Percentage Calculator

Answer the three questions people actually ask about percentages: what is X% of Y, X is what percent of Y, and how much did a value change. Each answer shows its working.

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Percentage (%)

Of value

Result

(10 ÷ 100) × 200 = 20

The three formulas

Almost every percentage question reduces to one of three forms. Knowing which one you are being asked is most of the work.

Part = (Percent ÷ 100) × Whole
Percent = (Part ÷ Whole) × 100
Change % = ((New − Old) ÷ |Old|) × 100

What is 20% of 80? → (20 ÷ 100) × 80 = 16
16 is what percent of 80? → (16 ÷ 80) × 100 = 20%
From 80 to 100, what changed? → ((100 − 80) ÷ 80) × 100 = +25%

Percentage change is not symmetrical

This is where most percentage mistakes come from. A 20% rise followed by a 20% fall does not return you to where you started: 100 rises to 120, then falls by 20% of 120, which is 24, leaving 96.

The reason is that each percentage is taken of a different base. A change of +25% is undone by −20%, not by −25%. When comparing two changes, always check which starting value each one refers to.

Percent versus percentage point

If an interest rate moves from 2% to 3%, that is a rise of one percentage point but a relative increase of 50%. Both statements are true, and they describe very different things.

Headlines routinely conflate the two. When a figure is itself a percentage, state changes in percentage points to avoid ambiguity.

Common percentage calculations

Question	Answer
10% of 200	20
15% of 60	9
20% of 80	16
25 is what % of 200	12.5%
100 increased by 20%	120
100 decreased by 20%	80
From 80 to 100	+25%
From 100 to 80	−20%

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For 15% of 60: 15 ÷ 100 = 0.15, and 0.15 × 60 = 9.

How do I work out what percentage one number is of another?

Divide the part by the whole and multiply by 100. For 25 out of 200: 25 ÷ 200 = 0.125, and 0.125 × 100 = 12.5%.

How do I calculate percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 80 to 100 that is (100 − 80) ÷ 80 × 100 = 25%.

Why does a 50% loss need a 100% gain to recover?

Because the second percentage is taken of a smaller base. Falling 50% from 100 leaves 50; getting back to 100 means adding 50 to 50, which is a 100% gain.

What is the difference between 20% off and 20% of?

"20% of 80" is 16 — the portion itself. "20% off 80" is 64 — the amount remaining after taking that portion away.