Percentage Calculator

What is a percent?

"Percent" means per hundred — the % symbol is shorthand for dividing by 100. Saying "20%" is the same as saying "20 out of every 100," or the decimal 0.20. Every percentage problem, no matter how it's phrased, boils down to one equation with three parts: a percent (P%), a whole (X), and a part (Y).

$Y = P\% \times X$

Know any two of the three values and you can always solve for the third. That's exactly what this calculator does — pick the question you're asking, and it rearranges the equation for you.

The three percent problems

1. Find the part — "P% of X"

This is the most common percent question: a discount, a tip, a tax, a share of a total.

Example — a $150 jacket, 10% off. How much is deducted?

1. Convert 10% to a decimal: 10 ÷ 100 = 0.10.
2. Multiply by the whole: 0.10 × 150 = 15.

10% of $150 is$15.

Example — a $45 bill, 15% tip.

1. 15% = 0.15.
2. 0.15 × 45 = 6.75.

The tip is $6.75.

2. Find the percent — "Y is what % of X?"

Use this when you have a part and a whole and want to know the share as a percentage.

Example — nutrition label. A serving has 12 mg of a nutrient; the daily target is 60 mg. What percent of the target is that?

1. Divide the part by the whole: 12 ÷ 60 = 0.20.
2. Multiply by 100: 0.20 × 100 = 20%.

12 mg is 20% of the 60 mg target.

Example — 6 out of 27 trees have fruit.

1. 6 ÷ 27 = 0.2222….
2. 0.2222… × 100 ≈ 22.22%.

About 22.22% of the trees have fruit. Answers like this round to two decimal places.

3. Find the whole — "Y is P% of what?"

Use this when you know a part and its percentage share, and need the total.

Example — 65 lb is 26% of your usual bench press. What's the usual weight?

1. Convert 26% to a decimal: 0.26.
2. Divide the part by that decimal: 65 ÷ 0.26 = 250.

Your usual bench press is 250 lb.

Example — 9 vanilla cupcakes need to be 60% of a batch.

1. 60% = 0.60.
2. 9 ÷ 0.60 = 15.

You need 15 cupcakes total for 9 of them to be 60%.

Always convert the percent to a decimal first

Forgetting this conversion is why calculations come out 100 times too big or too small. 10% of 150 is 15, not 1500 — the percent has to shrink to 0.10 before it touches the whole number.

Common mistakes

• Multiplying by the raw percent instead of the decimal. 10% of 150 is 0.10 × 150, not 10 × 150.
• Mixing up the part and the whole. The number right after "of" is the whole (X). Reversing part and whole gives an answer that's wildly off.
• Rounding too early. Round only the final answer — rounding 6 ÷ 27 to 0.22 before multiplying by 100 loses precision that shows up in the last digit.

Where percentages show up

• Shopping and discounts — "20% off" is easier to reason about once you can convert it to a dollar amount.
• Grades and test scores — a raw score like 27 out of 32 converts to a percentage for easy comparison.
• Finance — interest rates, tips, and taxes are all percent-of-a-number problems.
• Statistics — expressing a part of a population as a percentage of the whole.