Percentage calculator
Find a percentage, a share, an adjusted value or relative change with a clear comparison base.
Fill in the fields and the result will appear here automatically.
The same two numbers can answer different percentage questions. Fifteen percent of 200 is a share; increasing 200 by fifteen percent produces a new total. This calculator separates those tasks into five modes and changes the input labels to show which value is the base. For adjustments, enter the original number first and the percentage second. For relative change, enter the starting and final values. Use it to check a markup, a budget share or a change in a measured value. Percentage points and recovery of an original value are explained below, but they do not have dedicated form modes.
How it works
Formula and logic
The five operations are A / 100 × B; A / B × 100%; A × (1 + B / 100); A × (1 − B / 100); and (B − A) / A × 100%. Change also reports the signed difference B − A, rather than its absolute magnitude. With a positive starting value, a positive percentage means an increase. A negative starting value changes that interpretation, so the result includes a warning. General percentage arithmetic allows negative values and percentages above 100; these are not retail-discount limits. Unknown modes, malformed inputs, zero denominators and numeric overflow return an explicit error. Display usually uses two decimal places and may preserve extra significant digits for small nonzero results. Internal arithmetic does not round to the displayed value between steps.
Example
Five ordinary checks: 15% of 200 = 30; 50 out of 200 = 25%; increase 200 by 15% = 230; decrease 200 by 15% = 170; change from 100 to 130 = +30%, with difference B − A = 30. Boundary checks: 0% of 200 is 0, but a share of 50 out of a whole of 0 has no defined percentage and returns an error. From −100 to −50, the formula gives −50% although the number rises by 50; the negative base prevents the usual reading of the sign. A sequence from 100 up 10% gives 110, then down 10% gives 99. A rate moving from 10% to 12% rises by 2 percentage points, or 20% relative to the old rate.
Fields and units
- Mode — list option
- Value A — unitless
- Value B — unitless
How to use
- — Select percent of a number, share of a whole, percentage addition, subtraction or change.
- — For percent of a number, A is the percentage and B the number. For a share, A is the part and B the whole.
- — For addition or subtraction, A is the starting number and B the percentage. For change, A is the starting value and B the final value.
- — Enter finite numbers and check the comparison base. Zero is valid except for a whole in share mode or a starting value in change mode.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- ONS: percentages and percentage points
- Limitation
- General percentage arithmetic. The result does not determine contractual, banking or tax rules; relative change from a negative base needs separate interpretation.
FAQ
Which value is the base when I find a percentage share?
Enter the part as A and the whole as B. Spending 50 from a budget of 200 is 25%, not 400%. Percent-of-a-number mode has a different input order: A supplies the percentage and B the base number. Follow the changing field labels rather than memorising one order for every mode.
When should I use percentage points instead of relative percentage change?
Use points for the difference between rates: 12% minus 10% is 2 percentage points. Relative change divides that difference by the old rate, giving (12 − 10) / 10 × 100 = 20%. Entering 10 and 12 in change mode reports 20%; it does not report the point difference.
Why do matching percentage increases and decreases fail to cancel?
The second operation uses the changed base. Increasing 100 by 10% gives 110; decreasing that by 10% subtracts 11, leaving 99. Their combined factor is 1.1 × 0.9 = 0.99, which is a 1% decrease from the original amount.
What happens with zero or a negative starting value in change mode?
Zero makes the denominator zero, so a move from 0 to 50 has no finite relative percentage under this formula. A negative start is accepted mathematically, but the resulting sign does not describe the direction in which the number moves. Read the signed difference B − A as well.
How can I recover an amount before a percentage adjustment?
There is no dedicated reverse mode in the form. The manual formula is final / (1 + p / 100) after an increase, or final / (1 − p / 100) after a decrease. For example, a final 80 after a 20% reduction came from 100. A 100% reduction leaves zero and cannot identify the original amount uniquely.