How to Calculate Percentage: Formulas and Worked Examples
To calculate a percentage, divide the part by the whole and multiply by 100: percentage = part ÷ whole × 100. If you answered 45 of 60 questions correctly, 45 ÷ 60 = 0.75, and 0.75 × 100 = 75%. Every other percentage question, from percent change to reverse percentages, is this same formula rearranged.
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This guide shows how to calculate percentage in each everyday situation: taking a percentage of a number, finding what percent one number is of another, working back to the whole, percentage increase and decrease, percentage difference and reverse percentages. If you only need the answer, the free percentage calculator shows it together with the formula filled in with your numbers.
How to calculate percentage: the basic formula
"Percent" means "per hundred", so 75% is 75 hundredths, or 0.75. Every percentage problem involves three quantities:
- the whole: the total, or the starting value;
- the part: the portion you are looking at;
- the percentage: how big the part is, measured in hundredths of the whole.
If you know any two of them, you can find the third. This is the percentage formula in its three forms:
| You want | Formula | Example |
|---|---|---|
| The percentage | part ÷ whole × 100 | 45 ÷ 60 × 100 = 75% |
| The part | whole × percentage ÷ 100 | 60 × 75 ÷ 100 = 45 |
| The whole | part ÷ percentage × 100 | 45 ÷ 75 × 100 = 60 |
How to find a percentage of a number
To find X% of Y, turn the percentage into a decimal by dividing it by 100, then multiply: X% of Y = X ÷ 100 × Y.
- 15% of 80 = 0.15 × 80 = 12
- 7.5% of 240 = 0.075 × 240 = 18
- 120% of 50 = 1.2 × 50 = 60
The last example shows that a percentage can be more than 100%. That simply means the part is larger than the whole you are comparing it with.
What percent is X of Y?
This is what most people mean when they ask how to find a percentage. Divide the part by the whole, then multiply by 100.
- 18 out of 24: 18 ÷ 24 = 0.75, so 75%
- 7 out of 8: 7 ÷ 8 = 0.875, so 87.5%
- A 2 tip on a $64 bill: 12 ÷ 64 = 0.1875, so 18.75%
The number after "of" or "out of" is almost always the whole, so it goes on the bottom of the fraction.
Finding the whole from a part
Sometimes you know a part and its percentage, but not the total. Divide the part by the percentage written as a decimal: whole = part ÷ (percentage ÷ 100).
- 12 is 15% of what number? 12 ÷ 0.15 = 80. Check: 15% of 80 is 12.
- 27 people, 45% of those surveyed, answered yes. The survey had 27 ÷ 0.45 = 60 respondents.
How to calculate percentage increase and decrease
To calculate percentage change, use the percent change formula, which compares a new value with an old one:
percent change = (new − old) ÷ old × 100
A positive result is a percentage increase; a negative result is a percentage decrease. The old value is always the base you divide by.
Percentage increase. A subscription goes from $80 to $92 a month. The change is 92 − 80 = 12, and 12 ÷ 80 = 0.15, so the price rose by 15%.
Percentage decrease. Daily website visits fall from 250 to 210. The change is 210 − 250 = −40, and −40 ÷ 250 = −0.16, a 16% decrease.
To apply a change instead of measuring one, multiply by 1 plus or minus the percentage as a decimal:
- 200 increased by 15% = 200 × 1.15 = 230
- 200 decreased by 15% = 200 × 0.85 = 170
Percent change is undefined when the old value is 0, because you cannot divide by zero. Going from 0 to 10 visitors is an increase of 10, but not a percentage of anything.
Percentage difference vs percent change
Percent change has a direction: one value is clearly the starting point. Sometimes neither number is the reference, for example two quotes from different suppliers or two measurements of the same object. Then you want the percentage difference, which compares the gap with the average of the two values:
percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
The vertical bars mean "absolute value": take the gap as a positive number. For 40 and 60, the gap is 20, the average is 50, and 20 ÷ 50 × 100 = 40%. Swap the two numbers and the answer is still 40%.
The same pair of numbers under each formula:
| Calculation | Divided by | Result |
|---|---|---|
| Percent change, 40 → 60 | 40 | +50% |
| Percent change, 60 → 40 | 60 | −33.33% |
| Percentage difference, 40 and 60 | 50 (the average) | 40% |
Use percent change when there is a clear before and after. Use percentage difference when you are comparing two values side by side and neither one is the baseline.
Reverse percentage: finding the original price
Reverse percentage problems give you the number after a percentage change and ask for the number before it. The usual mistake is to take the percentage of the new number, which uses the wrong base.
After an increase. A jacket costs 50 including 20% tax. The 50 is 120% of the pre-tax price, so the original is 150 ÷ 1.20 = 25. Check: 25 plus 20% is 50. Subtracting 20% of 50 would give 20, which is wrong.
After a discount. You paid $66 after a 25% discount. You paid 75% of the original price, so the original was 66 ÷ 0.75 = $88. Check: 25% of $88 is