The baseline determines the answer
These tools use the formulas below. Amounts being compared should use the same units. Enter 20 for 20%; do not enter 0.2 unless you mean 0.2%. Properly grouped numbers such as 1,000 and 1,00,000 are accepted. Use a decimal point, not a decimal comma.
| Calculation | Formula | Check |
|---|---|---|
| Percentage of an amount | Rate ÷ 100 × amount | 15% of 200 = 30 |
| Part as a percentage | Part ÷ total × 100 | 30 of 200 = 15% |
| Percentage change | (New − original) ÷ original × 100 | 80 → 100 = 25% |
| Percentage difference | Absolute gap ÷ average × 100 | 80 vs 100 ≈ 22.22% |
| Percentage points | New rate − original rate | 20% → 25% = +5 points |
| Before a discount | Final ÷ (1 − rate ÷ 100) | 800 ÷ 0.8 = 1,000 |
| Before an increase | Final ÷ (1 + rate ÷ 100) | 1,200 ÷ 1.2 = 1,000 |
Input conventions and undefined cases
- Percentage of an amount and part-to-total: signed inputs are supported. A part-to-total denominator cannot be zero.
- Percentage change: the original must be positive. The new amount may be zero or negative. A zero original makes the usual formula undefined; negative originals need a convention this tool does not choose.
- Percentage difference: both values must be non-negative. Neither is the starting point. One zero and one positive value give 200%. Two zeros are reported as 0% by convention even though the formula is 0 ÷ 0; the dedicated tool labels this case.
- Reverse percentage: the final amount and rate must be non-negative. A discount must be below 100%. A 100% discount cannot identify a unique original. Increases above 100% are allowed.
Rounding and precision
Choose up to 0, 2, 4 or 8 decimal places. This changes the displayed answer, not the input values used by the calculation. Thousands separators improve readability. A non-zero answer that rounds to zero is marked approximately zero with an explanatory note.
The tools use JavaScript numbers, which use binary floating-point arithmetic. Very long decimal inputs, very large values and extremely small differences may lose precision. Some values outside the supported range are rejected. An accepted input is not a promise of exact decimal arithmetic. For accounting, legal, medical or other consequential work, verify the method and result with an appropriate specialist system.
Why similar questions give different answers
80 to 100 is a 25% increase because 80 is the original. 100 to 80 is a 20% decrease because 100 is the original. Comparing 80 and 100 equally gives about 22.22% difference because their average is 90. Moving from 20% to 25% is 5 percentage points, or a relative increase of 25%.
How we check changes
During development we check representative exact answers, reversed inputs, zero cases, invalid formats, displayed precision and the calculator controls. We also check opening-screen layouts and navigation at selected browser sizes. These checks do not cover every device, input or future browser change.
Report a reproducible issue
Use Contact / report an error. Include the calculator name, mode, sample inputs, precision setting, expected answer and actual answer. If possible, include the browser and screen size. Use sample numbers instead of confidential information.