Toolrack

Percentage Calculator

Result—
Number plus this %—
Number minus this %—

Every common percentage question in one place — percent of a number, percent change, what percent one number is of another, and reversing a percentage that has already been applied.

The four calculations

QuestionFormula
What is X% of Y?Y × X ÷ 100
X is what % of Y?X ÷ Y × 100
Change from A to B(B − A) ÷ A × 100
Original before +X%Final ÷ (1 + X ÷ 100)
Original before −X%Final ÷ (1 − X ÷ 100)

The base matters more than the number

Almost every percentage mistake comes from applying the figure to the wrong base. A 20 percent tax added to 100 gives 120, but 20 percent of 120 is 24 — so subtracting 20 percent from the total does not return you to 100. Whenever a percentage has already been applied, you divide to undo it.

The same logic explains stacked discounts, VAT extraction and the loss-recovery asymmetry. They are all one rule wearing different clothes: identify which number the percentage was taken from.

Frequently asked questions

What is the difference between percentage points and percent?

If a rate goes from 5 percent to 7 percent, that is a rise of 2 percentage points but a 40 percent increase. Both statements are true and they describe the same change. Reporting the larger number without saying which measure it is remains one of the most common ways statistics mislead.

Why does a 50 percent gain not cancel a 50 percent loss?

Because each is calculated against a different base. Drop 100 by 50 percent and you have 50; add 50 percent to 50 and you have 75, not 100. Recovering from a 50 percent fall needs a 100 percent gain. This asymmetry gets worse as losses deepen — a 90 percent fall needs a 900 percent gain to break even.

How do I remove a percentage that was already added?

Divide, do not subtract. If a price of 120 includes 20 percent tax, the pre-tax price is 120 ÷ 1.2 = 100, not 120 − 20 percent = 96. Subtracting takes the percentage of the larger number and always under-returns. The reverse-percentage tab handles this.

How do I apply two discounts in a row?

Multiply the remaining fractions rather than adding the discounts. Thirty percent off followed by another 20 percent off leaves 0.7 × 0.8 = 0.56, so a 44 percent total discount, not 50 percent. Stacked discounts always come to less than their sum.

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