Percent of a Percent Calculator
Find a percent of a percent by multiplying two or more percentages, optionally applied to a starting value
By Waqar Mushtaq · Last updated:
A percent of a percent comes up whenever one share is taken of another share: 40% of voters are under 35, and 60% of those voted early -- what percent of all voters are young early voters? Or 30% of a company's revenue comes from one region, and 25% of that region's revenue is from one product. The answer is found by multiplying the percentages, not adding or subtracting them. This calculator multiplies two to five percentages, optionally applies the result to a starting value, walks through each step so you can see the share shrink (or grow, for percentages above 100%), and shows the same chain with other common first percentages.
How to Calculate a Percent of a Percent
O(n) in the number of percentagesp₁, p₂ = the two percentages · p = the combined percentage
More than two percentages, and the result applied to a starting value V
Convert each percentage to a decimal by dividing by 100, multiply the decimals together, then multiply by 100 to turn the product back into a percentage.
Example -- two percentages: what is 25% of 80%? 0.25 × 0.80 = 0.20, so 25% of 80% is 20%.
Example -- applied to a value: 25% of 80% of 1,000. 80% of 1,000 is 800, and 25% of 800 is 200 -- the same as 20% of 1,000.
Example -- three percentages: 25% of 80% of 60%. 0.25 × 0.80 × 0.60 = 0.12, so the answer is 12%.
Order doesn't matter. Multiplication is commutative, so 25% of 80% and 80% of 25% are both 20%. Only the running figures in the step-by-step breakdown change.
The result is smaller than every percentage under 100%. Taking a part of a part always leaves less than either part on its own. A percentage above 100% grows the share instead: 150% of 20% is 30%.
To take a single percentage of a number, see the Decimal to Percent Converter; for a value that rises or falls by a percentage, see the Percent Change Calculator.
Use Cases
Subgroups in Surveys and Statistics
Work out what share of a whole population a subgroup represents -- for example, if 40% of respondents are under 35 and 60% of those answered "yes," then 24% of all respondents are under-35 "yes" answers.
Probability of Independent Events
The chance of two independent events both happening is the product of their probabilities. A 30% chance of rain on each of two days gives a 30% × 30% = 9% chance of rain on both days.
Business and Finance Shares
Find what share of total revenue one product line in one region makes up, or your share of a company's profits when you own a percentage of a firm that owns a percentage of another.
Commissions, Splits, and Fees
Work out a cut of a cut -- an agent who keeps 50% of a 6% commission earns 3% of the sale price, which this calculator turns straight into a dollar figure when you enter the price as the value.
Frequently Asked Questions
How do you calculate a percent of a percent?
Divide each percentage by 100 to get decimals, multiply them, then multiply the result by 100. For example, 50% of 20% is 0.50 × 0.20 = 0.10, which is 10%.
Why not just subtract or add the percentages?
"Of" means multiply. 25% of 80% is a quarter of 80%, which is 20% -- not 80% − 25% = 55% or 80% + 25% = 105%. Adding or subtracting percentages is only right when they are shares of the same whole, such as 30% of a budget plus 20% of the same budget.
Is a percent of a percent the same as percentage points?
No. Percentage points describe the difference between two percentages (5% to 8% is a 3 percentage-point rise). A percent of a percent describes a share of a share, and is always found by multiplying.
Can I take a percent of a percent of a number?
Yes. Multiply the combined percentage (as a decimal) by the number. 25% of 80% of 1,000 is 0.25 × 0.80 × 1,000 = 200. Enter the number in the optional "of Value" field and the calculator shows the running value at every step.
What happens with a percentage over 100%?
It works the same way, but that step grows the share instead of shrinking it. 150% of 20% is 1.5 × 0.20 = 0.30, or 30%.
Does the order of the percentages matter?
Not for the final answer -- multiplication gives the same product in any order, so 20% of 50% equals 50% of 20% (both 10%). The order only changes the intermediate figures shown in the step-by-step breakdown.
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.