Percentage of a Percentage: How Compounding Percentages Work

Why you multiply instead of add

Convert both percentages to decimals and multiply: 20% of 50% = 0.20 × 0.50 = 0.10 = 10%. This calculator's ordinary 'X% of Y' mode does exactly this — enter 20 for X and 50 for Y (treating 50 as the number 50, which represents 50%), and it returns 10, matching the percentage-of-a-percentage answer directly.

Adding percentages together (20% + 50% = 70%) answers a completely different question — it's only correct when you're combining two separate percentages of the same base, not when one percentage is being applied to another percentage.

Where this actually comes up

Compounding discounts: '25% off, plus an extra 10% off' is 10% of the already-discounted 75%, not a flat 35% off. Tax-on-a-fee calculations: a 3% processing fee on an amount that already includes 8% sales tax requires multiplying the two rates' effects together, not summing them. Commission on commission, interest on a fee, or any scenario where one percentage rate is applied on top of another all follow this same multiply-don't-add rule.

The stacked-discount example is the most common real-world version: 25% off then an extra 10% off works out to a 32.5% total discount (multiply 0.75 × 0.90 = 0.675, so you pay 67.5% — a 32.5% discount), not the 35% naive addition would suggest.

The quick mental check

If the answer to 'X% of Y%' ever comes out larger than both X and Y individually, something's wrong — multiplying two percentages (each under 100%) always produces a result smaller than either one alone, since you're taking a fraction of a fraction. That's a fast sanity check that catches the 'I added instead of multiplied' mistake before it costs real money.