The Percentage Calculator solves the eight percentage problems that cover nearly everything: what is X% of Y, X is what percent of Y, percentage change, percentage difference, adding a percentage, subtracting a percentage, reverse percentage, and fraction to percentage. Choose the mode that matches your question, enter the two values, and get the result rounded to four decimal places.
The Modes and Their Formulas
| Problem | Formula | |---|---| | What is X% of Y? | (X / 100) x Y | | X is what percent of Y? | (X / Y) x 100 | | Percentage change (X to Y) | ((Y - X) / |X|) x 100 | | Percentage difference | |X - Y| / |(X + Y) / 2| x 100 | | Add Y% to X | X x (1 + Y / 100) | | Subtract Y% from X | X x (1 - Y / 100) | | Reverse: X is Y% of what? | X / (Y / 100) | | Fraction X/Y to percent | (X / Y) x 100 |
Worked examples
Percent of: 15% of 240 = 36. What percent: 36 is what percent of 240? 36 / 240 x 100 = 15%. Change: from 80 to 100 is (100 - 80) / 80 = +25%. Difference: between 80 and 100 is 20 / 90 (their average) = 22.22%. Add: 225**. Subtract: 150**. Reverse: a sale price of 200** (enter X = 150, Y = 75: 200). Fraction: 3/8 = 37.5%, and the mode also reports the decimal, 0.375.
Change versus difference: the distinction that matters most
The two comparison modes answer different questions and are routinely confused. Percentage change is directional and anchored: it needs an original value, and swapping the values changes the answer's size as well as its sign (80 to 100 is +25%, 100 to 80 is -20%, because the anchor moved). Percentage difference is symmetric and anchorless: it compares both values against their mean, so 80 versus 100 is 22.22% in either order, which is why scientists and statisticians use it when neither value is "before" or "reference." Choosing wrongly is not a rounding issue: reporting a price comparison as 25% when the symmetric figure is 22.22% overstates by an eighth. The calculator includes both so the choice is conscious; if one of your numbers is the original, the base, or the control, you want change (or the "what percent" mode); if the two are peers, you want difference.
The guards, and why they exist
Several modes refuse inputs that cannot produce a meaningful percentage: "what percent of" and "fraction" reject a zero reference (division by zero is not a large percentage, it is no percentage); change rejects a zero starting value (growth from nothing is undefined in percentage terms, which is why reports say "from a negligible base" instead); subtracting 100% or more is rejected because it would zero or negate the value, almost always a sign the wrong mode was chosen. Reverse percentage rejects 0% for the same division reason. These refusals are the calculator protecting you from the four commonest percentage errors in spreadsheets, where the same operations fail silently into error values or plausible nonsense.
Everyday fluency checks
Three habits catch most percentage mistakes before a calculator is even needed. First, name the base: every percentage is of something, and most disputes ("profits rose 5%" versus "margin fell 2 points") are base disputes; note that a move from 10% to 12% is two percentage points but a 20% relative increase, and the change mode computes the second while headlines often mean the first. Second, percentages do not add symmetrically: a 25% fall needs a 33.3% rise to undo it, because the base changed (the reverse mode exists for exactly this recovery arithmetic). Third, successive percentages multiply rather than add: two successive 10% discounts are 19% off, not 20%, as the subtract mode applied twice demonstrates. The Percentage Increase Calculator on this site specializes in the change family with more guidance; this page is the general toolkit.
Frequently Asked Questions
How do I find the original price before a discount or tax?
That is the reverse mode: divide the final figure by the percentage it represents. A 200. For a discount, divide by what remains: a $150 price after 25% off is 75% of the original.
Why is my percentage change over 100% or negative when I expected otherwise?
Over 100% simply means the value more than doubled relative to its base (80 to 200 is +150%). A negative sign means the new value is below the starting one. If the magnitude surprises you, check the anchor: the calculator divides by the first value you enter in change mode, so entering the pair in reverse order legitimately changes the percentage.
Can percentages be averaged?
Not by a plain mean, unless every percentage shares the same base. Averaging 50% of 10 and 10% of 1,000 gives 30%, while the true combined figure is (5 + 100) / 1,010, about 10.4%. Add the underlying amounts and recompute, which is what the "what percent" mode is for.