Percentage Calculator
Calculate percentage change, markups, discounts, percentage of values, and reverse ratios.
Parameters & Inputs
Summary & Breakdown
Formula & Worked Expression
About the Percentage Calculator
Percentages represent dimensionless ratios expressed as fractions of 100, forming the basis of everyday retail discounts, tipping, tax calculations, and investment returns.
This multi-functional percentage tool covers all four standard quantitative scenarios: finding a percentage of a number, evaluating what portion one number represents of another, computing relative percentage change, and adjusting a baseline up or down.
Clear step-by-step formulas eliminate ambiguity between percentage change and percentage points.
How the Calculations Work
Calculates proportional values using fundamental percentage relationships: Value = (X / 100) * Y, or Percent = (X / Y) * 100%, or Relative Change = ((Y - X) / |X|) * 100%.
Delta% = [(Y - X) / |X|] * 100% | Target = Baseline * (1 ± Rate / 100)
Variables & Definitions
- X: First input parameter (percentage or starting baseline)
- Y: Second input parameter (total base or resulting quantity)
- Delta%: Relative proportional change
What is 15% of 250? Divide 15 by 100 to obtain 0.15, then multiply by 250: 0.15 * 250 = 37.50.
Key Terms Explained
Basis Points (bps)
One-hundredth of a percentage point (0.01% or 0.0001), commonly used in bond yield spreads.
Percentage Points
The simple arithmetic difference between two percentage figures, distinct from percentage change.
Markup vs Margin
Markup is profit divided by cost; margin is profit divided by sale price.
Relative Change
Proportional difference scaled against the original baseline value.
Practical Tips & Pitfalls to Avoid
Watch the direction of change
A 50% loss requires a 100% gain to break even back to the original starting amount.
Distinguish percent points from percent change
Moving from 4% to 5% is a 1 percentage point rise, but a 25% relative increase.
Use decimal multipliers for speed
To calculate 20% tip, simply multiply your bill total by 0.20.
Avoid negative denominator pitfalls
When calculating percentage growth on negative values, take the absolute value of the base.
Frequently Asked Questions
Subtract the starting value from the new value, divide that difference by the starting value, and multiply by 100.
Because the 20% increase is calculated on the smaller discounted base ($100 - 20% = $80; $80 + 20% = $96).
Take 10% of the number (move the decimal left one spot), halve that amount to get 5%, and add the two together.
Divide the part by the whole and multiply by 100 (e.g., 25 / 200 = 0.125 * 100 = 12.5%).
Yes. Any quantity that exceeds its baseline reference is greater than 100% (e.g., doubling represents a 200% proportion of the original).