Percentage Calculator

What this calculator does

So, a percentage question turns up, and there are really only three of them wearing different clothes. What is 20% of this bill? This score is what percent of that total? And how far did this number move from last month to now? This one tool answers all three.

Pick the question that matches yours from the dropdown, type your two numbers, and it works it out.

What "percent" means

The word comes from the Latin per centum, meaning "per hundred", and that is all a percent is: a count out of a hundred. 25% is 25 out of 100, which is the fraction 25/100, the decimal 0.25, or a quarter. Writing everything out of the same 100 is what makes percentages so handy: a 20% discount, a 3% interest rate and a 19% tax all sit on the same scale, so you can compare them at a glance without hunting for a common denominator.

Using the calculator

1. Choose the calculation type from the dropdown. The input boxes change to suit it.
2. Type your two numbers.
3. Press Calculate.

The first two questions give a plain number; the change question gives a percentage, positive for an increase and negative for a decrease.

The three questions, and their formulas

Each one is a single short calculation.

• What is X% of Y? Finding a part of a total: a discount, a tip, a tax. The formula is (X ÷ 100) × Y.
• X is what percent of Y? Finding a proportion: a test score, a market share, how much of a budget is spent. The formula is (X ÷ Y) × 100.
• Percentage increase or decrease from X to Y? Finding a change between a starting value X and an ending value Y. The formula is ((Y − X) ÷ X) × 100.

Three worked examples

One of each, to see the formulas in action.

• What is 20% of 150? (20 ÷ 100) × 150 = 0.2 × 150 = 30. A 20% discount on a 150 item saves 30.
• 30 is what percent of 150? (30 ÷ 150) × 100 = 0.2 × 100 = 20%. Scoring 30 out of 150 is 20%.
• Change from 80 to 100? ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%, an increase.

A caution: the starting number matters

For a change, the answer is always measured against the starting value, the one you began with. That has a consequence people often miss: a rise and a fall that look the same size do not cancel out. Going from 100 up to 200 is a 100% increase, but coming back from 200 down to 100 is only a 50% decrease, because the second change is measured against the larger starting number, 200. The percentage always depends on where you started.

Going deeper

This is the all-in-one tool. For a single kind of problem with more room to explain it, there are focused tools: the percent increase calculator, the percent decrease calculator, and the percent change calculator. To move between forms, see the decimal to percent and percent to fraction calculators.

Questions people ask

How do I find X% of a number?

Divide the percent by 100 and multiply by the number. For 20% of 150: (20 ÷ 100) × 150 = 30.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100. For 30 out of 150: (30 ÷ 150) × 100 = 20%.

How do I find the percentage change between two numbers?

Subtract the old from the new, divide by the old, and multiply by 100. A positive answer is an increase, a negative one a decrease.

What does percent actually mean?

Per hundred. 25% is 25 out of 100, the same as 25/100 or 0.25.

Why doesn't a 100% rise and then a 50% fall cancel out?

Because each change is measured against its own starting value. The rise is measured against the smaller number and the fall against the larger one, so they are not the same size.

References

A note on the idea behind it. A percentage is a fraction with a fixed denominator of 100, from the Latin per centum, "per hundred". The three standard forms, a part of a total, a proportion, and a change relative to a starting value, cover almost every everyday percentage problem. For further reading, see Percentage.

1. Percent, from Latin per centum ("per hundred"), a fraction expressed out of 100.