Skip to content
ChalkCalculator

Everyday

Percentage Calculator

Every common percentage question in one place, including the reverse one people get wrong by hand.

Pick what you are working out and enter two numbers.

What is X% of Y?

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

Six distinct questions, each with its own formula, rather than one box that makes you rearrange the algebra yourself. Pick the question you actually have and the steps are shown alongside the answer.

Two of these are worth calling out. Percentage change uses the absolute value of the starting number in the denominator, so a change from −50 to −25 reads as a 50% improvement rather than a −50% one. Using the signed value flips the direction of every change that starts negative.

Reverse percentage is not "subtract the percentage". A jacket on sale for $80 after 20% off was $100, not $96 — the discount applied to the original price, not the sale price. That is the single most useful mode here and the one most often got wrong.

The formula

Exactly what happens to your numbers, step by step.

  1. The six questions

    X% of Y                   =  X ÷ 100 × Y
X is what percent of Y    =  X ÷ Y × 100
change from X to Y        =  (Y − X) ÷ |X| × 100
X increased by Y%         =  X × (1 + Y ÷ 100)
X decreased by Y%         =  X × (1 − Y ÷ 100)
X is Y% of what number    =  X ÷ (Y ÷ 100)

A worked example

A jacket is on sale for $80 after a 20% discount. What was the original price?

What you enter

Mode
Reverse percentage
Known amount
$80
Is this percent
80%

Step by step

The sale price is 80% of the original
100% − 20% = 80%
Divide, do not add back
80 ÷ 0.80
Original price
$100
The common wrong answer
80 × 1.20 = $96

The original price was $100.00

Adding 20% back to $80 gives $96, which is wrong by $4. The discount was 20% of $100, not 20% of $80 — percentages are not symmetric in that way.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

  • Percentage change from zero is undefined and is reported as such rather than shown as infinity.
  • Percentage change uses the absolute value of the starting number, so direction is preserved with negative numbers.
  • Answers are shown to six decimal places where the result is not exact.

What this cannot tell you

  • It cannot tell you which number is the base, and that choice changes the answer. Going from 40 to 50 is a 25% rise; going from 50 to 40 is a 20% fall. The same gap, two different percentages.
  • Percentage changes do not add up or reverse. A 20% fall followed by a 20% rise does not return to the start — it lands 4% below it.
  • Percentage points and percent are different things. Moving from 4% to 6% is a rise of two percentage points, or of 50%, and the two are easy to confuse when both are described as 'a 2% increase'.
  • It works on the numbers you give it. If those are already percentages of something else, compounding them requires multiplication rather than addition.

Questions people ask

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply. 15% of 200 is 0.15 × 200 = 30.

How do I work out the original price before a discount?

Divide the sale price by the percentage it represents. An item at $80 after 20% off is 80% of the original, so $80 ÷ 0.80 = $100. Adding the percentage back gives the wrong answer.

Why is a 50% loss not canceled by a 50% gain?

Because the second percentage applies to a smaller number. Lose 50% of $100 and you have $50; gain 50% of $50 and you have $75. Getting back to $100 requires a 100% gain.

What is the difference between percent and percentage points?

A rate moving from 4% to 5% is a rise of one percentage point, but a 25% increase. Both are correct and they mean different things — which is why the distinction matters in reporting.

Further reading

Related calculators

Sources and review

This calculator uses standard arithmetic with no external rules or published rates, so there is nothing to cite beyond the formulas shown above.

Methodology version 1.0.0 · Last reviewed

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, September 20). Percentage Calculator (Methodology version 1.0.0). https://chalkcalculator.com/percentage-calculator/

Link to it from your site

<a href="https://chalkcalculator.com/percentage-calculator/">Percentage Calculator</a> from Chalk Calculator