MethodCalculator

Percentage Calculator

Three everyday percentage problems in one place. Fill in any form below and the answer appears instantly, with the arithmetic explained underneath.

What is X% of Y?
%

20% of 150 = 3020 ÷ 100 × 150 = 30

X is what percent of Y?

30 is 20% of 15030 ÷ 150 × 100 = 20%

Percentage change from X to Y

From 50 to 75 is an increase of 50%(75 − 50) ÷ |50| × 100 = 50%

Results update as you type.

What is a percentage?

A percentage is a fraction with 100 as the denominator. "Per cent" literally means "per hundred", so 20% is the same as 20/100, 0.2 or one fifth. Percentages make quantities of different sizes comparable: a 5% pay rise means the same proportion whether you earn $30,000 or $300,000. Because every percentage is just a decimal in disguise, all percentage problems reduce to multiplying or dividing by that decimal.

The three percentage formulas

1. Percentage of a number. X% of Y = (X ÷ 100) × Y

Example: 20% of 150 = 0.20 × 150 = 30. This is the form you use for tips, discounts and interest.

2. Finding the percentage. X is (X ÷ Y) × 100 percent of Y

Example: 30 out of 150 = 30 ÷ 150 = 0.2, and 0.2 × 100 = 20%. Use this for test scores, market share and "what fraction of my budget" questions.

3. Percentage change. change = (new − old) ÷ |old| × 100

Example: a price goes from 50 to 75: (75 − 50) ÷ 50 = 0.5, so the price rose by 50%. A negative result means a decrease. The old value is always the base, which is why a rise and an equal-sized fall do not cancel out.

How to use this calculator

  1. Pick the form that matches your question. If you know the percentage and the base, use the first form.
  2. Type the two numbers. Decimals and negative numbers are accepted.
  3. Read the answer and the one-line working under it. Press Reset to restore the example values.

Common mistakes

  • Using the wrong base. Percentage change always divides by the starting value, not the ending one.
  • Adding percentages of different bases. 10% of your rent plus 10% of your food bill is not 20% of anything.
  • Confusing percent and percentage points. Moving from 4% to 6% is a 2-point rise but a 50% increase.
  • Reverse discounts. If a $60 price is already 25% off, the original was 60 ÷ 0.75 = $80, not 60 × 1.25 = $75.

Need the same ideas with fractions or ratios? See the fraction calculator and the ratio calculator.

Frequently asked questions

How do I calculate a percentage of a number?

Convert the percentage to a decimal by dividing by 100, then multiply. For 20% of 150, compute 0.20 × 150 = 30. On a calculator you can also type 150 × 20 % and most models return 30 directly.

What is the difference between percentage change and percentage points?

Percentage change compares the new value to the old one as a ratio: going from 10% to 15% is a 50% increase. Percentage points measure the plain difference between two percentages: 15% minus 10% is 5 percentage points. News reports often mix the two, so check which one is meant.

Why can a 50% increase followed by a 50% decrease leave me below where I started?

Because each change is measured against a different base. 100 increased by 50% is 150. Decreasing 150 by 50% removes 75, leaving 25 less than the original 100. To undo a 50% increase you need a decrease of only 33.3%.

How do I calculate a discount or a price with tax?

For a discount, multiply the price by (100 − discount%) ÷ 100: a $80 item at 25% off costs 80 × 0.75 = $60. For tax, multiply by (100 + tax%) ÷ 100. The sales tax calculator on this site handles the tax case, including working backwards from a total.

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