Free Online Percentage Calculator
This percentage calculator handles every common percentage problem instantly — what percent one number is of another, percentage increase and decrease, percent change, and discounts. Enter your numbers in the tool above and get the answer in real time.
How to Calculate a Percentage
To find what percentage one number is of another, divide the part by the whole and multiply by 100. For example, 16 out of 20 is (16 ÷ 20) × 100 = 80%.
Percentage Increase and Decrease
To find a percentage increase, subtract the old value from the new value, divide by the old value, and multiply by 100. For a percentage decrease, do the same with the drop in value. The calculator above does both automatically.
Percentage Off (Discounts)
To find a sale price, multiply the original price by the discount percentage, then subtract. A 25% discount on $80 is $80 × 0.25 = $20 off, so you pay $60.
Percent vs Percentage Points
These two get mixed up all the time. If a savings rate goes from 2% to 3%, it rose by 1 percentage point, but by 50 percent, because 1 is half of 2. News stories about interest rates, polls and tax rates usually mean percentage points. When you compare two percentages, say which one you mean.
Finding the Original Number
A common reverse question: a jacket costs $68 after a 15% discount, so what was the full price? The sale price is 85% of the original, so divide instead of multiply: 68 ÷ 0.85 = $80. The same idea works for tax. If a receipt shows $56.50 including 13% tax, the pre-tax amount is 56.50 ÷ 1.13 = $50.
Mistakes That Give the Wrong Answer
- Adding percentages in a row. A 20% discount followed by another 10% off is not 30% off. It is 0.8 × 0.9 = 0.72, so 28% off in total.
- Reversing an increase with the same percentage. A price that rises 25% and then falls 25% ends lower than it started: 100 becomes 125, then 93.75.
- Dividing by the wrong number. Percentage change is always measured against the starting value, not the new one.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the part by the whole and multiply by 100. For example, 16 out of 20 = (16 ÷ 20) × 100 = 80%.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100.
How do I calculate a discount?
Multiply the original price by the discount percentage and subtract it from the price.
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The Three Percentage Questions
Almost every percentage problem is one of three: what is X% of Y (25% of 80 = 20), X is what percent of Y (20 is 25% of 80), and percentage increase or decrease (from 80 to 100 is a 25% rise). The calculator above handles all three — pick the one you need and type the numbers.
The Formulas Behind It
To find a percentage of a number, multiply: result = value × (percent ÷ 100). To find what percent one number is of another, divide and multiply by 100: percent = (part ÷ whole) × 100. For change between two numbers, use ((new − old) ÷ old) × 100 — a positive answer is an increase, a negative one a decrease.
Worked Examples
A $60 shirt with 25% off saves 60 × 0.25 = $15, so you pay $45. A test score of 42 out of 50 is (42 ÷ 50) × 100 = 84%. A salary rising from $50,000 to $54,000 is a ((54000 − 50000) ÷ 50000) × 100 = 8% increase. A tip of 18% on a $72 bill is 72 × 0.18 = $12.96.
Where You Use It
Percentages come up everywhere — sale discounts, tax and tips, test marks, interest rates, and comparing this month’s numbers to last month’s. Getting the base right (percent of which number) is the part people most often trip over, so the calculator labels each field to keep it clear.