Percentages
How to Calculate Percentage
To calculate a percentage, divide the part by the whole and multiply by 100. That one formula, rearranged, also finds a percentage of a number and works back to a whole from a part. This guide explains why it works, shows each version with worked examples, gives mental-math shortcuts and a conversion table, and covers the mistakes that cause most wrong answers.
How to calculate a percentage
A percentage tells you how many parts out of 100 something is. To find it, take the part you are interested in, divide it by the total it belongs to, and multiply the result by 100.
Example: 33 out of 55
A store had 55 orders yesterday and 33 of them were shipped the same day. What percentage shipped the same day?
60% of orders shipped the same day. The other 22 orders are the remaining 40%.
That is the whole method for the most common question. If you would rather not do the division by hand, the percentage calculator runs all three kinds of percentage question and shows the working with your numbers, and the what percent of calculator is set up for this exact part-of-whole case.
Any four function calculator handles it in three steps: type the part, divide by the whole, then multiply by 100.
What a percentage actually is
“Per cent” means “per hundred.” 60% means 60 for every 100, which is the fraction 60/100 and the decimal 0.60. These are three ways of writing one amount:
This explains the × 100 step. Dividing the part by the whole gives a decimal share, such as 0.6, meaning six tenths of the whole. Percentages express the share per hundred instead, so the decimal is scaled up by 100. Nothing about the amount changes; only the way it is written. That is also why converting a percentage back to a decimal means dividing by 100: 60% = 60 ÷ 100 = 0.6.
Percentages exist because they make comparisons easy. Is 33 out of 55 better than 41 out of 70? The fractions are hard to compare; the percentages are not. 33 out of 55 is 60%, and 41 out of 70 is about 58.57%, so the first is slightly higher.
The percentage formula and its three forms
Every basic percentage problem involves three quantities: the part, the whole and the percentage. If you know two, you can find the third. All three versions come from one relationship.
| You want | Formula | Example |
|---|---|---|
| The percentage | part ÷ whole × 100 | 33 ÷ 55 × 100 = 60% |
| The part (a percentage of a number) | percentage ÷ 100 × whole | 18 ÷ 100 × 350 = 63 |
| The whole | part ÷ (percentage ÷ 100) | 48 ÷ 0.32 = 150 |
You do not need to memorize the three separately. Write the one-line formula, put in the two values you know, and solve for the third with ordinary algebra. The next two sections cover the second and third rows in detail.
How to find the percentage of a number
To find a percentage of a number, change the percentage to a decimal by dividing it by 100, then multiply by the number. There are three ways to get the same answer, and it pays to know all of them.
Method 1: convert to a decimal and multiply
Example: 18% of 350
18% of 350 is 63. This method works for every percentage, including awkward ones like 7.25% or 140%. The percent to decimal calculator handles the conversion if the percentage itself is messy.
Method 2: build it from 10%, 5% and 1%
10% of any number is that number with the decimal point moved one place left, and 1% is the point moved two places. Most percentages can be built from those pieces.
This takes more lines on paper but is the easiest to do in your head, which is why it is the standard method for tips and discounts.
Method 3: use a fraction
Some percentages are simple fractions. 25% is one quarter, so 25% of 360 is 360 ÷ 4 = 90. 50% is a half, 20% a fifth, 75% three quarters. When the percentage matches a fraction you know, dividing is faster than multiplying by a decimal.
The swap trick
X% of Y always equals Y% of X, because both are X × Y ÷ 100. So 4% of 75 is the same as 75% of 4, which is 3. When one direction is hard, try the other.
How to find the whole from a part and a percentage
Sometimes you know a part and what percentage it represents, and need the total. Divide the part by the percentage written as a decimal.
Example: 48 is 32% of what?
48 students, 32% of a year group, signed up for a trip. How many students are in the year group?
There are 150 students. Always check the answer forwards; it takes one multiplication and catches the most common error, which is multiplying by 0.32 instead of dividing.
The same idea finds an original price after a discount or a markup, with one extra step: work out what percentage the price you paid represents. If you paid $68 after 15% off, you paid 85% of the original, so the original was 68 ÷ 0.85 = $80. The reverse percentage calculator is built for these.
Percentages in everyday calculations
The same formula sits under most day-to-day percentage tasks. The only skill is recognizing which quantity is the part, which is the whole, and which is missing.
Example: a test score
You scored 43 out of 50.
86% is a B on the common 90/80/70/60 US scale, though scales vary by school. The grade calculator does this from the number of questions you got wrong.
Example: a discount
A jacket priced at $85 is 30% off.
You save $25.50 and pay $59.50. Multiplying by 0.70 directly works because paying after 30% off means paying the remaining 70%. The percent off calculator also handles stacked discounts and tax.
Example: a tip
A 20% tip on a $47.60 bill.
The tip is $9.52. The tip calculator adds rounding and bill splitting.
Changes over time, such as a price going from $40 to $50, are a slightly different calculation, because the base is the starting value rather than a total. The percentage increase formula guide covers increases and decreases in full.
Fractions, decimals and percentages
Converting between the three forms is moving the decimal point or dividing. A fraction becomes a decimal when you divide the top by the bottom; a decimal becomes a percentage when you multiply by 100. These are the values worth knowing on sight, shown here with what each one is of 640 to illustrate the mental-math approach.
| Percentage | Decimal | Fraction | Of 640 |
|---|---|---|---|
| 1% | 0.01 | 1/100 | 6.4 |
| 5% | 0.05 | 1/20 | 32 |
| 10% | 0.1 | 1/10 | 64 |
| 12.5% | 0.125 | 1/8 | 80 |
| 20% | 0.2 | 1/5 | 128 |
| 25% | 0.25 | 1/4 | 160 |
| 33.33…% | 0.333… | 1/3 | ≈ 213.33 |
| 50% | 0.5 | 1/2 | 320 |
| 75% | 0.75 | 3/4 | 480 |
| 100% | 1 | 1/1 | 640 |
For other fractions, the fraction to decimal chart lists halves through sixteenths, and the decimal to percent calculator converts any decimal you end up with.
Common mistakes
- Dividing the wrong way round. The whole goes on the bottom. 33 ÷ 55 is 60%; 55 ÷ 33 is about 166.67%, a different and usually meaningless answer.
- Multiplying by the percentage instead of its decimal. 18 × 350 is 6,300, not 63. Divide the percentage by 100 first.
- Losing a zero with small percentages. 4.5% is 0.045, not 0.45. A slip here makes the answer ten times too big.
- Taking the percentage of the wrong total. If 15% off is followed by sales tax, the tax applies to the reduced price, not the original.
- Adding percentages that have different wholes. 50% of one class and 60% of another class do not make 55% of the combined group unless the classes are the same size. Add the parts and wholes first, then divide.
- Rounding before the last step. Keep full decimals until the final answer, then round once.
If a percentage looks wrong, ask whether it is sensible. Most of a total should give over 50%; a small slice should give a small percent. That one check catches most of the errors above. For scores out of a total, the X out of Y as a percentage guide has ready-made tables.
Frequently asked questions
What is the formula for percentage?
The percentage formula is percentage = part ÷ whole × 100. The whole is the total, and the part is the share of it you are measuring. For example, 33 out of 55 gives 33 ÷ 55 × 100 = 60%. Rearranged, the same relationship finds a part, percentage ÷ 100 × whole, or a whole, part ÷ (percentage ÷ 100).
How do I find the percentage of a number?
Divide the percentage by 100 to make it a decimal, then multiply by the number. To find 18% of 350, calculate 0.18 × 350 = 63. You can also build it from easy pieces: 10% of 350 is 35, 5% is 17.5 and 3% is 10.5, which add up to 63. Both routes give the same answer.
How do I calculate the percentage of marks?
Divide the marks you scored by the total marks available and multiply by 100. If you scored 412 out of 500, the calculation is 412 ÷ 500 = 0.824, which is 82.4%. When different papers carry different weights, combine them as a weighted average rather than adding percentages, so each paper counts in proportion to its weight.
What is 30% of 250?
30% of 250 is 75. Convert 30% to 0.3 and multiply: 0.3 × 250 = 75. In your head, 10% of 250 is 25, so 30% is three times that, 75. The same three-times-10% approach works for 30% of any number.
How do you calculate a percentage without a calculator?
Use 10%, 5% and 1% as building blocks. 10% is the number with the decimal point moved one place left, 5% is half of that, and 1% is the point moved two places. Combine them: 15% is 10% plus 5%, and 18% is 10% plus 5% plus three lots of 1%. For simple fractions like 25% or 50%, divide by 4 or 2.
How do you convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For 7/20, 7 ÷ 20 = 0.35, which is 35%. If the denominator divides evenly into 100, you can scale instead: 7/20 is the same as 35/100. Fractions with denominators such as 3 or 7 produce repeating decimals, so their percentages have to be rounded.
How do I work out what percentage something is of a total?
Divide the amount by the total and multiply by 100. If you spent $1,320 of a $4,400 monthly budget on rent, rent took 1,320 ÷ 4,400 × 100 = 30%. If you calculate this for every item in a budget, the percentages should add up to 100%, give or take a small rounding difference.
Why do you multiply by 100 to get a percentage?
Because a percentage is a number out of 100. Dividing the part by the whole gives a share of 1, such as 0.6, meaning six tenths. Multiplying by 100 restates that same share as a number per hundred, 60, which is what the percent sign means. The amount does not change, only how it is written.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/how-to-calculate-percentage/