Free Percentage Calculator

Pick a formula, enter two numbers and see the answer with the working shown. Covers percent of a number, percent change, adding or subtracting a percent and more.

Formula

What Is a Percentage Calculator?

Quick answer: A percentage calculator turns two numbers into the third one in a percent problem. Pick one of 15 formulas in the Formula drop-down, type your two numbers, press Calculate, and read the result with the working underneath. Or skip the reading and try it with your own numbers.

A percent is a proportion out of 100, a rate per hundred (per cent, literally), so 25 percent means 25 hundredths, or 0.25. This percent calculator folds its 15 phrasings into four jobs: find a part (what is 15 percent of 80), find a percent, find the whole, or change a number by a percent.

We would rather you hear the gaps now: there is no named percentage difference formula, and zero or negative numbers are rejected. The sections called 'Percent Change vs Percentage Difference vs Percentage Points' and 'What This Percentage Calculator Cannot Do' spell out both.

How to Use This Percentage Calculator

One form, five moves. The labels below match the screen, quirks included.

Pick the sentence. Open the Formula drop-down and choose the line that reads like your question. The row under it rebuilds itself to match, so the first entry reads 'What is [P] % of [X] ?' with a number box for each bracket.
Type your two numbers. The placeholder letters inside the boxes show which number goes where: P is the percent, X the whole or starting number, and Y the part or result. Find the word 'of' in your question first: the number right after it is the whole, unless it says what, in which case that is the number you are solving for.
Press the Calculate button. Pressing Enter in either box does the same thing.
Read the Result card. It lists First Number, Second Number and Result, then a 'How we get?' list with the working. Take the Result row, to three decimals, as your answer.
Copy it or print it. The copy icons sit beside First Number and Result. Download PDF is a shortcut to your browser's print dialog, where you choose Save as PDF; we do not build a file on our side. The round arrow, tooltip Calculate Another, opens a blank calculator.

The calculation runs on our server, and the page only rewrites labels and placeholders when you change the Formula, so it does no arithmetic of its own. After Calculate the page reloads and both number boxes come back empty, so changing one number means retyping both. Copy the Result before you start the next sum. The Formula you picked stays selected. This free percent calculator needs no sign-up and no account.

Each box takes digits and a decimal point, above zero, with up to two decimals. Now pick a formula and press Calculate.

Which Percentage Formula Should You Pick?

The 15 entries do four jobs: find a part, find a percent, find the whole, change a number. The table groups them that way, but the drop-down interleaves them, so match the label, not the position. Labels are copied as printed, odd capitals and all.

Your question	Formula to select	First box	Second box	Example and result
What is 20 percent of 50?	What is P % of What	P	X	20 and 50 gives 10
20 percent of 50 is what?	P % of X is What	P	X	20 and 50 gives 10
What out of 200 is 15 percent?	What out of X is P%	X	P	200 and 15 gives 30
25 is what percent of 200?	Y is what percentage of X	Y	X	25 and 200 gives 12.5
45 out of 60 is what percent?	Y out of X is What%	Y	X	45 and 60 gives 75
What percent of 200 is 50?	What % of X is Y	X	Y	200 and 50 gives 25
30 is 15 percent of what?	Y is P% of What	Y	P	30 and 15 gives 200
15 percent of what is 30?	P % of What is Y	P	Y	15 and 30 gives 200
30 out of what is 15 percent?	Y of out what is P%	Y	P	30 and 15 gives 200
150 plus 20 percent	X Plus P % is What	X	P	150 and 20 gives 180
Percent growth, 80 to 100	X Plus What % is Y	X	Y	80 and 100 gives 25
What plus 8 percent is 108?	What Plus P% is Y	P	Y	8 and 108 gives 100
200 minus 15 percent	X minus P% is What	X	P	200 and 15 gives 170
Percent drop, 100 to 80 (second number smaller)	X minus What P% is Y	X	Y	100 and 80 gives 20
What minus 20 percent is 80?	What minus P% is Y	P	Y	20 and 80 gives 100

The three rows in each of the first three groups run the same arithmetic in different words, so pick the one that reads like your question. The box order is the real trap. 'What % of X is Y' takes the whole first, so 200 and 50 gives 25. 'Y is what percentage of X' takes the part first, so 50 and 200 gives 25.

Fifteen entries cover only nine distinct calculations, because each of the first three jobs is the same sum said three ways. The first three rows are the plain percentage of a number calculator, so start there for any 'what is X percent of Y' question, with your percent in the P box.

In plain words, the part equals the percent divided by 100, times the whole; the percent equals the part divided by the whole, times 100; and the whole equals the part divided by the percent, times 100.

Percentage Calculator Examples With Real Numbers

Each row was typed into the tool and checked against arithmetic done separately with fractions, then shown to three decimals, so you can retype it and compare. The tax row has a catch, explained below.

Question	Formula to select	Enter	Result shown
An 18 percent tip on a 64 dollar bill	What is P % of What	18 and 64	11.52
43 correct answers out of 50	Y out of X is What%	43 and 50	86
25 returned items out of 200	Y is what percentage of X	25 and 200	12.5
3 slices of an 8 slice pizza	Y out of X is What%	3 and 8	37.5
1 vote out of 3	Y is what percentage of X	1 and 3	33.333
35 percent off a price of 120	X minus P% is What	120 and 35	78
A 4.5 percent salary raise on 52,000	X Plus P % is What	52000 and 4.5	54340
Price after tax: 59.99 plus 8.25 percent	X Plus P % is What	59.99 and 8.25	64.939

3 out of 8 is 3 divided by 8, which is 0.375, and times 100 that is 37.5. A test score percentage, like 43 out of 50, or a grade percentage is the same division. The 33.333 for 1 out of 3 is a rounded display, since the true value repeats forever.

A fraction is a percent waiting to be converted: divide the top by the bottom for a decimal, multiply by 100 for decimal to percent, divide by 100 for percent to decimal. So 1 of 2, 1 of 4 and 1 of 5 give 50, 25 and 20. The OpenStax Prealgebra lesson on understanding percent defines a percent as a ratio with 100 in the denominator and converts a fraction by writing it as a decimal first. Type your own numbers into the same boxes. If a retyped row disagrees with the table, check the box order first.

Percentage Increase and Decrease: How to Calculate Percent Change

Percent change answers one question: how far did a number move, measured against where it started? The percent change formula, in words, is the new value minus the old one, divided by the old value, times 100. A positive result is a percent increase and a negative one is a percentage decrease. Eurostat's definition of percentage change writes the same thing as the later value divided by the earlier value, minus 1, times 100.

Percent change has no entry under its own name in the Formula drop-down, so you reach it through 'X Plus What % is Y', with the old value in the first box and the new value in the second. That one entry is the percentage change calculator here. A positive answer makes it a percentage increase calculator, a negative one a percentage decrease calculator. In our tests, 80 and 100 gave 25. A drop carries a minus sign: 100 and 80 gives -20, a 20 percent decrease, and 60 and 40 gives -33.333. An unexpected sign usually means the pair is the wrong way round.

The starting value is the base value, which is why the same gap of 20 is a 25 percent rise from 80 to 100 but a 20 percent fall from 100 to 80. To see a decrease as a positive number, 'X minus What P% is Y' works, with one condition: the second number must be the smaller one. 100 and 80 gives 20, and 60 and 40 gives 33.333. Send every rise to 'X Plus What % is Y'.

One limit: The old value has to be above zero, so a change from 0 or from a negative figure cannot be calculated here.

Percent Change vs Percentage Difference vs Percentage Points

These three get swapped often, and only percent change has a formula in the drop-down. Percent change works on before and after values, and it is a relative change: the absolute change, which is just the gap, gets divided by the old value. Percentage difference compares two values that have no order, dividing the gap by the average of two values, so it reads the same whichever you list first. A percentage point is the plain gap between two percentages.

We have no percentage difference formula, but a two-step route works. Take 40 and 60: the gap is 20 and the average is 50. Choose 'Y out of X is What%', type 20 and 50, and the Result shows 40. Percent change for the same pair reads differently, because 40 to 60 is 50 while 60 to 40 is -33.333.

Say a rate climbs from 40 percent to 50 percent. That is 10 percentage points, yet 'X Plus What % is Y' with 40 and 50 returns 25, the relative rise. Both are correct, and they answer different questions: how far apart two rates are, and how much bigger one is than the other.

Which one to quote: If you have two values and no 'before', you want a difference. If one number clearly came first, you want a change. If both numbers are already percentages and you only want the gap between them, say points.

Add or Subtract a Percentage, and Find the Original Number

To increase by a percentage, choose 'X Plus P % is What' and put the number first: 150 and 20 gives 180, and 52000 and 4.5 gives 54340. To decrease by a percentage, choose 'X minus P% is What': 200 and 15 gives 170, and 120 and 35 gives 78. A retail markup and markdown work this way too: each is one multiplication, by 1 plus or minus the percent as a decimal. For sale prices there is a Discount Calculator, and for a price with tax added or taken out at a rate you type in, a Sales Tax Calculator.

Undoing a percentage trips people up, because the percent was taken from the original number and not from the one in front of you. A 35 percent discount multiplies the original price by 0.65, so undoing it means dividing the sale price by 0.65, not adding 35 percent of the sale price back. Add it back and you get 78 plus 27.3, which is 105.3, wrong by 14.7. Choose 'What minus P% is Y', type 35 and 78, and you get 120. That entry is your reverse percentage calculator: it does the dividing. Tax works the same way: 'What Plus P% is Y' with 8 and 108 gives 100.

Finding the whole from a part and a percent runs the same way round. Pick 'Y is P% of What' and enter 30 and 15 to get 200. Three more reverse questions, side by side:

Question	Formula	Enter	Result
Total 110 with 10 percent tax, what was the price?	What Plus P% is Y	10 and 110	100
12 is 8 percent of what?	Y is P% of What	12 and 8	150
60 percent of what is 9?	P % of What is Y	60 and 9	15

For 'X minus P% is What' and 'What minus P% is Y', keep the percent below 100, because a discount that takes off the whole price leaves no original to recover.

Common Percentage Mistakes and How to Avoid Them

Swapping the boxes. The part and the whole trade places between phrasings, so read the row under the drop-down before you type.
Chaining percentages. A rise and a fall of the same percent do not cancel: 80 plus 25 percent is 100 with 'X Plus P % is What', and 100 minus 25 percent is 75, not 80, with 'X minus P% is What'. Our post on why stacked discounts do not add up shows the shopping version.
Using the wrong base. Percent change divides by the old value, so put the old value in the first box of 'X Plus What % is Y'.
Mixing up percent and percentage points. A rate that moves from 20 percent to 25 percent has gone up 5 points but is 25 percent higher than before.
Rounding too early. Round once, at the end. Cut 1 out of 3 to 33 percent first, and 33 percent of 600 gives 198, not 200. Chained runs lose a little at every hop.

Going deeper: Mental shortcuts and the hand method live in our guide on how to calculate percentages by hand.

How the Result, Rounding and Steps Work

This percentage calculator with steps shows two sets of numbers, and they will not match digit for digit. The Result row is rounded to three decimal places, half up, with trailing zeros dropped, so you see 12.5 and 10 rather than 12.500 and 10.000. Small ratios are where the rounding bites: 1 out of 100,000 shows 0.001, and 1 out of 1,000,000 shows Result 0, because 0.0001 percent no longer fits in three decimals.

The 'How we get?' list, the step-by-step working under the Result row, prints the unrounded value instead, about 14 significant digits of a floating-point number. For 1 out of 3, the Result row says 33.333 while the last line ends in 33.333333333333%. For 1 out of 1,000,000 the working reads p = 1.0E-6, scientific notation, and ends at 0.0001%. When a small result reads 0, the working holds the real figure.

Money needs one more step from you, because the tool does not round to cents. 59.99 plus 8.25 percent shows 64.939 against an unrounded 64.939175, which is 64.94 in dollars. 24.99 minus 15 percent shows 21.242 for an unrounded 21.2415.

Typed input is where the browser takes over. In our tests, Chromium (Chrome's engine) and WebKit (Safari's engine) drop commas, the percent sign and dollar signs as you type, so 1,000 becomes 1000 and still calculates. Firefox keeps what you typed, marks the box invalid and does not submit. Negative numbers and more than two decimals are stopped by all three engines in their own wording.

Zero is the entry that gets past all three engines and reaches our server. The page then comes back with a toast message, 'The first must be greater than 0.' (or 'The second must be greater than 0.'), because both boxes need a number above zero. Both boxes are empty by then and the Formula snaps back to the first option, so check it before you retype.

Reading the working: In our tests, the Result row of all 15 formulas matched arithmetic done separately with fractions, once rounded to three decimals. If a step line and the Result row ever disagree, believe the Result row.

What This Percentage Calculator Cannot Do

Eight limits to know before you rely on a number.

No named percentage difference formula. Use the two-step route from earlier: type the gap and the average into 'Y out of X is What%'.
No zero and no negative numbers. Both boxes need a value above zero, so a change from 0 or from a negative figure, or a question like 0 is what percent of 50, is not supported.
No fractions as input. Type decimals instead, 0.5 rather than 1/2.
Two decimals in, three out. The boxes stop at two decimals, so round a number like 12.345 yourself before you type it.
No chained changes in one run. Calculate each step, then type the result into the next run. The boxes keep two decimals, so each hop rounds a little.
A smaller second number. 'X minus What P% is Y' reads a decrease, so put the larger old value first.
No currency, units or cents. The boxes take plain numbers, and rounding to cents is yours to do.
No share link and no history list. Opening the page again shows an empty form, so copy a result before you calculate again.

The calculation happens on our server, so each Calculate reloads the page and sends your two numbers to it.

Who Uses It, and More Free Calculators

Students checking homework are the obvious audience. The Common Core grade 7 percent standard, 7.RP.A.3 in the Common Core State Standards, names percent increase and decrease, markups, markdowns, tax and tips. Shoppers comparing discounts and anyone checking a raise or a grade use the page the same way.

Average Calculator: find the mean of a list of scores.
Probability Calculator: work out the chance of an event from counts, then use this page for the percent.
All free online calculators: the full list of math tools.

Frequently Asked Questions

Frequently Asked Questions (FAQs) is a list of common questions and answers provided to quickly address common concerns or inquiries.

How do you calculate a percentage of a number?

Divide the percent by 100, then multiply by the number. For 20 percent of 50, that is 0.2 times 50, which is 10. In the calculator, pick 'What is P % of What', type 20 and 50 and press Calculate. That entry takes the percent first and the number second.

How do I work out what percent one number is of another?

Take the part, divide by the whole and multiply by 100; the whole is the number after the word 'of'. For 25 out of 200, 25 divided by 200 is 0.125, so the answer is 12.5 percent. In the calculator, pick 'Y is what percentage of X' and put the part in the first box and the whole in the second.

How do you calculate percentage increase or decrease?

Subtract the old value from the new one, divide by the old value and multiply by 100. A positive number is an increase and a negative one is a decrease. Pick 'X Plus What % is Y' with the old value first: 80 and 100 gives 25, and 100 and 80 gives -20. When the second number is the smaller one, 'X minus What P% is Y' shows the drop as 20.

How do percent change and percentage difference differ?

A percent change needs a before and an after, and it divides by the old value. Percentage difference compares two values with no order and divides their gap by their average. The calculator has no percentage difference formula, but for 40 and 60 you can pick 'Y out of X is What%' and type the gap 20 and the average 50 to get 40.

Why does increasing a number by a percentage and then decreasing it by the same percentage not give the original?

The second percentage is taken from a different base. 80 plus 25 percent is 100, and 100 minus 25 percent is 75, not 80. Getting from 100 back to 80 takes a 20 percent cut. You can check each step with 'X Plus P % is What' (80 and 25) and 'X minus P% is What' (100 and 25).

How do I find the original price before a discount or tax?

Do not add the percent of the final price back, because the percent was taken from the original. If 35 percent off leaves 78, pick 'What minus P% is Y' and type 35 and 78 to get 120. For tax, 'What Plus P% is Y' with 8 and 108 gives 100. Keep a discount percent below 100, because 100 percent leaves nothing to work back from.

How do I add or subtract a percentage from a number?

Adding takes a multiplier of 1 plus the percent written as a decimal, and subtracting takes 1 minus it. 150 plus 20 percent is 150 times 1.2, which is 180, and 200 minus 15 percent is 200 times 0.85, which is 170. Use 'X Plus P % is What' or 'X minus P% is What', number first and percent second.

Why does the calculator say the number must be greater than 0?

Because the calculator applies one rule to both boxes: each number must be above zero. Your browser lets 0 through, so the page comes back with 'The first must be greater than 0.' (or 'The second must be greater than 0.'). That rejects even 0 percent of 50. Negative numbers and more than two decimals are stopped by your browser first.

Can I save or print my calculation?

You can copy a result or print it, but the page offers no history list and no share link, and a fresh visit shows an empty form. The copy icons beside First Number and Result copy those values, and the Download PDF button opens your browser's print dialog, where you choose Save as PDF. Copy or print what you need before you calculate again.

Is the percentage calculator free, and do I need an account?

Yes, it is free, with no sign-up and no account. You pick a formula in the Formula drop-down, type two numbers and press Calculate. The calculation runs on our server, so the page reloads with the Result card and the working, and both number boxes come back empty.