How to Calculate Percentage: Formulas and Real-Life Examples

Percentages show up everywhere: discounts, taxes, exam scores, interest and growth. The math is simple once you know which formula to use. This guide covers the common percentage calculations with worked examples, and you can check each one with the percentage calculator.

What a percentage means

Percent means "per hundred". So 25% means 25 out of every 100, which is 0.25 as a decimal or 25/100 as a fraction. To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100.

Find a percentage of a number

Formula: part = (percentage / 100) x whole

Example: what is 15% of 800? (15 / 100) x 800 = 0.15 x 800 = 120.

Find what percentage one number is of another

Formula: percentage = (part / whole) x 100

Example: you scored 42 out of 60. (42 / 60) x 100 = 0.7 x 100 = 70%.

Percentage increase and decrease

Formula: percentage change = ((new value - old value) / old value) x 100

• Increase: a salary rises from 50,000 to 55,000. (55,000 - 50,000) / 50,000 x 100 = 10% increase.
• Decrease: a price falls from 200 to 150. (150 - 200) / 200 x 100 = -25%, a 25% decrease.

Discounts and final price

Formula: final price = original price x (1 - discount / 100)

Example: a jacket costs 3,000 and has a 20% discount. 3,000 x (1 - 0.20) = 3,000 x 0.80 = 2,400. You save 600.

Adding tax or a markup

Formula: total = price x (1 + rate / 100)

Example: an item costs 1,000 with 18% tax. 1,000 x 1.18 = 1,180.

Percentage points vs percent

If an interest rate rises from 4% to 6%, that is an increase of 2 percentage points, but a 50% increase in the rate ((6 - 4) / 4 x 100). Mixing these up is a common source of confusion in news and reports.

Check your work

Enter your numbers in the Percentage Calculator to confirm the answer, and use a quick estimate to see if it is reasonable: 10% of a number is that number divided by 10.

Practice problems

• What is 35% of 240? (Answer: 84)
• A price rises from 80 to 100. What is the percentage increase? (Answer: 25%)
• A phone costs 20,000 with a 15% discount. What do you pay? (Answer: 17,000)

Frequently asked questions

Why is a 50% increase followed by a 50% decrease not back to the start?

Because the second percentage applies to a bigger number. 100 up 50% is 150, and 150 down 50% is 75, not 100.

How do I calculate the original price after a discount?

Divide the discounted price by (1 - discount rate). If a 20% discount gives 2,400, the original was 2,400 / 0.80 = 3,000.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value with an old one in a direction. Percentage difference compares two values symmetrically, without treating either as the starting point.