Percentage Calculator

Part = percent ÷ 100 × whole Percent = part ÷ whole × 100 Whole = part ÷ (percent ÷ 100)

Percent

The rate, written the way people say it: 15 means fifteen percent, not fifteen hundredths. Internally it is divided by a hundred before it multiplies anything, which is the step the whole page turns on

Part

The piece of the whole that the rate selects — 15 percent of 200 is 30, so 30 is the part. It can be larger than the whole when the percentage is above 100, and negative when the difference goes the other way

Whole

The base the rate is applied to: 200 in fifteen percent of 200. Its floor is zero rather than one, because a whole of zero is a legitimate base — the answer is zero — even though dividing by it is not defined

The pair you fill

Any two of the three. Which pair you chose is what selects the question being answered; there is no mode field and nothing else to configure, which is why leaving a stale third number behind causes an error rather than a silent correction

Three searches bring people here, and they are three different sentences. What is 15 percent of 200 — the classic, the one a tip, a tax or a discount is made of, where the rate and the base are known and the amount is wanted. Forty-five is what percent of 60 — a score, a completion rate or a share, where the two numbers are known and the rate is wanted; note that this is the question where a result above 100 is possible and not an error, since a part can exceed its whole. And thirty is 15 percent of what — the one people get wrong, because the answer is a division by a rate smaller than one, so the whole comes out larger than the part and the arithmetic has to run backwards. Two more uses are worth naming because they are where the percentage point confusion bites. Comparing two rates — a rate that goes from 20 percent to 25 percent has moved five percentage points, which is a rise of a quarter of itself, so the same pair of numbers supports two true statements with different sizes. And working out a change against a base — 200 rising to 250 is an increase of 50, which is 25 percent of the original 200 and not 20 percent of the new 250, because the whole in the percentage formula is always the number you started from.

1. What is 15 percent of 200

   1. Convert the rate: 15 ÷ 100 = 0.15
   2. Multiply by the whole: 0.15 × 200 = 30
   3. The part is 30, and the other two outputs are the numbers you entered

   The default case and the most common of the three questions. The step that matters is the first one: the 15 in the box is not fifteen hundredths yet, and a formula that multiplies 15 by 200 without dividing by a hundred first gives 3,000 — a plausible-looking number that is a hundred times too large.

2. 45 is what percent of 60

   1. Divide the part by the whole: 45 ÷ 60 = 0.75
   2. Convert to a percentage: 0.75 × 100 = 75

   The reverse question: two numbers, and the rate between them is the unknown. Forty-five out of sixty is three quarters, and three quarters is 75 percent. A part larger than its whole is allowed here and gives a percentage above 100 — 90 out of 60 is 150 percent — which is what makes this the right form for a result that overshot a target rather than a share of one.

3. 30 is 15 percent of what

   1. Convert the rate: 15 ÷ 100 = 0.15
   2. Divide the part by the rate: 30 ÷ 0.15 = 200

   The same three numbers as the first example, asked from the other end — and this is the question people get wrong, because the answer is larger than the number they started with. Dividing by 15 instead of by 0.15 gives 2, which is off by a factor of a hundred and looks close enough to a real answer to go unnoticed.

4. A price with 7.5 percent off, against a 240 base

   1. Convert the rate: 7.5 ÷ 100 = 0.075
   2. Multiply by the whole: 0.075 × 240 = 18

   A rate with a decimal in it, which is where a mental estimate stops working: 7.5 percent of 240 is 18, so the reduced price is 222. Reading the same rate as 7.5 of 240, or as three quarters of a percent, are the two mistakes this shape of input invites.

It wants two fields filled and not three. If all three boxes hold numbers and they do not agree, the page reports an error rather than overwriting one of them, because silently changing input the reader typed is the worse failure of the two. That has a practical consequence worth stating plainly: the page opens with the rate and the whole already filled in, so to ask the question with the part and the whole you have to clear the rate box first. The agreement check is exact to about fifteen significant digits, so a third number you rounded by hand — typing 30.2 when the pair you filled gives 30.15 — counts as a disagreement, and the field has to be emptied rather than adjusted. Results are shown to four decimal places, which means a percentage smaller than 0.0001 of the whole prints as zero, and a rate like one part in three prints as 33.3333 rather than as a fraction. The page does no compounding, no averaging and no change over time: it is one multiplication or one division, so a percentage change from one period to the next, a compound growth rate and a share of a total are all different pages. It also does not know whether your percentage is a rate, a share, a change or a tax, and it will happily compute 15 percent of a base that makes no sense for the question you had in mind — which is why the limitation that matters most is the one about percentage points: a rate that rises from 20 percent to 25 percent has moved five percentage points, and entering 5 into the rate box to see what that is worth answers a different question. Finally, the whole is allowed to be zero but not to be negative: a base below zero is a sign convention this page has no way to read, while a base of exactly zero is a real value that produces a real answer.

How do I work out a percent of a number?

Divide the percentage by a hundred and multiply by the number: 15 percent of 200 is 0.15 × 200 = 30. The division by a hundred is the step that gets dropped, and dropping it turns 30 into 3,000. The same shortcut works in reverse when the numbers are friendly — 10 percent is a tenth, 25 percent is a quarter, 50 percent is a half — and those are worth using as a check on the arithmetic.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by a hundred. Forty-five out of sixty is 45 ÷ 60 = 0.75, which is 75 percent. The result can exceed 100 — 90 out of 60 is 150 percent — and that is a real answer, not an error: it means the part overshot the whole, which is exactly what a result against a target is supposed to be able to show.

Why does the page say I filled in too many fields?

Because it solves for the third value and will not overwrite a number you typed. Two fields determine the third, so when all three hold numbers it checks them against each other and reports an error if they disagree. The page opens with the percentage and the whole filled in, so to work with the part and the whole you clear the percentage box; the third number is meant to be empty, not merely ignored.

What is the difference between a percentage point and a percent?

A percentage point is an absolute difference between two percentages; a percent is a relative one. A rate going from 20 percent to 25 percent has risen five percentage points, and it has also risen 25 percent of itself. Both statements describe the same move, and quoting one when the other was meant is the classic way a percentage answer misleads. As a rule, changes in rates are quoted in percentage points and changes in quantities in percent.

Can a percentage be negative, or more than 100?

Both are allowed and both are common. A price falling by 20 percent is minus 20 as a rate, and a loss of 30 against a base of 200 is minus 15 percent as a part. Above 100 is what a result that overshot its target looks like: 90 out of 60 is 150 percent. This page accepts either, because a formula that refuses a negative rate refuses every decline.

What happens if the whole is zero?

Two different things, depending on which pair you filled. Fifteen percent of zero is zero, and the page computes it — a whole of zero is a real base whose part is nothing. But 5 is what percent of zero has no answer, because it divides by the whole; and 30 is 15 percent of what has no answer when the rate is zero and the part is not, because it divides by a rate that is zero. The box accepts zero, and the error appears only where the arithmetic actually fails.

• NIST Special Publication 811, Chapter 7, section 7.10.2 (%, percentage by, fraction) — the symbol % stands for the number 0.01, so 15 percent is 0.15 and the conversion is a shift of the decimal point rather than a separate operation — National Institute of Standards and Technology (United States)
• Percent — a ratio or fraction is converted to a percentage by multiplying by 100 and appending the percentage sign, and 15% of 200 is worked the same way in either direction — Wolfram MathWorld (United States)
• Fraction — numerator, denominator and the solidus, together with the rule that a reduced fraction has the common terms cancelled out of both, which is what makes part over whole the natural way to write this identity — Wolfram MathWorld (United States)