"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 mistake is forgetting to convert the percentage to a decimal before multiplying — treating "20% of 85" as 20 × 85 instead of 0.20 × 85, which overshoots by a factor of 100. A close second is applying the percentage to the wrong base number, especially in percent-off or percent-more situations: 20% off $50 means subtracting 20% of the original $50, not 20% of some other figure, and stacking two percentage changes (say, a 10% increase followed by a 10% decrease) does not bring you back to the original number, because the second 10% is calculated on a different, already-changed base.
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, because a rough check catches typos and misplaced decimal points fast. 10% of any number just moves the decimal point one place left (10% of 85 = 8.5), and every other common percentage can be built from that: 20% is double 10%, 5% is half of 10%, 15% is 10% plus 5%. Estimating 20% of 85 as "roughly 17" before computing it exactly is a fast sanity check against a fat-fingered calculator entry.
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. For the reasoning behind both worked out in more depth with additional practice examples, see the How to Calculate a Percentage guide.