Quick Answer: Solve common percentage questions, including percentage of a number, what percent one number is of another, percentage difference, and percentage increase or decrease.
How This Calculator Works
Percentages convert a relationship into parts per hundred. This calculator evaluates the most common percentage formulas and keeps each result in the same numeric scale as the question.
Worked Scenario: Scenario: Measuring a Price Change
A product moves from 200 to 250. The percentage change compares the difference against the starting value.
Scenario Inputs
- Starting value: 200
- Ending value: 250
- Difference: 50
Outcome: The change is 50 divided by the original value of 200, then multiplied by 100. That produces a 25% increase.
Formula and Methodology
Percentage of a value: Result = (Percent / 100) * Value
Percent one value is of another: Percent = (Part / Whole) * 100
Percentage difference: Difference% = |A - B| / ((|A| + |B|) / 2) * 100
Percentage change: Change% = (New - Old) / |Old| * 100
Variables
- Percent: The percentage rate expressed as parts per hundred
- Part: The value being compared against a whole
- Whole: The reference value used as the denominator
- Old/New: The starting and ending values used for percentage change
Assumptions
- Inputs are treated as plain numeric values without units.
- Percentage change uses the first value as the starting value and the second value as the ending value.
- Percentage difference uses the average magnitude of the two values as the denominator.
Limitations
- Division by zero returns 0 where a percentage relationship is mathematically undefined.
- Results are rounded to six decimal places for display stability.
Practical FAQs
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the value. For example, 15% of 200 is 0.15 multiplied by 200, which equals 30.
What is the difference between percentage difference and percentage change?
Percentage change compares a new value to an old value. Percentage difference compares two values symmetrically by dividing their absolute difference by their average.
Can the percentage change be negative?
Yes. If the ending value is lower than the starting value, the percentage change is negative and represents a decrease.