"Percentage" questions actually come in three different shapes, and most of the confusion around percentages comes from applying the wrong one. This calculator handles the two most common: finding what percentage one number is of another ("30 is what percent of 150?"), and finding a percentage of a number ("what is 20% of 85?"). Both use the same underlying relationship — percent means "per hundred" — just rearranged depending on which piece is missing.
The Two Formulas
To find what percent A is of B, divide A by B and multiply by 100: (A ÷ B) × 100. If 30 students out of 150 chose art class, that's (30 ÷ 150) × 100 = 20%. To find a percentage of a number, convert the percentage to a decimal (divide by 100) and multiply: 20% of 85 is 0.20 × 85 = 17. Both directions rely on the same fact — that a percentage is just a fraction with a denominator of 100 — but going from "part and whole" to "percent" divides first, while going from "percent and whole" to "part" multiplies first, and mixing that order up is the single most common source of wrong answers.
Worked example one: a shirt normally costs $40, and you want to know what $6 in savings represents as a percentage. (6 ÷ 40) × 100 = 15%. Worked example two: a recipe calls for 250g of flour, and you want 30% more for a bigger batch. 30% of 250 is 0.30 × 250 = 75g, so the new total is 250 + 75 = 325g.
Common Mistakes With Percentages
The most common slip-up happens at the multiplication step itself — skipping the decimal conversion and running "20% of 85" as a straight 20 × 85 rather than 0.20 × 85, which inflates the answer a hundredfold without anyone noticing the mistake at a glance. Right behind it is applying a percentage to the wrong base: 20% off a $50 item means removing 20% of that original $50, not 20% of the discounted price, and two stacked changes (a discount followed by a markup, say) never cancel out cleanly, because the second percentage is always computed against an already-shifted number.
Tips, Tax, and Interest
Percentages also show up constantly in situations where the "whole" isn't obviously stated — tip calculations, sales tax, and interest are all percentage-of-a-number problems wearing different clothes. A 18% tip on a $64 bill is 0.18 × 64 = $11.52; a 7% sales tax on a $200 purchase is 0.07 × 200 = $14. Interest is the same mechanic repeated over time: simple interest on a loan is just principal × rate × time, applying the percentage-of-a-number formula once per period rather than compounding it, which is why simple interest grows in a straight line while compound interest curves upward — each period's interest gets calculated on a slightly larger base than the last.
It's also worth being comfortable estimating percentages roughly before reaching for exact arithmetic, since a quick mental check is often what catches a mistyped digit before it becomes a wrong final answer. A tenth of anything is just its digits shifted one place — 224 at 10% is roughly 22 — and most other round percentages branch off that same anchor point without much extra work. Sanity-checking a computed answer against that rough mental estimate takes only a second and catches a surprising number of fat-fingered entries before they go unnoticed.
If what you actually need is percentage *change* — how much a number has grown or shrunk between two values — that's a related but distinctly different calculation, covered by the Percentage Change Calculator, since it uses the original value as the base rather than treating the two numbers as an unordered part-and-whole. The dedicated percentage learn guide covers both formulas from this page in additional depth, with further practice examples.