What is a percentage?

A percentage is a way of writing a number as a part of 100. The word comes from the Latin per centum, which means "by the hundred". So 25% means 25 out of every 100, which is the same as the fraction 1/4 or the decimal 0.25. Percentages make it easy to compare amounts of different sizes, which is why they appear in discounts, taxes, test scores, interest rates, nutrition labels, news reports and business results.

How this percentage calculator works

The calculator has five modes. Choose the question that matches your problem, enter two numbers and press Calculate. It also shows the calculation step by step so that you can check it yourself.

• What is X% of Y? Result = X ÷ 100 × Y. Example: 15% of 80 = 15 ÷ 100 × 80 = 12.
• X is what % of Y? Result = X ÷ Y × 100. Example: 12 is 15% of 80, because 12 ÷ 80 × 100 = 15.
• Percentage change from X to Y. Result = (Y − X) ÷ X × 100. Example: from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase.
• Increase a number by X%. Result = number × (1 + X ÷ 100). Example: 50 increased by 20% = 60.
• Decrease a number by X%. Result = number × (1 − X ÷ 100). Example: 50 decreased by 20% = 40.

How to use the calculator

1. Pick the question you want to answer from the drop-down list.
2. Type your two numbers into the boxes. The labels change to match the mode you chose.
3. Press Calculate (or the Enter key) to see the result and the step-by-step calculation.
4. Look at the table below the calculator for common percentages of your number, such as 10%, 20% or 25%.

Worked examples

Discount. A jacket costs $120 and is 30% off. The discount is 30% of 120 = $36, so you pay 120 − 36 = $84. You can also multiply by 70% (100% − 30%): 120 × 0.70 = $84.

Tax and tip. A restaurant meal costs $45. With 8% sales tax the tax is $3.60 and the total is $48.60. An 18% tip on $45 is $8.10.

Test score. You answered 42 questions correctly out of 50. The score is 42 ÷ 50 × 100 = 84%.

Price change. A product rises from $80 to $100. The change is $20, and 20 ÷ 80 × 100 = a 25% increase.

Why a 20% increase and a 20% decrease do not cancel out

This is one of the most common surprises with percentages. Start with $100 and increase it by 20%: you get $120. Now decrease $120 by 20%: you lose $24 and end up with $96, not $100. The second percentage is taken from a larger number, so the decrease is bigger in dollars. For the same reason, a price that rises from $80 to $100 is a 25% increase, but falling from $100 back to $80 is only a 20% decrease. Always check which number is the starting point, because percentage change is always measured against the starting value.

Percentage points and percent are different

When one percentage changes to another, there are two different ways to describe the change. If a loan rate rises from 4% to 6%, it went up by 2 percentage points (6 − 4). In relative terms it rose by 50%, because 2 ÷ 4 × 100 = 50. News stories and reports sometimes mix these up, so look carefully at the wording. You can use mode 3 of this calculator to find the relative change between two percentages.

Where you will use percentages in everyday life

• Shopping: sale prices, coupons and "buy more, save more" offers.
• Money: interest on savings, loan rates, investment returns and inflation. Try our Compound Interest Calculator or Loan Payment Calculator.
• Work and school: grades, pay raises, commissions and project progress.
• Health and cooking: nutrition labels, recipe scaling and body measurements.
• Statistics and news: poll results, unemployment rates and population growth.

Quick mental math tricks

• 10%: move the decimal point one place to the left. 10% of 60 is 6.
• 5%: take half of 10%. 5% of 60 is 3.
• 15%: add 10% and 5%. 15% of 60 is 6 + 3 = 9.
• 1%: move the decimal point two places to the left. 1% of 250 is 2.5.
• 25%: divide by 4. 25% of 80 is 20.
• 50%: divide by 2.

Common mistakes to avoid

• Using the wrong base. Percentage change is always divided by the starting value, not the new value.
• Adding percentages together. A 10% discount followed by another 10% discount is 19% in total, not 20%, because the second discount applies to the reduced price.
• Mixing percent and percentage points. See the section above.
• Forgetting to convert. To use a percentage in a formula, divide by 100 first. For example, 7% becomes 0.07.
• Rounding too early. Keep extra decimal places during the calculation and round only the final answer.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For example, 35% of 200 is 0.35 × 200 = 70. In this calculator, choose "What is X% of Y?".

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

Divide the first number by the second and multiply by 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.

How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, and multiply by 100. If the answer is negative, it is a decrease. Use the "Percentage change" mode to do this automatically.

Can a percentage be more than 100%?

Yes. A percentage over 100% means more than the whole. For example, if sales double, they have increased by 100%, and the new amount is 200% of the old amount.

Is my information stored?

No. All calculations run in your web browser and nothing you type is sent to our servers.

Helpful resources

• What Is Percent Change? (Robert Niles, Statistics Every Writer Should Know): a clear explanation of percent change and percentage points.
• Loan Payment Calculator and Compound Interest Calculator on this site: put percentages to work with loans and savings.

This calculator is for general information only. Always double-check important figures. See our Terms & Disclaimer.