PlenumHubThe three things this calculator does
"Percentage" questions usually come in one of three shapes, and each uses a different formula:
- X% of Y — for example, "what is 20% of 50?" Formula: (X ÷ 100) × Y.
- X is what % of Y — for example, "15 is what percent of 60?" Formula: (X ÷ Y) × 100.
- % increase/decrease from X to Y — for example, "a price went from 80 to 100, what's the change?" Formula: ((Y − X) ÷ X) × 100.
Pick the option that matches your question and the calculator does the rest.
Worked examples
20% of 50: (20 ÷ 100) × 50 = 10.
15 is what percent of 60? (15 ÷ 60) × 100 = 25%.
Change from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25% increase. Change from 100 to 80 the other way round is a 20% decrease — percent increase and decrease are not symmetric, because the base number (what you divide by) is different each time.
Common mistakes
A frequent error is assuming a 25% increase followed by a 25% decrease gets you back to the start. It does not: 100 up 25% is 125, and 125 down 25% is 93.75, because the second percentage is taken from a different base number. Always check which number the percentage applies to.
Another common trap is percentage points versus percent: if a rate moves from 10% to 15%, that is a 5 percentage-point increase, but a 50% relative increase (use the % change mode above for the second figure).
Where percentages show up
Discounts and markups, exam and survey scores, tax and tip rates, interest rates, and year-on-year comparisons in business are the most common everyday uses. For a dedicated tip calculation with per-person splitting, see our tip calculator.
Frequently asked questions
How do I calculate a percentage by hand?
Divide the percentage by 100 to get a decimal, then multiply by the number. For 20% of 50: 20 / 100 = 0.2, then 0.2 x 50 = 10.
Why are percent increase and percent decrease not opposites?
Because each is calculated from a different starting number (base). Going up 25% from 100 reaches 125, but coming back down 25% from 125 only reaches 93.75, not 100.
Can X or Y be negative?
Yes, for X% of Y and for percent change. For 'X is what % of Y', Y cannot be zero, since dividing by zero is undefined.
What is the difference between percent and percentage points?
Percentage points measure the raw difference between two percentages (15% - 10% = 5 points). Percent change measures the relative difference (a 50% increase). They answer different questions.