How it works
A percentage is a number out of 100. “15%” means 15 parts of every 100, or the fraction 15/100 = 0.15. Every percentage question is one of a few simple formulas; each card above uses one of them and updates as you type.
1. What is X% of Y?
result = X × Y ÷ 10015% of 200 = 15 × 200 ÷ 100 = 30.
2. X is what percent of Y?
percent = X ÷ Y × 10030 out of 200 = 30 ÷ 200 × 100 = 15%. This is how exam marks become percentages: 42 out of 50 is 84%.
3. Percentage increase or decrease
change % = (new − old) ÷ |old| × 100From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. From 100 back to 80 is −20%. The two are different because each is measured against its own starting value — a common source of confusion when prices rise and then fall.
4. Price after a discount
saving = price × discount ÷ 100 · final = price − savingWorked example. A jacket costs 250 with 20% off. Saving = 250 × 20 ÷ 100 = 50, so you pay 200. Two discounts in a row do not add up: 20% off and then another 10% off is 250 × 0.8 × 0.9 = 180, a total discount of 28%, not 30%.
5. Tip and splitting the bill
tip = bill × tip% ÷ 100 · each = (bill + tip) ÷ peopleA bill of 100 with a 15% tip split between 3 people: tip 15, total 115, each pays 38.33 (rounded to the cent).
Percentage points vs percent
If an interest rate rises from 5% to 6%, it went up by one percentage point, but by 20 percent of its old value. Card 3 above gives the second number. For VAT-style “add X%” sums you can also type 1250+14% straight into the scientific calculator.
Planning a loan or savings? Interest rates are percentages too — see the loan calculator and the compound interest calculator.