Why percentages trip people up
Percentages appear everywhere, from discounts and taxes to grades and pay raises, yet "how to calculate percentage" is among the most searched math questions online. The good news is that almost every situation uses one of five simple formulas.
1. Percent of a number
Multiply the number by the percent and divide by 100. 15% of 200 is 200 × 15 ÷ 100 = 30. A quick mental trick: 10% is the number with the decimal moved one place left, so 10% of 200 is 20, and 5% is half of that. Our percentage calculator does it instantly.
2. What percent one number is of another
Divide the part by the whole and multiply by 100. If you answered 42 of 50 questions correctly, 42 ÷ 50 × 100 = 84%. The grade percentage calculator applies exactly this formula.
3. Percentage change
Subtract the old value from the new value, divide by the old value and multiply by 100. A price going from $80 to $100 is a (100 − 80) ÷ 80 × 100 = 25% increase. Going back from $100 to $80 is a 20% decrease, not 25%, because the starting value changed. Try our percentage change calculator.
4. Reverse percentages
If a price including 20% tax is $120, the original price isn't $120 minus 20%. Divide by 1.20 instead: $120 ÷ 1.2 = $100. The same method finds the original price before a discount: a $60 item after 25% off was $60 ÷ 0.75 = $80.
5. Adding or subtracting a percentage
To add a percentage, multiply by (1 + rate). To subtract it, multiply by (1 − rate). A $50 meal with an 18% tip is $50 × 1.18 = $59. A $120 jacket at 25% off is $120 × 0.75 = $90.
Percentage points vs. percent
If an interest rate rises from 4% to 5%, it increased by one percentage point, but by 25% in relative terms. News reports often mix the two, so check which one is meant.
Practice makes it automatic
Use these formulas a few times with real receipts and they quickly become second nature. For anything important, double-check with a calculator.
Frequently asked questions
How do I calculate 15% of a number?
Multiply the number by 0.15; for example 200 × 0.15 = 30.
How do I calculate percentage increase?
(New − old) ÷ old × 100.
How do I find the original price before a discount?
Divide the sale price by (1 − discount rate).
What is a percentage point?
The simple difference between two percentages, such as 4% to 5% = 1 percentage point.