Percentage of a Percentage Calculator

This calculator works out what you get when one percentage is applied to another, rather than simply added together, which is the most common percentage mistake people make. You enter a first percentage and a second percentage, such as 20% and 50%, and optionally a dollar amount if you want the result applied to a real figure. The calculator instantly returns the combined percentage (for example, 20% of 50% equals 10%), the same result expressed as a decimal, and, when you enter an amount, the dollar value that percentage represents. It multiplies the two percentages and divides by 100, the shortcut behind every stacked calculation, so you see the answer update as you type without needing to work through the maths by hand. This is the right tool whenever one percentage is taken of another rather than the same base: a second discount stacked on an already-discounted price, a commission paid only on a margin rather than the full sale, or a portion of a portion, such as savings set aside from an amount you have already set aside from your pay. The worked examples below show each of these in a New Zealand context, including why 20% off followed by 10% off leaves you paying 72% of the original price, not 70%. Results are rounded for display, so treat very small decimal differences as rounding rather than error.

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10%
20% of 50% = 10%
As a decimal: 0.1

Tip: this is the same as multiplying the two percentages and dividing by 100.

How to work out a percentage of a percentage

Taking a percentage of a percentage means applying the second percentage to the result of the first, rather than adding the two together. The quickest way is to multiply the two percentages and divide by 100.

For example, to find 20% of 50%:

  • Write each percentage as a decimal: 20% is 0.20, and 50% is 0.50.
  • Multiply the decimals: 0.20 times 0.50 is 0.10.
  • Convert back to a percentage: 0.10 is 10%.

So 20% of 50% is 10%. The shortcut is 20 times 50, divided by 100, which also gives 10.

Common mistake: you cannot add the two percentages. 20% and 50% is not 70%. The second percentage is taken of the first, so the values multiply. Adding only works when both percentages apply to the same starting amount.

Worked New Zealand examples

Stacked discounts in a sale

A store advertises 20% off, then takes a further 10% off at the till. Shoppers often assume that is 30% off, but it is not.

The first discount leaves 80% of the price. The second discount takes 10% off that 80%, which is 10% of 80% equals 8%. So the price drops by another 8 percentage points, leaving 72% of the original. On a $250 jacket you pay $180, a total discount of 28%, not 30%.

Result: 72% of the original price, a 28% total discount.

Commission on a margin

A salesperson earns 15% commission, but only on the 40% gross margin of each sale rather than the full sale price. To see what share of the sale price the commission represents, work out 15% of 40%.

15% of 40% is 6%. On a $2,000 sale, the commission is 6% of $2,000, which is $120.

Result: the commission is 6% of the sale price.

A portion of a portion

You set aside 30% of your pay for savings, and you want to put 25% of that savings into a separate term deposit. How much of your total pay goes to the term deposit?

25% of 30% is 7.5%. If you earn $1,200 a week, that is 7.5% of $1,200, which is $90 a week.

Result: 7.5% of your pay goes to the term deposit.

The formula

Combined percentage equals (first percentage times second percentage) divided by 100. To apply it to an amount, multiply the amount by the first percentage as a decimal, then by the second percentage as a decimal.

Frequently asked questions

What is a percentage of a percentage?

It is the result of taking one percentage of another. For example, 20% of 50% means 20% of one half, which is 10%. You work it out by multiplying the two percentages together and dividing by 100.

Is 20% off then 10% off the same as 30% off?

No. A 20% discount leaves 80% of the price, and a further 10% off leaves 90% of that. You pay 0.80 times 0.90, which is 72% of the original price, a 28% total discount.

How do I apply the result to a dollar amount?

Work out the combined percentage first, then apply it to the amount. For 20% of 50% of $400, the combined percentage is 10%, and 10% of $400 is $40. Enter an amount above and the calculator does both steps.

Why can I not just add the two percentages?

Adding only works when both percentages apply to the same base. A percentage of a percentage applies the second percentage to the result of the first, so the values multiply. This is why stacked discounts and commissions on margins always need multiplication.

Who this calculator is for

This calculator is for anyone applying one percentage to another, such as a discount on an already-discounted price, or a commission taken from a margin.

What this calculator assumes

  • The two percentages and the base amount you enter.
  • Standard sequential percentage arithmetic.
  • Order matters: a percentage of a percentage is not the same as adding the two together.
  • Results are rounded for display.

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