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Percentage calculator

Three questions in one place: a percentage of a number, one number as a percentage of another, and the percentage change between two values.

Short answer: a percentage is a fraction of 100. "15% of 200" is200 × 15 ÷ 100 = 30; "30 is what percent of 200" is 30 ÷ 200 × 100 = 15%; and the change from 200 to 250 is (250 − 200) ÷ 200 × 100 = 25%.

The three questions people actually mean

Almost every percentage problem is one of these three, and mixing them up is the usual source of a wrong answer. A discount is the first form, a score or share is the second, and growth, inflation and sales change are the third.

Worked example

A ₹1,499 item at 30% off: 1,499 × 30 ÷ 100 = ₹449.70 off, so you pay ₹1,049.30. Then the price rises to ₹1,299 next month, which is a change of (1,299 − 1,049.30) ÷ 1,049.30 × 100 = 23.8% — not 30%, because the base moved.

Percentage questions

How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100: 15% of 200 is 200 × 15 ÷ 100 = 30. The first tab does this, and also shows the remaining amount so a discount calculation finishes in one step.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100: 30 out of 200 is 30 ÷ 200 × 100 = 15%. This is the form used for test scores, vote shares and completion rates.

Why does a 20% fall need a 25% rise to recover?

Because the base changes. 100 falling 20% is 80; getting back to 100 from 80 is a rise of 20 ÷ 80 = 25%. Percentage change is always measured against the value you started from, which is why the calculator shows the direction and the base it used.

What about percentage points?

A change from 4% to 6% is 2 percentage points but a 50% increase, because 2 ÷ 4 = 0.5. News reports mix the two constantly; the third tab reports the relative change, and the page notes the absolute difference so the distinction is visible.

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