Percentage Calculator
Percent of a number, percent change and 'X is what % of Y'.
Reviewed by the Calculation Machine team · Updated 24 October 2026 · How we check our maths
Your values
ⓘ Live results
- 45% of 180
- 81
- 45 is what % of 180?
- 25%
- Change from 45 to 180
- 300%
- 45 increased by 180%
- 126
- 45 decreased by 180%
- -36
Working
- 145% of 180 = 45 ÷ 100 × 180 = 81
Quick answer
To find a percentage of a number, divide the percentage by 100 and multiply by the number: X% of Y = X ÷ 100 × Y. To find what percent X is of Y, divide X by Y and multiply by 100. For example, 15% of 240 is 0.15 × 240 = 36, and 15 is 6.25% of 240.
What the Percentage calculator does
Type in two numbers and this calculator answers the five percentage questions people ask most often, all at once: X% of Y, what percent X is of Y, the percent change from X to Y, X increased by Y%, and X decreased by Y%. Pick the row that matches the wording of your problem.
The order of the numbers matters. "15% of 240" and "240% of 15" happen to give the same answer (36), but "15 is what percent of 240" (6.25%) and "240 is what percent of 15" (1,600%) do not. Put the percentage or the starting value in the first box.
For shopping and money questions, the dedicated discount calculator, sales tax calculator and tip calculator handle the extra steps such as stacking discounts or splitting a bill.
The formula
X% of Y = X ÷ 100 × Y X as % of Y = X ÷ Y × 100 % change from X to Y = (Y − X) ÷ |X| × 100 X increased by Y% = X × (1 + Y ÷ 100) X decreased by Y% = X × (1 − Y ÷ 100)
| Symbol | Meaning | Unit |
|---|---|---|
| X | First number: the percentage, the part, or the starting value depending on the question | any |
| Y | Second number: the whole, the new value, or the percentage to add or remove | any |
| 100 | Converts between a fraction and a percentage (per cent = per hundred) | — |
These are the standard definitions taught in school arithmetic: a percent is a ratio expressed per hundred. Percent change divides by the starting value, so it is undefined when X is 0. For a change between two values that are already percentages (5% to 7%), report the difference in percentage points (2 points) as well as the relative change (40%).
Worked examples
Tip or commission on a bill
You want 15% of a $240 restaurant bill.
Inputs
- First number15
- Second number240
Result
- 15% of 24036
- 15 is what % of 240?6.25%
- Change from 15 to 2401500%
- 15 increased by 240%51
- 15 decreased by 240%-21
15% of 240 is 36, so the tip is $36. A quick mental check: 10% is $24 and 5% is half that, $12.
Price drop as a percent
A jacket was $80 and is now $64. You want the percentage discount.
Inputs
- First number80
- Second number64
Result
- 80% of 6451.2
- 80 is what % of 64?125%
- Change from 80 to 64-20%
- 80 increased by 64%131.2
- 80 decreased by 64%28.8
Read the "Change from 80 to 64" row: −20%, a 20% markdown. Note that 80 is 125% of 64, so going back up from $64 to $80 is a 25% increase, not 20%.
Small rate on a large amount
A 7.5% fee on a $1,200 invoice.
Inputs
- First number7.5
- Second number1200
Result
- 7.5% of 120090
- 7.5 is what % of 1200?0.625%
- Change from 7.5 to 120015900%
- 7.5 increased by 1200%97.5
- 7.5 decreased by 1200%-82.5
The fee is $90. Decimals work in either box, so rates such as 7.5% or 0.25% need no rounding.
Which row answers your question
Match the words in your problem to the row:
| If the question says… | Use | Example with 20 and 50 |
|---|---|---|
| "What is 20% of 50?" | X ÷ 100 × Y | 10 |
| "20 is what percent of 50?" | X ÷ Y × 100 | 40% |
| "Percent increase from 20 to 50" | (Y − X) ÷ X × 100 | 150% |
| "Add 50% to 20" | X × (1 + Y ÷ 100) | 30 |
| "Take 50% off 20" | X × (1 − Y ÷ 100) | 10 |
Mistakes that give the wrong percentage
- Dividing by the wrong base. Percent change always divides by the old value. From 50 to 40 is a 20% fall; from 40 to 50 is a 25% rise.
- Adding percentages in sequence. A 10% rise followed by a 10% cut leaves you at 99% of where you started, not 100%. Multiply the factors: 1.10 × 0.90 = 0.99.
- Reversing a markup. To remove 20% VAT from a gross price, divide by 1.20; subtracting 20% of the gross price takes off too much. The VAT calculator does this for you.
- Mixing up points and percent. An interest rate moving from 4% to 5% is up 1 percentage point, or 25% in relative terms.
Mental shortcuts
- 10%: move the decimal point one place left (10% of 340 = 34).
- 5%: half of 10%. 1%: move the decimal two places.
- Swap trick: X% of Y equals Y% of X, so 8% of 50 is the same as 50% of 8, which is 4.
- Fractions: 25% = ¼, 33⅓% = ⅓, 12.5% = ⅛. A fraction to decimal converter helps with less familiar ones.
How to use the Percentage Calculator
- 1Enter the percentage or the starting value as the first number.
- 2Enter the whole amount, the new value or the percentage to apply as the second number.
- 3Find the row whose wording matches your question and read the answer; the working line shows the arithmetic.
- 4For a fall in value, read the change row – a negative figure means a decrease.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. 30% of 90 is 0.30 × 90 = 27.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. 18 out of 24 is 18 ÷ 24 × 100 = 75%.
How do I calculate percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 40 to 52 is 12 ÷ 40 × 100 = 30%. The percentage change calculator also shows the difference and the reverse change.
Can a percentage be more than 100?
Yes. 150% of 20 is 30, and a value that triples has risen by 200%. Only shares of a fixed whole, such as a test score, are capped at 100%.
What does a negative result mean?
In the change row it means the second number is smaller than the first. In the "decreased by" row it means you removed more than 100%, which only makes sense for things like profit that can go below zero.
References
- Ratios and Proportional Relationships (Grades 6–7) — Common Core State Standards Initiative
- Guide for the Use of the International System of Units (SI), Special Publication 811 — National Institute of Standards and Technology
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Last reviewed: October 24, 2026
- Report an error