The four calculations
Percent of a number: multiply the number by the percentage divided by 100. 15% of 240 is 240 × 0.15 = 36. This is the one you use for tips, commissions and tax.
What percent is X of Y: divide X by Y and multiply by 100. 36 is 15% of 240. Use this for test scores, conversion rates and "what share of my income goes to rent."
Percent change: subtract the old value from the new, divide by the old value, multiply by 100. Going from 200 to 250 is a 25% increase. Going from 250 to 200 is a 20% decrease — not 25%, because the base changed. This asymmetry is why a 50% loss needs a 100% gain to recover.
Discount: multiply the price by (1 − discount/100). $80 at 25% off is $60. For stacked discounts, apply them one at a time; 20% off then 10% off is 28% off, not 30%.
Percentage points vs percent
If an interest rate rises from 4% to 5%, it went up one percentage point but 25 percent. News reports and rate announcements use both, often without saying which. When the number you're comparing is itself a percentage, ask which meaning is intended.
Common mistakes this calculator helps you avoid
- ✕Confusing percentage points with percent. A rate rising from 4% to 5% is up one point but 25 percent.
- ✕Averaging percentages. Two 50% growth years don't equal 100% — growth compounds (it's 125%).
- ✕Reversing a discount by adding the same percent back. 25% off then 25% up lands at 93.75% of the original.
- ✕Stacking discounts additively. 20% off then 10% off is 28% off, not 30%.
- ✕Using the wrong base for percent change. The change is measured against the starting value, not the ending one.
Key terms
- Percentage point
- The arithmetic difference between two percentages (5% − 4% = 1 point).
- Percent change
- (New − Old) ÷ Old × 100; asymmetric — a 50% loss needs a 100% gain to recover.
- Basis point
- One hundredth of a percentage point; 25 basis points = 0.25%.
- Markup vs. margin
- Markup is profit over cost; margin is profit over price. A 50% markup is a 33% margin.
Frequently asked questions
+How do I calculate a percentage increase?
(New − Old) ÷ Old × 100. If rent goes from $1,800 to $1,950, that's (150 ÷ 1,800) × 100 = 8.3% increase. Use the third row above.
+How do I find the original price before a discount?
Divide the sale price by (1 − discount as a decimal). A $60 sale price at 25% off was originally $60 ÷ 0.75 = $80.
+What is 30% of 150?
45. Multiply 150 by 0.30. The first row above handles any "X% of Y" question.
+How do I convert a fraction to a percentage?
Divide the top by the bottom and multiply by 100. 3/8 = 0.375 = 37.5%. The second row does this: enter 3 and 8.