How to calculate a percentage: 5 formulas with examples (of, change, increase, decrease)
Percentages come up in prices, grades, discounts and growth. These five formulas cover nearly every case.
1. What is X% of Y?
Y × X ÷ 100. 20% of 150 = 150 × 20 ÷ 100 = 30.
2. X is what percent of Y?
X ÷ Y × 100. 45 out of 60 = 45 ÷ 60 × 100 = 75%.
Skip the maths, try your own numbersPercentage CalculatorFree, instant, no sign-up →3. Percentage change
(new − old) ÷ old × 100. A price moving from 80 to 92 is (92 − 80) ÷ 80 × 100 = +15%. A negative result is a decrease.
4. Increase by a percentage
value × (1 + X ÷ 100). 200 increased by 12% = 200 × 1.12 = 224.
5. Decrease by a percentage
value × (1 − X ÷ 100). A 30% discount on 80 = 80 × 0.70 = 56.
The mistake to avoid
Percent increases and decreases are not symmetrical. Raise 100 by 20% and you get 120. Cut 120 by 20% and you get 96, not 100. To undo a 20% rise you need a cut of 16.7%.
Also keep percent and percentage points apart. A rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate.
Type your numbers into the calculator below to try any of the five.
Percentages in real life: prices and discounts
A 25% discount on a $64 jacket is $64 × 0.25 = $16 off, so you pay $48. A faster way is to multiply by 0.75. When tax is added after the discount, the tax is calculated on $48, not $64.
Stacking discounts: 20% plus 10% is not 30%
Two successive discounts multiply. A 20% discount followed by 10% means you pay 0.80 × 0.90 = 0.72 of the price, which is a 28% total discount. The order does not matter, but the sum of percentages does not equal the combined discount.
Find the original price from a sale price
If a sale price is $80 after a 20% discount, the original is not $96. You are paying 80% of the original, so original = 80 ÷ 0.80 = $100. The same method works for tax: a price of $110 including 10% tax came from $110 ÷ 1.10 = $100.
Percentage change vs percentage difference
Use percentage change when you compare an old value with a new value: (new − old) ÷ old. Use percentage difference when neither value is the reference, for example comparing two quotes: the difference divided by the average of the two. Be clear which you mean.
Percent vs percentage points
If a savings rate rises from 3% to 4.5%, it rises by 1.5 percentage points but by 50% in relative terms. News reports often mix these up. Always check which one is being described, especially for interest rates, polls and exam pass rates.
Exam marks and grades
A score of 42 out of 55 is 42 ÷ 55 × 100 = 76.4%. If a paper is marked out of different totals, convert each to a percentage before you compare them. For weighted grades, multiply each percentage by its weight and add: 80% × 0.4 + 70% × 0.6 = 74%.
Growth over several periods
If a value grows 10% a year for 3 years, the total growth is 1.10³ − 1 = 33.1%, not 30%. Percentages compound. For an average yearly rate over many periods, use the compound annual growth rate: (end ÷ start)^(1 ÷ years) − 1.
Mental maths shortcuts
- 10%: move the decimal one place left. 5% is half of that.
- 1%: move the decimal two places left.
- 15%: add 10% and 5%.
- Percentages are symmetrical in one way: 8% of 50 equals 50% of 8, so choose the easier calculation.
Check your answer
A result should make sense. A 20% increase must give a bigger number, and a 20% decrease must give a smaller one. If your calculation gives the opposite, you probably divided by the wrong base.
Troubleshooting: common problems and fixes
- My answer looks too high or too low. Check the base. Percentage change divides by the old value, and "X% of Y" multiplies by Y.
- I get a different result after two changes. Percent changes multiply. Do them in sequence, not by adding the percentages.
- A negative percentage appears. A negative result means a decrease.
- Percentages do not add up to 100. Rounding can cause small differences. Use more decimals if needed.
- I need to compare unlike items. Convert each to a percentage of its own total before you compare.
Is the calculator accurate?
The calculator uses standard percentage formulas and displays results to a sensible number of decimals. For financial or legal decisions, check rounding rules in your contract or tax law. Your numbers stay on your device.
More free Zyphub tools you may need
- Percentage Calculator: % of, % change, increase and decrease.
- GST / VAT / Sales Tax Calculator: Add or remove tax from any price.
- Tip Calculator: Tip and split the bill.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12.
How do I calculate percentage increase?
(New − old) ÷ old × 100. From 80 to 92 is (92 − 80) ÷ 80 × 100 = 15% increase.
What is the difference between percent and percentage points?
Percentage points are the arithmetic gap between two percentages. A move from 4% to 5% is 1 percentage point but a 25% relative increase.
How do I find the original price after a discount?
Divide the sale price by 1 minus the discount rate. $80 after 20% off was $80 ÷ 0.80 = $100.
Why is 20% off then 10% off not 30% off?
Because the second discount applies to the already reduced price. The combined discount is 28%.
How do I calculate percentage of marks?
Divide the marks obtained by the total marks and multiply by 100.
How do I calculate a percentage discount?
Subtract the sale price from the original price, divide by the original price and multiply by 100.