Percentage Calculator
Six percentage calculations, each with the formula and the working shown.
What is X% of Y?
X is what percent of Y?
Percentage increase or decrease
Add or subtract a percentage
Discount and sale price
Tip calculator
The three percentage formulas worth memorising
Part of a whole result = whole × percent ÷ 100
What percent percent = part ÷ whole × 100
Percentage change change = (new − old) ÷ old × 100Percentage points are not percent
If a conversion rate rises from 4% to 6%, that is an increase of 2 percentage points but 50 percent. Mixing the two is the most common statistical error in business reporting, and the difference is rarely small — a headline "support fell 5%" means something very different from "support fell 5 points".
Percentage changes do not cancel out
A price that rises 50% then falls 50% does not return to where it started. 100 → 150 → 75. To reverse a rise of p percent you need a fall of p ÷ (100 + p) × 100 percent — undoing a 50% rise takes a 33.3% cut. This is why a stock that drops 50% must gain 100% to break even.
Working backwards from a total
To find the original price from a discounted one, divide rather than adding the percentage back. An item costing 70 after 30% off was 70 ÷ 0.7 = 100, not 70 × 1.3 = 91. The same applies to extracting tax from a gross figure: at 20% VAT, the net is gross ÷ 1.2.
Stacked discounts
"30% off, then an extra 20% off" is not 50% off. It is 0.7 × 0.8 = 0.56, so 44% off. Sequential percentages multiply; they never add.
Tipping conventions
| Country | Customary tip |
|---|---|
| United States | 18–22% at restaurants; tipping is part of staff income |
| Canada | 15–20% |
| United Kingdom | 10–12.5%, often already added as a service charge |
| Most of Europe | Rounding up, or 5–10% for good service |
| Japan, South Korea | No tipping — it can cause offence |
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 200 is 200 × 15 ÷ 100 = 30. A quick mental shortcut: 10% is the number with the decimal point moved one place left, and 5% is half of that.
How do I work out percentage increase?
Subtract the old value from the new one, divide by the old value, and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase.
What is the difference between percent and percentage points?
Percentage points measure the arithmetic gap between two percentages; percent measures the relative change. Going from 4% to 6% is +2 points and +50 percent.
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). An item at 70 after 30% off originally cost 70 ÷ 0.7 = 100.
How much should I tip?
18–20% is standard in the United States; 10–15% in Canada and the UK, where a service charge is often included; little or nothing in Japan and much of continental Europe. Check the bill for a service charge before adding more.
Is 50% off then 20% off the same as 70% off?
No. The second discount applies to the already-reduced price: 0.5 × 0.8 = 0.4, so it is 60% off, not 70%.