Percentage Calculator
Work out percentages, shares and percentage change in one place.
What is X% of Y?
Result
37.5
(15 ÷ 100) × 250
X is what % of Y?
Result
25%
(45 ÷ 180) × 100
Percentage change
Result
+25%
An increase of 30
About Percentage Calculator
Percentages express one quantity as a share of another scaled to 100, which makes very different magnitudes comparable at a glance.
This calculator covers the three questions people actually ask - what is X percent of Y, X is what percent of Y, and what is the percentage change from X to Y - and shows the formula behind each answer.
The three formulas
P% of Y = (P ÷ 100) × YX is what % of Y = (X ÷ Y) × 100Change = ((New − Old) ÷ |Old|) × 100
How Percentage Calculator works in your browser
The tool covers the four percentage questions that get confused with one another: what is X% of Y; X is what percent of Y; the percentage change from X to Y; and reversing a percentage to recover an original value.
The last two are where mistakes usually happen. Percentage change is (new − old) / old, always divided by the *original* value — which is why a rise from 50 to 75 is +50% while the fall back from 75 to 50 is −33%, not −50%. And a 20% discount is reversed by dividing by 0.8, not by adding 20%: taking 20% off 100 gives 80, and adding 20% to 80 gives 96.
Arithmetic uses double-precision floating point, so results are shown rounded. For money, round once at the end rather than at each step, and check the result against the figure the institution concerned actually charges.
When to use it
- Working out the original price from a sale price and a discount percentage.
- Calculating percentage growth between two reporting periods correctly.
- Adding or removing a tax or service charge from a total.
- Checking a percentage figure someone else has quoted before you rely on it.
Frequently asked questions
What is the difference between percentage change and percentage points?
Going from 10% to 12% is a two percentage point rise but a 20% relative increase. The two are often confused in reporting.
Why is percentage change not symmetric?
Because it is relative to the starting value. A rise from 100 to 150 is +50%, but the fall back from 150 to 100 is -33.3%.
How is a negative starting value handled?
The change is divided by the absolute value of the start, which keeps the sign of the change meaningful.