Find a portion of a total, express one value as a percentage of another, or compare an old value with a new one. The three modes answer different questions. Match the mode to your wording before entering the numbers.
Find a percentage of a number
For a percent of b, the calculation is a divided by 100, multiplied by b. For example, 15% of 80 is 12. This is the amount represented by the percentage. If 15% is a reduction from 80, subtract 12 from 80 to obtain 68; the percentage amount and the remaining amount are different results.
Enter 15 to mean 15%, rather than 0.15. Entering 0.15 asks for 0.15%, which is one hundredth as much. This small input distinction is a common reason for a result that seems unexpectedly low.
Express one value as a percentage of another
For a is what percent of b, divide a by b and multiply by 100. If you completed 18 items out of 24, the calculation is 18 divided by 24, multiplied by 100, giving 75%. The second value is the total or comparison base.
Reversing the inputs changes the question. Twenty-four as a percentage of eighteen is about 133.33%, not 75%. A result above 100% is possible when the first value is greater than the base. A zero base makes this calculation undefined because division by zero has no valid percentage result.
Calculate change from an old value to a new one
The change mode uses the new value minus the old value, divided by the absolute value of the old value, multiplied by 100. A change from 80 to 100 is therefore +25%. A change from 100 to 80 is -20%. The percentages differ because their starting bases differ.
For a negative starting value, this tool deliberately uses the starting value's magnitude as the denominator. From -40 to -20, the numeric increase is 20 and the reported change is +50%. Other contexts use different conventions for negative bases, so state this convention when sharing such a result. A zero starting value remains undefined.
Percentage points are a different comparison
When a rate moves from 20% to 25%, the difference is 5 percentage points. Its relative percentage increase is 25%, calculated from 20 to 25 in change mode. Decide whether you need the simple difference between rates or the relative change before describing the result.
If an answer looks implausible, recheck the mode, input order and base. Use the same units for values being compared. Small nonzero bases can produce very large percentage changes, which may be mathematically consistent even when they are not the clearest way to explain a situation.
Frequently asked questions
Can I use decimals or negative numbers?
Yes. Read the formula and sign carefully, especially for negative bases. In change mode the denominator is the absolute starting value; the other comparison mode uses its entered base directly.
Why is a change from zero undefined?
Percentage change divides by the starting value's magnitude. With a zero starting value, that denominator is zero. You can state the absolute increase instead, such as an increase from 0 to 12 by 12 units.
Is rounding exact?
Displayed results may be rounded, and browser arithmetic has finite precision. Keep the original inputs when carrying a calculation into another step instead of repeatedly reusing a rounded display value.