Percentage Calculator

Most percentage mistakes are not arithmetic errors. They are the wrong question: a percentage change computed where a percentage difference was meant, a discount reversed by subtracting the same percentage that was added, or a rate applied three times and reported as three times the rate.

This calculator separates the seven common questions into their own inputs, so the one you pick is the one you get — what is X% of Y, X is what percent of Y, the increase or decrease from one value to another, the symmetric difference between two values, a percentage added to and taken off a number, the reverse question of what a figure is a percentage of, and the same percentage compounded over several periods.

Every result carries the expression that produced it, so you can check the answer rather than trust it. Nothing is sent anywhere; the arithmetic runs in your browser as you type.

These are three different measurements and they are routinely mixed up. Percentage change is directional: it needs to know which value came first, because it divides the gap by the starting value. Going from 40 to 60 is a 50% increase.

Percentage difference has no starting value. It compares two figures that are simply two figures — this month against that month's equivalent, one supplier's quote against another's — and divides the gap by their midpoint instead. The same 40 and 60 are 40% apart, and swapping them gives the same answer, which is exactly the property that makes it symmetric.

Percentage points are the third thing. If a rate moves from 4% to 6%, that is a rise of two percentage points and a rise of fifty percent. Both statements are true and they describe the same movement, which is why the distinction gets abused in headlines. Points compare two percentages by subtraction; change compares them by division.

One caveat on the difference mode: the midpoint is taken over the magnitudes of the two values. For two positive numbers that is the textbook formula exactly. For values that straddle zero, where the plain average can be zero or negative, this keeps the reference positive so the answer stays a distance rather than flipping sign.

Increase 100 by 20% and you get 120. Decrease 120 by 20% and you get 96, not 100, because the second percentage is taken from a larger base. The add-and-subtract mode shows both directions on the same number side by side, which makes the asymmetry visible: the amount added and the amount taken off are the same only because they are both computed from the number you typed.

The same asymmetry is why recovering from a loss takes a bigger gain than the loss itself: a 50% fall needs a 100% rise to get back to where it started.

Order matters less than people expect for plain percentages, because multiplication commutes — a 10% discount then 18% tax is the same total as 18% tax then a 10% discount. It stops being true the moment a rule involves a threshold: a tax that applies only above a certain amount, or a discount capped at a value. Then the order decides which side of the threshold you land on.

This is the reverse question, and subtracting the discount from the sale price is the wrong move. If an item is 15% off and costs 340, then 340 is 85% of the original, so the original is 340 x 100 / 85 = 400. Taking 15% off 340 instead gives 289, which is 111 short.

The reverse mode asks it directly: Y is X% of what. It is the same operation behind extracting a pre-tax amount from an inclusive invoice total, working out a headline salary from a net figure and a known deduction rate, or recovering a base figure from any number that has already had a percentage applied to it.

The one input that has no answer is a percentage of zero. Nothing is 0% of anything, so the calculator shows a dash rather than an enormous number.

Apply 10% three times and the total is 33.1%, not 30%, because each period is taken on the result of the last one rather than on the original. The gap widens fast: 10% over ten periods is 159%, not 100%.

The compound mode takes a rate, a starting value and a number of periods, and shows the final figure, the total change as a single percentage, and the overall multiplier. That multiplier is the useful number to keep: it collapses every period into one multiplication, so you can apply the same growth to a different starting value without recomputing anything.

It works in both directions. A negative rate is depreciation — a 10% annual write-down over three years leaves 72.9% of the original value, not 70%. Values below minus 100% per period have no meaning here and the calculator says so rather than inventing a figure.