How do I calculate a percentage of a value, one value as a percentage of another, or percentage change?
The word percentage covers several different operations. The correct equation depends on whether the unknown is an amount, a share of a base, or a change between an old and new value.
Multiplication, comparison and change
A% of B = (A ÷ 100) × B; A as % of B = (A ÷ B) × 100Change from A to B = [(B − A) ÷ A] × 100; Difference = B − ASeveral answers from the same two values
The default values are reused across the calculator’s outputs to show how the same two numbers answer different percentage questions.
Illustrative inputs; currency amounts below use USD. Rates and prices are assumptions, not live quotes.
- Value A
- 25
- Value B
- 200
Step-by-step calculation
- 25% of 200 = 25 ÷ 100 × 200 = 50.
- 25 as a percentage of 200 = 25 ÷ 200 × 100 = 12.5%.
- Change from 25 to 200 uses the starting value: (200 − 25) ÷ 25 × 100 = 700%.
Intermediate figures are rounded for reading. Results use the full calculation precision.
Reading each output by its denominator
Check the output label before reading the number. ‘A percent of B’ multiplies, ‘A is what percent of B’ divides, and change uses the original value as its reference.
Direction and zero-base errors
Swapping the two values changes the denominator and therefore the answer. Percentage relationships are directional even when the absolute difference is unchanged.
- Both values represent comparable quantities where a comparison is intended.
- The denominator must be non-zero for division-based outputs.
- Displayed rounding can hide small differences in intermediate values.
Calculations related to percentage
The following tools examine neighbouring parts of the same calculation without changing the inputs or assumptions used above.
References
Sources and conventions
- OpenStax: percentage arithmetic
Mathematical background; any tax, tip or discount percentage in the example is user-supplied.
Quick answers
Frequently asked questions
Which value is the starting value for percentage change?
Value A is the starting value and Value B is the ending value.
Why does reversing A and B change the percentage?
Percentages depend on the chosen base value, so reversing the values changes the denominator.
What happens when a base value is zero?
Calculations that would divide by zero return zero in this calculator.
Calculation method and limitations · Report an error
Educational content only. This guide is not financial advice.
