% increase |
| 3 defective items in a batch of 12 | 3 ÷ 12 × 100 | 25% |
| $250 down on a $2,000 purchase | 250 ÷ 2,000 × 100 | 12.5% |
| Jacket is $45 after 25% off — original price? | 45 ÷ 0.75 | $60 |
How to use this calculator
- Choose the type of problem: "What is X% of Y?", "X is what % of Y?", or "% change from X to Y".
- Enter X and Y. Their meaning follows the mode — in percent-change mode X is the old value and Y the new one.
- Read the result and the sentence beneath it, which restates the calculation in words so you can check you picked the right mode.
Percentages can legitimately be negative (a decrease) or above 100% (more than double), so the calculator does not limit them.
On the keypad, % after + or − takes that percent of the first number (500 + 10 % = gives 550, 200 − 10 % = gives 180). After × or ÷ it turns the number into a decimal: 200 × 15 % shows 0.15, and pressing = gives 30.
What this calculator does not do
- No modes for percentage points, percent error, percent difference or reverse percentages; use the formulas above.
- No answer for a change from 0 to any other number, or for a percentage of 0 — both are undefined.
- The Result shows two decimals; the "X% of Y" sentence keeps up to 12 significant digits ("7% of 300 = 21"), the other sentences two decimals.
Mental-math shortcuts
- 10%: move the decimal point one place left. 10% of $64.50 is $6.45.
- 5%: half of 10%. 15%: 10% plus 5% ($6.45 + $3.225 = $9.675, or $9.68). 20%: double 10%.
- 25%: divide by 4. 50%: halve. 33⅓%: divide by 3.
- 1%: move the decimal two places, then multiply for any odd percentage (7% of 300: 1% is 3, so 21).
- Swap the numbers: X% of Y equals Y% of X. 8% of 50 feels hard; 50% of 8 is obviously 4.
Common mistakes
- Averaging percentages. If one class of 20 students scores 90% and another of 80 students scores 70%, the overall average is not 80% — it is (18 + 56) ÷ 100 = 74%. Weight by the group sizes.
- Adding successive discounts. "30% off, then an extra 20% off" is not 50% off. 0.70 × 0.80 = 0.56, so it is 44% off.
- Dividing by the new value. Percent change always uses the starting value as the base.
- Confusing percent with percentile. Scoring 90% means you got 90 of 100 marks; scoring in the 90th percentile means you scored higher than 90% of test-takers.
Related tools
- Tip calculator — tip and split a restaurant bill
- Test score calculator — marks to percentage and letter grade
- Percent change vs percentage points
- How to calculate percentages in your head
Sources
- NIST — Guide to the SI, Chapter 7: Rules and Style Conventions for Expressing Values of Quantities (section 7.10.2, the percent symbol)
- U.S. Bureau of Labor Statistics — Math calculations to better utilize CPI data (percent change and index-point change)
Frequently asked questions
How do I calculate a percentage of a number?
Convert the percent to a decimal by dividing by 100, then multiply. 15% of 80 is 0.15 × 80 = 12. For quick mental estimates, find 10% by moving the decimal point one place left, then scale: 15% is 10% plus half of 10%.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. If you scored 42 out of 50, that is 42 ÷ 50 × 100 = 84%. The number after "of" is the whole — it always goes on the bottom, so it cannot be 0.
How do I calculate percent increase or decrease?
Subtract the old value from the new value, divide by the old value, and multiply by 100. A price going from $80 to $100 is (100 − 80) ÷ 80 × 100 = +25%. A negative result is a decrease. Always divide by the original value, not the new one; if the original is negative, divide by its size, so −50 to −25 is +50%.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. 7⁄8 = 0.875 = 87.5%. Going the other way, write the percent over 100 and simplify: 40% = 40⁄100 = 2⁄5.
What is the difference between percentage and percentage points?
Percentage points measure the simple difference between two percentages; percent measures the relative change. If interest rises from 4% to 6%, that is an increase of 2 percentage points but a 50% increase (2 ÷ 4). Use "points" whenever you compare two rates directly.
Can a percentage be greater than 100?
Yes. A percentage over 100 means more than the whole, or more than double when it is a change: a store that sold 60 units last month and 150 this month grew 150%, and 150 is 250% of 60. Percentages above 100 are common for growth rates and returns; for a share of a whole, such as the part of a pie, they cannot occur.
How do I calculate a discount?
Multiply the price by the discount percent to get the saving, then subtract — or multiply the price by (1 − discount) to go straight to the sale price. 30% off $89.99 is $89.99 × 0.70 = $62.99. Two stacked discounts multiply rather than add: 30% off then 20% off is 0.70 × 0.80 = 0.56, or 44% off in total.
How do I find the original price before a percentage was added or taken off?
Divide by (1 ± rate). If a total of $140.71 includes 8.25% sales tax, the pre-tax price is 140.71 ÷ 1.0825 = $129.99. If $45 is the price after 25% off, the original was 45 ÷ 0.75 = $60. Dividing by the rate itself, or subtracting the percent of the final price, gives the wrong answer.