Percentage calculator.

What is a percentage?

A percentage is a number expressed as a fraction of 100. The word comes from per cent, meaning per hundred, and the symbol is %. Saying 35% is the same as saying 35 out of 100, the decimal 0.35, or the fraction 35 over 100. It is just a tidy way to describe a part of a whole.

Because every percentage is out of the same 100, percentages make different quantities easy to compare. That is why they turn up everywhere, from discounts and tips to interest rates, test scores and statistics.

The percentage formula

Almost every percentage question comes from one relationship: the percentage times the first value equals the second value, or P times V1 equals V2. Give the calculator any two of those three and it solves for the third, which is exactly what the tools on this page do.

To find a percent of a number, convert the percent to a decimal by dividing by 100, then multiply. To find what percent one number is of another, divide the part by the whole and multiply by 100. To find the whole from a part and a percent, divide the part by the percent in decimal form.

How to find a percentage of a number

This is the most common question, and the calculator at the top handles it. Divide the percent by 100 and multiply by the value. For 20% of 80, that is 0.20 times 80, which is 16. A quick mental shortcut: 10% is the number with the decimal point moved one place left, so 10% of 80 is 8, and 20% is double that, 16.

The same method works for tips and discounts. A 15% tip on a $40 bill is 0.15 times 40, which is $6.

Percentage change: increase and decrease

Percentage change measures how much a value has gone up or down from a starting point. Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive answer is an increase, a negative answer is a decrease. Going from 100 to 150 is a 50% increase; going from 150 to 100 is a 33.3% decrease.

Notice the two are not the same size, because each is measured against a different starting number. That asymmetry catches a lot of people out, so it is worth checking which value is the starting point.

Percentage difference versus percentage change

Percentage difference compares two values when neither is obviously the starting point. You divide the absolute difference between them by their average, then multiply by 100. For 10 and 6, the difference is 4 and the average is 8, so the percentage difference is 50%.

Use percentage change when one value comes before the other, like a price last month and this month. Use percentage difference when you are simply comparing two separate values, like two measurements. They answer different questions and usually give different numbers.

Everyday uses

Percentages run through daily life: a discount in a sale, the tip on a meal, the interest on a loan or savings account, sales tax added at the till, a grade on a test, or the change in a price or a portfolio. Getting comfortable moving between a percent, a decimal and a fraction makes all of these quicker.

When a problem feels fiddly, come back to the one formula, P times V1 equals V2, decide which value you are missing, and let the calculator do the arithmetic.