Percentage Calculator

Nine percentage questions in one calculator

Choose your question in Calculation, worded the way people ask it: a percentage of a number, what percent one number is of another, the whole behind a part, percent change, an increase or decrease by a percentage, the value before a change, percent difference, percentage points, or several changes in a row. Only the boxes that question needs appear. Every answer comes with a sentence in plain words, the steps, and the exact value when the one on screen is rounded.

How to use it

1. Choose the question in Calculation. Each section below also has a link that opens its question in the calculator.
2. Type your numbers. 1,850, 1850 and -40 all work, and percentage boxes take 24 or 24%. The ± button makes a number negative on a phone keypad.
3. Read the answer as you type; Calculate isn’t needed but moves you to the result.
4. Decimal places sets the rounding on screen only. Auto shows a result in full when its decimal ends within 6 places, and otherwise rounds to 2 decimal places (2 significant digits for values below 1).

Try loads four cases from this page: a score of 42 out of 56, the repeating 5 out of 30, a change from −40 and a fall of 50% followed by a rise of 50%. Swap exchanges the two values in the change and difference questions. Copy answer copies just the number, and Save for comparison keeps up to three results side by side with the change between them.

How to calculate a percentage of a number

Divide the percentage by 100 and multiply by the number: 24% of 1,850 is 0.24 × 1,850 = 444. “Of” means multiply, and a percent is a number of hundredths.

$$\text{part} = \frac{P}{100} \times \text{whole}$$

• $P$ is the percentage (24 for 24%).
• The whole is the total you take the percentage of.
• The part is the share of it that the percentage stands for.

Worked example: 24% of 1,850 survey replies. A survey has 1,850 replies and 24% chose the first option.

1. Percentage as a decimal: 24 ÷ 100 = 0.24.
2. Part: 0.24 × 1,850 = 444 replies.
3. The other 76% is 1,850 − 444 = 1,406 replies. The whole increased by 24% would be 1,850 + 444 = 2,294.

A percentage of a percentage works the same way, and the answer is a share of the original whole: 20% of 30% is 0.2 × 30% = 6%. If 30% of the replies came from one region and 20% of those chose the first option, those replies are 6% of all 1,850, which is 111.

The Other percentages of 1,850 table under the answer repeats the calculation for 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50% and 75%, so 10% of 1,850 (185) is there without retyping anything. Open this question in the calculator.

What percent is X of Y?

Divide X by Y and multiply by 100: 444 is 444 ÷ 1,850 × 100 = 24% of 1,850. The same division turns a score into a percentage. 42 out of 56 is 42 ÷ 56 = 0.75, which is 75%, and as a fraction in lowest terms it is 3/4.

Some divisions never end. 5 out of 30 is 16.67% on screen, and the calculator adds that the exact value is 16 2/3%: the decimal is 16.666… with the 6 repeating. It works with fractions of the numbers you type, so it can tell a result that ends from one that repeats. Open this question in the calculator.

X is P% of what?

Divide the part by the percentage as a decimal: if 444 is 24% of a number, the number is 444 ÷ 0.24 = 1,850. Dividing by the percentage itself first gives 1% of the whole, 444 ÷ 24 = 18.5, and 100 times that is the whole. With 0% there is no answer to find: 0% of every number is 0. Open this question in the calculator.

How to calculate percentage change (increase or decrease)

Subtract the starting value from the new one, divide by the starting value and multiply by 100. From 1,250 to 1,550 the change is 1,550 − 1,250 = 300, and 300 ÷ 1,250 × 100 = +24%, an increase.

$$\text{percent change} = \frac{B - A}{|A|} \times 100$$

• $A$ is the starting value and $B$ the new value.
• A positive result is an increase and a negative one a decrease; the calculator says which in words.

The same 300 measured back from 1,550 is only 300 ÷ 1,550 = 19.35%, so the change back from 1,550 to 1,250 is −19.35%. The base is always the value you start from, which is why a rise and the fall that undoes it have different sizes. Open this question in the calculator.

Increasing or decreasing a number by a percentage

Multiply by 1 plus or minus the percentage as a decimal. 1,250 increased by 24% is 1,250 × 1.24 = 1,550. 640 decreased by 15% is 640 × 0.85 = 544: the decrease is 0.15 × 640 = 96, and 640 − 96 = 544. Under the answer, a table shows the same starting value changed by 5% to 50%. Open this question in the calculator.

How to find the original number before a percentage increase or decrease

Divide the new value by 1 plus the increase, or by 1 minus the decrease. After a 24% increase a value of 1,550 was 1,550 ÷ 1.24 = 1,250 before it. The increase was 24% of the original, so 1,550 is 124% of the original, not 24% more than itself.

The tempting shortcut takes 24% off 1,550 and gets 1,550 × 0.76 = 1,178, which is 72 too low. The calculator shows that wrong figure next to the right one. It works the other way for a decrease: a value of 600 after a 25% decrease was 600 ÷ 0.75 = 800 before it, while adding 25% of 600 gives 750. Open this question in the calculator.

Percentage difference vs percentage change

Use percent change when one value came first, and percent difference when neither is the starting point, such as two shops’ prices or two measurements of the same thing. Percent difference divides the gap by the average of the two sizes, so it comes out the same whichever value you enter first:

$$\text{percent difference} = \frac{|A - B|}{(|A| + |B|) \div 2} \times 100$$

For 1,250 and 1,550 the gap is 300 and the average is 1,400, so the percent difference is 300 ÷ 1,400 × 100 = 21.43%. It sits between the two percent changes, +24% and −19.35%, because its base sits between the two values. When both values are 0 the calculator gives 0%. Open this question in the calculator.

Percent vs percentage points

A change in percentage points is the plain difference between two percentages; a percent change compares that difference with the starting percentage. If a share of 24% becomes 30%, it rises by 6 percentage points, and 6 ÷ 24 × 100 = 25% is the relative increase. For small starting percentages the two drift far apart: a rate going from 3.5% to 4.2% rises 0.7 points but 20% in relative terms.

The calculator gives both side by side, plus the change in basis points (one basis point is a hundredth of a percentage point, so 6 points are 600 basis points). Open this question in the calculator.

Several percentage changes in a row

Percentage changes in a row multiply rather than add up. Turn each change into a multiplier (1 + change ÷ 100), multiply the multipliers, and subtract 1. A rise of 24% followed by a fall of 24% is 1.24 × 0.76 = 0.9424, an overall change of −5.76%: 1,250 becomes 1,550 and then 1,178, not 1,250. Adding the percentages would suggest 0%.

The Value after each change table shows each step and downloads as a CSV file. The calculator also gives the change that would return to the start. After −50% and then +50%, 100 has become 75, and getting back to 100 needs +33.33%. The order of the changes makes no difference to the final value. Open this question in the calculator.

Percentage change with negative numbers or zero

With a negative starting value, the calculator divides by its size (its absolute value), so the sign still tells you which way the value moved. From −40 to 10 the change is 10 − (−40) = 50, and 50 ÷ 40 × 100 = +125%. Formulas that divide by −40 itself give −125%, which reads as a fall although the value rose. The calculator warns when this applies and shows the other number. For negative values the change as an amount is often the clearer thing to report.

From a starting value of 0 there is no percent change at all, because nothing can be divided by 0. The calculator says so and gives the change as an amount instead: from 0 to 35 is a change of +35. The same happens with a whole of 0 in “What percent is X of Y?”.

Reading the result

• The headline is the answer, with a sentence that puts it back into words (“24% of 1,850 is 444”). When the screen shows a rounded value, a second line gives the exact one, as a fraction and with its repeating digits.
• The tiles add the numbers people usually want next: the rest of the whole, the fraction and decimal forms, the change back, or the common wrong answer beside the right one.
• Part of the whole draws the part and the rest as one bar whenever the part fits inside a positive whole, with the share of each in the legend.
• How this was calculated lists each step with your numbers and ends with a spreadsheet formula.
• The tables repeat a percent-of or an increase or decrease at common percentages, or follow a chain of changes step by step. Each downloads as a CSV file.

Assumptions and limitations

• Numbers are worked out as exact fractions of what you typed and rounded once, for display only. Copy answer copies the value as shown.
• Percent change, and the relative change in the points question, divide by the size of the starting value. Some textbooks and spreadsheet formulas divide by the value itself, which gives the opposite sign when it is negative.
• Finding the value before a change assumes it was positive or zero, as prices, counts and measurements are; that makes the answer unique.
• A chain of changes starts from a positive value, and each fall is at most 100%.
• Inputs can be as large as 1,000,000,000,000,000 in size, and percentages up to 1,000,000%.

Common percentage mistakes

• Taking the percentage of the wrong base. “What was it before a 24% rise?” divides by 1.24; subtracting 24% of the new value gives 1,178 instead of 1,250.
• Expecting a change to undo itself. +24% and then −24% ends 5.76% lower, because the fall is taken from the larger value.
• Calling a change in points a percent change. 24% to 30% is 6 points, but 25% in relative terms.
• Typing a decimal into a percentage box. 0.15 in the Percentage box means 0.15%, not 15%. The calculator points this out when you enter a small value without a % sign.
• Dividing by a negative starting value. It flips the sign of the answer; divide by its size, or report the change as an amount.

Discounts, sales tax on a receipt and margins follow the same rules with a price as the base, and the guide to percentage mistakes works through more of them.