Percentage Calculator

How to use the percentage calculator

Pick the question you are actually asking, then type two numbers. The first three modes measure: what is X percent of Y, for a slice of a known total; X is what percent of Y, for turning a part into a rate; and percentage change from X to Y, for how much something rose or fell between two figures you already have.

The last two APPLY a percentage rather than measuring one. Add X percent to Y, or take X percent off it, and the answer comes with the multiplier the change is equivalent to — 1.2 for a twenty percent rise, 0.8 for a twenty percent fall. That multiplier is what makes several changes in a row behave correctly.

The default, 15 percent of 200, returns 30, which is the kind of tip-or-discount arithmetic people reach for most. Each mode is a single line of arithmetic, so the value of the tool is less in the calculation than in making sure you have chosen the question that matches what you want to know.

Use the first mode whenever you know the rate and want the amount: 15 percent of a $200 bill, 8 percent tax on a price, 20 percent off a sticker. It answers how much a given piece is worth.

The second mode runs it the other way, turning a part and a whole into a rate: 25 is what percent of 200 gives 12.5 percent, which is how 18 correct out of 24 becomes a 75 percent score or a $25 fee on a $200 order becomes a percentage you can compare against something else.

Both are exact, and both are easier to check than they look, because dividing by 100 and multiplying are operations you can reverse in your head.

The distinction worth carrying away is between a percentage and a percentage point. If an interest rate moves from 4 percent to 5 percent, that is a rise of one percentage point but a 25 percent increase in the rate, because 1 is 25 percent of 4.

Both statements are true and they are not interchangeable, which is why the same news can be reported as a modest one-point move or a dramatic quarter increase. Use percentage points when you are comparing two rates directly, and percent change when you want the relative size of the move.

Why does undoing a fall take a bigger percentage?

The third mode is the one people most often get backward, because percentage change is always measured against the starting value. Going from 200 to 250 is a 25 percent increase, since the gap of 50 is a quarter of 200. The return trip from 250 back to 200 is a 20 percent decrease, not 25, because that same gap of 50 is only a fifth of 250.

This asymmetry means successive changes never simply cancel: a 20 percent fall followed by a 20 percent rise leaves you at 96 percent of where you started, not 100, and a 50 percent fall needs a 100 percent rise to recover. To reverse a fall of any size, the required gain is always larger than the loss.

The formula, worked line by line

Each mode is a single line, and the only real difference between them is which two numbers you know and which one you are solving for. All five come from the same relationship between a part, a whole and a rate, rearranged — three that measure a percentage and two that apply one.

The third line carries the asymmetry that causes the most confusion. Because the denominator is the starting value rather than the ending one, swapping the two inputs does not simply flip the sign of the answer. That single detail is behind percentage changes that appear not to cancel and behind most arguments about whether a number went up or down by more.

what is X% of Y       →  (X ÷ 100) × Y
X is what % of Y       →  (X ÷ Y) × 100
% change from X to Y   →  ((Y − X) ÷ X) × 100
(15 ÷ 100) × 200 = 30

Worked example with the defaults, 15 percent of 200: (15 ÷ 100) × 200 = 0.15 × 200 = 30. Flip to the second mode and 25 is what percent of 200 comes out as (25 ÷ 200) × 100 = 12.5 percent. Both are everyday slices, a tip on a bill or a score out of a total.

In the third mode, going from 200 to 250 is ((250 − 200) ÷ 200) × 100 = +25 percent, while the return trip from 250 to 200 is ((200 − 250) ÷ 250) × 100 = −20 percent. The gap of 50 never changed; only the base it was measured against did.

That asymmetry compounds when changes follow one another, because successive percentages multiply rather than add. A 20 percent fall followed by a 20 percent rise is 0.80 × 1.20 = 0.96, so you end at 96 percent of where you started and are 4 percent down despite the two headline rates cancelling on paper.

Percentages versus percentage points

Keep percentages and percentage points apart, especially where both numbers are already rates. A move from 4 percent to 5 percent is one percentage point and a 25 percent increase; a move from 50 percent to 60 percent is ten percentage points and a 20 percent increase.

Neither phrasing is wrong, but they describe different things, and a figure quoted without saying which is genuinely ambiguous. When the numbers matter, state the unit. This page is general information about arithmetic and carries no advice about any particular rate you might be comparing.

Questions people ask