Percentage Calculator

How the percentage calculator works

"Percent" means "per hundred", so a percentage is just a fraction with 100 as the denominator: 15% is 15/100, or 0.15. Every percentage problem links three quantities — the part, the whole and the percentage — through one relationship. If you know any two, you can find the third. The calculator rearranges that relationship depending on which question you choose.

part = (percentage ÷ 100) × whole
percentage = (part ÷ whole) × 100
whole = part ÷ (percentage ÷ 100)

Internally the tool uses full floating-point precision and only rounds for display (up to four decimal places, with thousands separators). Negative numbers and decimals are accepted, so you can work with refunds, temperatures below zero or fractional percentages such as 2.75%.

Worked examples

Example 1: What is 15% of 80?

Convert 15% to a decimal (0.15) and multiply: 0.15 × 80 = 12. This is the classic tip or discount calculation — a 15% tip on an $80 bill is $12.

Example 2: 12 is what percent of 48?

Divide the part by the whole and multiply by 100: 12 ÷ 48 = 0.25, and 0.25 × 100 = 25%. If you answered 12 questions right out of 48, you scored 25%.

Example 3: 30 is 25% of what number?

Divide the part by the percentage as a decimal: 30 ÷ 0.25 = 120. If a $30 deposit is 25% of the total price, the full price is $120.

How to read the result

The large number is the answer to the question you selected. Below it, the bar shows the percentage visually against a full 100% bar, which helps you sanity-check the size: if you asked for 15% of something, the bar should be a little under a sixth full. The line underneath shows the exact arithmetic so you can repeat it by hand or on a phone calculator.

When a percentage is above 100%, the bar is shown full because the part is larger than the whole. That is not an error: 150% of 40 is 60, and 60 is 150% of 40. Percentages above 100 are common in growth figures, markups and year-over-year comparisons.

Choosing the right question type

Most mistakes with percentages come from picking the wrong base, not from bad arithmetic. A quick way to decide is to look for the word "of" — the number that follows "of" is usually the whole. "What is 20% of 250?" has 250 as the whole. "45 is what percent of 60?" has 60 as the whole. "18 is 30% of what?" means the whole is the unknown.

• What is X% of Y? — discounts, tips, sales tax, commission, portions of a budget.
• X is what % of Y? — test scores, survey results, market share, how much of a goal you have reached.
• X is Y% of what? — working backwards from a deposit, a tax amount or a sample to the full total.

Limits of the formula

The formulas are exact, but the answer is only as meaningful as the base you give it. A percentage of zero is always zero, and asking "X is what percent of 0" has no answer because dividing by zero is undefined — the calculator will tell you so instead of showing a misleading number. Likewise, "X is 0% of what" has no solution.

Be careful when chaining percentages. Taking 10% off and then adding 10% does not return you to the start: 100 → 90 → 99. For questions about how much something went up or down, use the percentage change calculator; for applying a rise or a cut to a starting number, use the increase or decrease calculators. Finally, displayed values are rounded to four decimal places, so for money you may want to round to cents yourself according to your local rules.

Quick mental-math tricks

To find 10% of any number, move the decimal point one place left (10% of 340 is 34). From there, 5% is half of that (17), 20% is double (68) and 15% is 10% plus 5% (51). Percentages are also reversible: 8% of 50 is the same as 50% of 8, which is 4. These shortcuts are handy for checking that the calculator's answer is in the right ballpark.