Percentage Calculator

What is a percentage calculator?

A percentage calculator solves the percentage problems you meet every day: how much is 20 percent of a price, what percent a test score is, or by how much a value has gone up or down. Enter two numbers, choose the type of question and the answer appears instantly, together with a short sentence and the formula behind it.

A percentage is simply a number out of 100. The word comes from the Latin per centum, which means by the hundred. So 25 percent means 25 out of every 100, or one quarter. Because the idea is so simple, percentages are used everywhere, from shop discounts and tax to interest rates, exam marks and statistics.

Percentage formulas you need to know

These six formulas cover almost every percentage question. Our calculator uses them for you, but it helps to know what happens behind the screen.

• Percent of a number: Percentage / 100 x Number. For example, 20% of 500 is 20 / 100 x 500 = 100.
• What percent one number is of another: Part / Total x 100. For example, 45 out of 60 is 45 / 60 x 100 = 75%.
• Percentage change: (New value - Old value) / Old value x 100. For example, a rise from 80 to 100 is 25%.
• Increase by a percentage: Number x (1 + Percentage / 100). For example, 200 increased by 15% is 230.
• Decrease by a percentage: Number x (1 - Percentage / 100). For example, 200 decreased by 15% is 170.
• Find the total from a part: Part / (Percentage / 100). For example, if 30 is 12% of a number, the number is 250.

How to calculate a percentage step by step

Take the question: what is 25 percent of 80? Divide 25 by 100 to get 0.25, then multiply 0.25 by 80. The answer is 20. A quick trick is to find 10 percent first by moving the decimal point one place to the left, so 10 percent of 80 is 8. Then build the rest: 20 percent is 16, and 5 percent is half of 10 percent, which is 4, so 25 percent is 20.

To find what percent one number is of another, divide the part by the whole and multiply by 100. If you scored 432 out of 600, divide 432 by 600 to get 0.72, then multiply by 100 to get 72 percent.

Percentage increase and decrease

Percentage change tells you how much a value has grown or shrunk compared with where it started. Subtract the old value from the new value, divide by the old value and multiply by 100. A positive result is an increase and a negative result is a decrease.

Notice that the starting point matters. A price that rises from 80 to 100 has gone up by 25 percent, but a price that falls from 100 back to 80 has dropped by only 20 percent. The same gap of 20 is a different percentage depending on the number you start from. For the same reason, adding 10 percent and then taking away 10 percent does not bring you back to the start: 100 becomes 110, then 99.

Percentage calculator for discounts, tax and tips

Most everyday uses of percentages are about money. Here is how to handle the common cases:

• Discounts: To find the sale price, decrease the original price by the discount percentage. A 25% discount on 80 saves 20 and leaves a price of 60.
• Sales tax or VAT: To add tax, increase the price by the tax rate. At 8% tax, a price of 50 becomes 54.
• Tips: To work out a tip, find the percentage of the bill. A 15% tip on a bill of 40 is 6.
• Profit and markup: Percentage change shows how much a selling price is above the cost price.
• Interest: A rate of 5% a year on 1,000 adds 50 in one year before compounding.

Percentages for students: marks and grades

Teachers often give marks as a number out of a total. To convert them, use the what percent formula. A score of 72 out of 90 is 72 / 90 x 100 = 80%. To see how a test counts towards a final grade, find the percent of the weighting: a test worth 30 percent of the course and scored at 80 percent adds 24 points to the final grade.

Percent and percentage points are not the same

When a rate moves from 4 percent to 6 percent, it has risen by 2 percentage points, but it has increased by 50 percent compared with the old rate. News reports and financial documents mix these up all the time, so always check which one is meant. Use percentage change for relative differences and plain subtraction for percentage points.

Common percentage mistakes

• Dividing by the wrong number: Percentage change always divides by the old value, not the new one.
• Forgetting to divide by 100: 20 percent is 0.20 in a calculation, not 20.
• Adding percentages with different bases: A 10% discount followed by another 10% is 19% off in total, not 20%.
• Mixing up percent and percentage points: They describe different things, as explained above.
• Rounding too early: Round only the final answer to avoid small errors.

Why use our free percentage calculator?

• Five calculators in one: Percent of a number, what percent, percentage change, increase or decrease, and finding the total.
• Instant results: The answer updates as soon as you type.
• Clear steps: You see the sentence and the formula, so you can learn and check your work.
• Private: Your numbers stay in your browser and are never uploaded.
• Free: No signup, no limits and nothing to install.