Percentage calculator
Answer four common percentage questions with the denominator and every step made clear.
The rate to apply; negative percentages are allowed.
The value the percentage is applied to; negative values are allowed.
The percentage is divided by 100, then multiplied by the entered value.
- Percentage (%)
- 20%
- Value
- 150
- Calculated amount
- 30
Relative input sizes
This is the entered percentage applied once to the entered value; no compounding is included.
Included
- A percentage of a value
- One non-negative value as a percentage of a positive whole
- Directional percentage change measured against the original value
- Symmetric percentage difference using the two-value average
Not included
- Percentage-point change or statistical percentage error
- Compounding, repeated growth or annualized rates
- Measurement uncertainty or confidence intervals
- Rounding rules for tax, legal, regulated or financial reporting
What this means
A percentage always describes a relationship, so the important question is which value is the denominator. “Percentage of a value” turns a rate into an amount. “What percentage?” compares a part with its whole.
Percentage change is directional: the original value is the baseline, so changing 80 to 100 is +25%, while changing 100 to 80 is −20%. Reversing the values changes the answer because the denominator changes.
Percentage difference is symmetric. Neither value is treated as the baseline; their average is the denominator. Reversing the two values therefore leaves the result unchanged. Other fields sometimes use different difference conventions, so this page names its convention explicitly.
Formula & worked example
percentage of a value = percentage ÷ 100 × value percentage share = part ÷ whole × 100 percentage change = (new value − original value) ÷ original value × 100 percentage difference = |first value − second value| ÷ ((first value + second value) ÷ 2) × 100
Compare 80 with 100 as a directional change and as a symmetric difference
- Change from 80 to 100: (100 − 80) ÷ 80 × 100
- +25%
- Average of 80 and 100: (80 + 100) ÷ 2
- 90
- Difference: 20 ÷ 90 × 100
- 22.222222%
The change is +25% because 80 is the baseline. The symmetric difference is about 22.222222% because the average, 90, is the denominator.
How this calculation works
The calculation follows the formulas, definitions and assumptions explained on this page. The references below support the method and any stated boundaries.
Official sources
- OpenStax — General applications of percent — Amount, base and rate relationships, including change measured against an original value
- NIST Dataplot — Percentage difference — Average-denominator percentage difference and the existence of alternative conventions