How to Calculate Percentages (The Formulas, in Plain English)

Percentages turn up everywhere: the tip on a dinner bill, the discount in a shop, the score on a test, the interest on a loan. The math behind them is genuinely simple once you see the few patterns it follows. This guide breaks down the three calculations you will use most, with plain everyday examples, and then points you to a tool that does the arithmetic for you.

The one idea behind every percentage

A percent is just a number out of 100. “25 percent” means 25 out of every 100, which is the same as the fraction 25/100, or 0.25 as a decimal. That single conversion, percent to decimal by dividing by 100, is the key that unlocks every formula below.

Once a percentage is a decimal, you can multiply and divide with it like any other number. That is really all there is to it.

Finding X percent of a number

This is the most common question: what is a given percentage of some amount? The formula is direct.

X percent of Y = (X divided by 100) times Y.

Worked examples:

• A 20 percent tip on a 45 dollar bill: 0.20 times 45 = 9 dollars.
• 15 percent off a 60 dollar jacket: 0.15 times 60 = 9 dollars off.
• 8 percent tax on a 250 dollar purchase: 0.08 times 250 = 20 dollars.

The pattern never changes. Convert the percent to a decimal, then multiply by the amount.

Finding what percent one number is of another

Sometimes you have two numbers and want to know how they relate. You got 42 questions right out of 50, so what is your score as a percentage?

X is (X divided by Y) times 100 percent of Y.

Worked examples:

• 42 out of 50 on a test: (42 divided by 50) times 100 = 84 percent.
• 3 sales from 12 calls: (3 divided by 12) times 100 = 25 percent.
• 180 dollars saved of a 600 dollar goal: (180 divided by 600) times 100 = 30 percent.

Divide the part by the whole, then multiply by 100 to turn it back into a percentage.

Percentage increase and decrease

Prices rise, populations grow, and bills get marked down. To express a change as a percentage, compare the change to where you started.

Percent change = (new value minus old value) divided by old value, times 100.

A positive result is an increase, a negative one is a decrease.

• A rent that went from 1000 to 1100: (1100 minus 1000) divided by 1000 times 100 = 10 percent increase.
• A price cut from 80 to 60: (60 minus 80) divided by 80 times 100 = 25 percent decrease.
• A salary raised from 50000 to 54000: (54000 minus 50000) divided by 50000 times 100 = 8 percent increase.

Always divide by the original value, not the new one. That is the mistake people make most often.

Skip the arithmetic entirely

Knowing the formulas is useful, but you do not have to run them by hand every time. The free Percentage Calculator handles all three cases, percent of a number, one number as a percent of another, and percent change, in a single tool.

Type in your numbers and read off the answer. The Percentage Calculator runs entirely in your browser, so there is no sign-up and nothing you enter is sent anywhere. It is the quickest way to check a tip, confirm a discount, or work out a grade without second-guessing your math.

Related calculators

Percentages branch into a few specific everyday jobs, and there is a focused tool for each. When you are shopping a sale, the Discount Calculator tells you the final price after a markdown in one step. To turn a set of numbers into a single representative figure, the Average Calculator adds them up and divides for you. And if you deal with tax-inclusive pricing, the VAT Calculator adds or removes value-added tax cleanly.

The short version

To calculate a percentage: convert the percent to a decimal, then multiply or divide depending on the question. Use “percent of a number” for tips and tax, “one number as a percent of another” for scores, and “percent change” for increases and decreases. When you would rather not do it by hand, the Percentage Calculator gives you the answer in seconds.