How this instrument works
Taking one percentage of another means treating the first figure as an ordinary number and asking what share of it the second one represents. Convert both to fractions, multiply, and read the product back off as a percent: (p₁ ⁄ 100) × (p₂ ⁄ 100) × 100 = p₁ × p₂ ⁄ 100. The two divisions that arrive from expressing each figure as a fraction collapse into the single division by 100 left standing in the formula, because one factor of 100 comes back when the product is re-expressed on the percent scale.
Fifty percent of twenty percent is ten percent — a result smaller than either number that produced it, since the second figure shrinks whatever base the first one already shrank. The instinct to add the two numbers instead (20 + 50 = 70) is answering a different question, the one about percentage points, not this one. Here the second figure acts ON the first as a scaling factor, the way a tax rate applies to a commission rate rather than sitting beside it as a separate quantity to be summed.
Two boundary cases pin the formula down. Set the first figure to 100 and the second passes straight through unchanged, since taking any percentage of 'the whole' returns that same number — a fixed point worth remembering. Set either field to zero and the result falls to zero regardless of the other figure, the same way multiplying by zero collapses any product. Because multiplication commutes, swapping which figure is called first and which is second never changes the number that comes out, even though the two fields describe different roles in a real scenario.
- Enter the base rate into First percentage — the figure the second percentage will act on, such as a conversion rate, a discount rate, or a survey share.
- Enter the rate being taken of that base into Second percentage (of the first) — a share of the first figure specifically, not of the original 100% total.
- Read Combined percentage: the instrument multiplies the two entries and divides by 100, and shows that exact working beside the result.
- To check it by hand, convert each entry to a decimal, multiply the two decimals together, then move the decimal point of the product two places right.
Worked example — a two-stage conversion funnel
An online store finds that 20% of visitors add a product to their cart; that figure goes into First percentage. Among those cart-adders, 50% go on to complete checkout, entered as Second percentage (of the first). Combined percentage reads 10.0, since 20 × 50 ⁄ 100 = 10 — meaning 10% of ALL visitors end up buying, not 70%, because the checkout rate applies only to the smaller group that already added a cart, not to every visitor who landed on the site.
Run the boundary check the formula itself guarantees: raise First percentage to 100 and Combined percentage still reads 50, since 100 × 50 ⁄ 100 = 50 exactly — any figure taken of the whole passes through unchanged. Drop First percentage to 0 instead and Combined percentage falls to 0 no matter what the second figure says, confirming the formula collapses correctly at both edges of its range.
Questions
Why is 50% of 20% equal to 10%, and not 70%?
Because the second figure multiplies the first rather than adding to it: 50% of 20% means (20 ⁄ 100) × (50 ⁄ 100) × 100 = 10. Adding the two numbers instead (20 + 50 = 70) answers a different question, about percentage points stacked together, not about one percentage taken of another.
Does this calculate two discounts applied one after another?
Not quite — successive discounts multiply what remains of a price each time: 20% off leaves 80% of the price, and a further 50% off that leaves 80% × 50% = 40% of the original, a 60% total discount. This instrument instead finds one percentage taken directly of another, useful for nested rates and shares rather than sequential price cuts.
Does the order of the two percentages matter?
No — multiplication commutes, so p₁ × p₂ ⁄ 100 gives the same number whichever field holds which value; 20% of 50% and 50% of 20% both equal 10%. The two fields still describe different roles in a real scenario, since one is the base and the other is taken of it, even though the arithmetic itself does not care which is which.
What happens if the second percentage is above 100%?
The formula keeps working past 100 without any special case: 150% of 20% is 30%, since 20 × 150 ⁄ 100 = 30 — a larger figure than the 20% base itself, the way '150% of' means one and a half times something in ordinary speech. Percentages above 100% are routine wherever a rate can exceed its own reference point.
How is this different from percentage change or percentage points?
Percentage change measures relative movement away from a starting value, and percentage points is a plain subtraction between two already-percent figures, such as 6% minus 4% equaling 2 points. This calculator does neither — it treats one figure as a straightforward multiplier of another, the way a tax rate might apply to a commission rate rather than to a plain dollar figure.
What if either percentage entered is 0%?
Combined percentage reads 0 regardless of the other field's value, since anything multiplied by zero is zero: 0% of 50% is 0%, and 50% of 0% is likewise 0%. It is the same collapsing behavior any product formula shows at the edges of its range.