Percentage Calculator
Result: 30
- Mode
- What is X% of Y?
- Equation
- 15% × 200 = 30
- Result
- 30
What this calculator does
The Percentage Calculator answers five related questions with one form. You can find a percentage of a value, express one value as a percentage of another, recover the whole from a percentage, measure the difference between two values, or measure the change from a starting value to an ending value.
Percentages are a way of writing a fraction with a denominator of 100. Saying that 15% of 200 is 30 is the same as saying that 15 out of every 100 equals 30 out of 200. The same idea appears in discounts, interest rates, test scores, business growth, and many everyday comparisons.
How to use this calculator
- Choose the question you want to answer from the Mode menu.
- Enter the two values requested by the form. The labels change with the mode.
- Click Calculate.
- Read the equation and the result. The equation shows how the answer was produced.
The default example asks for 15% of 200. The result is 30, and the equation is 15% × 200 = 30.
Percentage formulas
The calculator uses these formulas:
X% of Y = (X / 100) × Y
X is what % of Y = (X / Y) × 100
X is Y% of what = X / (Y / 100)
Difference = |V1 − V2| / ((V1 + V2) / 2) × 100
Change = (New − Old) / Old × 100
The percentage difference formula divides by the average of the two values. The percentage change formula divides by the starting value. That difference matters: the same pair of numbers can produce different percentages depending on which question you ask.
What the results mean
For the default example, 15% of 200 is 30. If you instead ask what percent 30 is of 200, the answer is 15%. If you ask what number 30 is 15% of, the answer is 200. These three questions describe the same relationship from different directions.
A positive percentage change means the ending value is higher than the starting value. A negative percentage change means it is lower. A change from 100 to 120 is a 20% increase, while a change from 120 to 100 is a 16.67% decrease. The direction of the comparison changes the denominator.
Percentage difference is always non-negative because it uses the absolute difference between the values. It is useful when neither value is clearly the starting point, such as comparing the prices of two products or the results of two measurements.
Assumptions and limitations
- The calculator accepts ordinary decimal numbers and removes commas from formatted input.
- Division by zero is rejected with a message instead of returning an undefined result.
- Results are rounded for display to at most six decimal places. The underlying calculation uses the unrounded values.
- The percentage change mode uses the first value as the starting point and the second value as the ending point.
- The calculator does not compound percentages across multiple periods. For compound growth, use the compound interest or investment calculator.
- Percentage points and percentages are not the same thing. A change from 10% to 12% is a two percentage-point increase, but it is a 20% relative increase.
Frequently asked questions
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an old value and divides by the old value. Percentage difference compares two values without choosing a starting point and divides by their average. Use change for before-and-after comparisons, and difference for side-by-side comparisons.
Can I enter negative values?
Yes. The calculator accepts negative numbers. A negative percentage change is reported when the ending value is below the starting value, and percentage difference uses the absolute gap between the two numbers.
Why do I get a different percentage when I swap the values?
Swapping the values changes the denominator in the percentage change formula. A move from 100 to 120 is a 20% increase, but a move from 120 to 100 is a 16.67% decrease. This is expected behavior, not an error.
Does the calculator round intermediate results?
No. It keeps the full calculation and rounds only the displayed result. Use the displayed equation if you need to reproduce the answer by hand.
Source
Reference: Calculator.net — Percentage Calculator.