Formula
P% of Q% = (P × Q) ÷ 100. Convert the first percentage to a decimal, then multiply by the second. Example: 20% of 50% = (20 × 50) ÷ 100 = 10%.
How to use this calculator
Enter two percentage values. The calculator returns P% of Q% — the result of applying the first percentage to the second. This is useful for successive discounts, commission calculations, probability, and any scenario where one percentage rate applies to another.
Formula
To find what P% of Q% equals, convert P to its decimal form and multiply by Q%:
$$P\% \text{ of } Q\% = \frac{P \times Q}{100}$$
Equivalently: divide P by 100 to get its decimal, then multiply that decimal by Q. The result is a percentage. Note that the result is always smaller than both P and Q (for positive inputs between 0 and 100) — because a fraction of a fraction is smaller than either fraction alone.
Worked examples
Example 1: 20% of 50%
$$20\% \text{ of } 50\% = \frac{20 \times 50}{100} = 10\%$$
20% of 50% is 10%.
Example 2: tax on commission
A salesperson earns 15% commission on sales. If 30% of that commission goes to income tax, what percentage of the original sale value is paid in tax?
$$30\% \text{ of } 15\% = \frac{30 \times 15}{100} = 4.5\%$$
The tax on the commission equals 4.5% of the original sale value. The salesperson retains 15% − 4.5% = 10.5% net.
Successive discounts and stacked percentages
One of the most important applications of percentage-of-a-percentage is understanding why stacked discounts or rates cannot be added together.
If an item is discounted by A%, and then an additional B% is taken off the already-reduced price, the total discount is:
$$\text{Total discount} = A + B - \frac{A \times B}{100}$$
The subtracted term — A×B/100 — is exactly "A% of B%". Without it, simply adding A and B overstates the combined effect.
Example: 20% off, then 25% off
$$\text{Total discount} = 20 + 25 - \frac{20 \times 25}{100} = 45 - 5 = 40\%$$
The total discount is 40%, not 45%. The 5% difference is 20% of 25% — the amount that was "double-counted" by naive addition.
To verify using the multiplier approach:
$$\text{Effective multiplier} = \left(1 - \frac{A}{100}\right) \times \left(1 - \frac{B}{100}\right)$$
For 20% and 25%: (1 − 0.20) × (1 − 0.25) = 0.80 × 0.75 = 0.60, meaning 60% of the original price remains — confirming a 40% total discount.
Key rule: two successive percentage discounts of A% and B% always give a total discount that is less than A + B. The shortfall is exactly A% of B%.
Common mistakes
Adding stacked percentages instead of compounding them
The most common error is treating successive percentage rates as additive. A 10% discount and an additional 10% discount do not give a 20% total discount — they give a 19% total discount (10 + 10 − 1 = 19), because the second 10% acts on the already-reduced price.
Confusing "P% of Q%" with "P% of a value that is Q%"
"20% of 50%" (this calculator) asks what percentage 20% of 50% represents — the answer is 10%. This is different from "20% of a value, where that value is 50% of something else." Both involve percentage of a percentage, but the framing matters for context.
Treating the result as a percentage point reduction
When a 30% tax rate is applied to a 15% commission, the result (4.5%) is an absolute percentage reduction on the base amount — not a percentage point reduction of the commission rate. Keeping track of what the "base" is at each step prevents errors.
Frequently asked questions
What is the formula for a percentage of a percentage?
P% of Q% = (P × Q) ÷ 100. Convert P to a decimal by dividing by 100, then multiply by Q. Example: 20% of 50% = (20 × 50) ÷ 100 = 10%.
What is 20% of 50%?
10%. Calculation: (20 × 50) ÷ 100 = 10%.
Is a 20% discount followed by a 25% discount the same as 45% off?
No — it is 40% off. The total discount = 20 + 25 − (20% of 25%) = 45 − 5 = 40%. Stacked discounts can never simply be added; the overlap is always P% of Q%.
Why can't you add stacked percentages?
Each successive percentage acts on a smaller base. The second rate applies to the already-reduced value, not the original. Adding them ignores this shrinking base and overstates the combined effect by exactly P% of Q%.
What is 30% of 15%?
4.5%. Calculation: (30 × 15) ÷ 100 = 4.5%.
When do you need to calculate a percentage of a percentage?
Common scenarios: successive retail discounts, commission structures where part of the commission is taxed, probability calculations combining two rates, and VAT or sales tax on a discounted price.