How to calculate a percentage

A practical guide to percentages: what they actually mean, how to work them out on paper or in your head, and the handful of mistakes that produce most wrong answers.

What a percentage actually is

Per cent comes from the Latin per centum — “by the hundred”. Saying 20% is saying “20 out of every 100”. That is the entire concept; everything else is arithmetic.

Percentages exist because raw fractions are hard to compare. Is 17/40 better than 21/50? Hard to say at a glance. As percentages — 42.5% and 42% — the comparison is immediate. Forcing every fraction onto the same denominator of 100 is what makes them useful.

This means three forms are interchangeable, and converting between them is most of the skill:

Percentage: 25%
Decimal: 0.25 — divide the percentage by 100
Fraction: 25/100, which simplifies to 1/4

Step 1: work out which question you are asking

Almost every wrong percentage answer comes from solving the wrong question, not from bad arithmetic. Three quantities are involved — the part, the whole and the percentage — and you always know two of them. Identify the missing one and the method follows:

Missing the part? “What is 20% of 500?” → divide the percentage by 100 and multiply.
Missing the percentage? “25 out of 200 is what percent?” → divide, then multiply by 100.
Missing the whole? “50 is 20% of what?” → divide by the percentage as a decimal.

Step 2: do the arithmetic

Converting the percentage to a decimal first keeps things simple, because it turns every percentage problem into ordinary multiplication or division.

What is 20% of 500?

Convert the percentage to a decimal.20 ÷ 100 = 0.2
Multiply by the number.0.2 × 500 = 100

Answer100

Open this example in the calculator →

25 is what percent of 200?

Divide the part by the whole.25 ÷ 200 = 0.125
Multiply by 100.0.125 × 100 = 12.5%

Answer12.5%

Open this example in the calculator →

Doing it in your head

Mental percentages are almost always built from 10%, which you get by moving the decimal point one place to the left. Everything else assembles from there.

10% — move the decimal one place left. 10% of 340 is 34.
5% — half of 10%. That is 17.
1% — move the decimal two places left. That is 3.40.
15% — 10% plus 5%. That is 51.
20% — double 10%. That is 68.
25% — a quarter, so halve it twice. That is 85.

One more trick worth knowing: X% of Y always equals Y% of X. Working out 4% of 75 is awkward, but 75% of 4 is obviously 3 — and they are the same question. Whenever one direction looks unpleasant, try the other.

The mistakes that catch people out

Reversing a percentage by subtracting it

If a price rose 20% to $120, taking 20% off $120 gives $96 — not the $100 you started from. The rise was calculated on $100 and the fall on $120, so they are percentages of different numbers. To reverse it, divide by 1.2. The find-the-whole calculator does this directly.

Adding percentages of different totals

Scoring 80% on a 10-mark quiz and 60% on a 90-mark exam does not average to 70%. You scored 8 + 54 = 62 marks out of 100, which is 62%. Percentages can only be averaged directly when the totals behind them are the same size.

Confusing percent with percentage points

An interest rate moving from 4% to 5% has risen by 1 percentage point — and by 25%. Both are accurate; quoting whichever sounds more dramatic is a standard rhetorical move, and worth spotting.

Stacking discounts

“20% off plus an extra 10%” is 28% off, not 30%, because the second reduction applies to the already-reduced price. The discount calculator works through it.

Everyday situations

Tipping — 15% or 20% of the bill, built from 10%.
Sale shopping — checking whether an advertised reduction matches the two prices on the label.
Exam results — marks scored over marks available.
Pay rises — comparing a raise against inflation.
Loans and savings — the cash value of a quoted rate on your balance.
Business reporting — growth against the previous period.

For the formulas themselves, laid out side by side with the distinctions between them, see the percentage formula reference.

Frequently asked questions

How do I calculate a percentage without a calculator?

Find 10% by moving the decimal one place left, then build the number you need from it. 10% of 340 is 34, so 5% is 17, 20% is 68, and 25% is 85. Most everyday percentages can be assembled from 10%, 5% and 1%.

What is the fastest way to work out 15%?

Take 10%, halve it to get 5%, and add the two together. On a $48 bill: $4.80 plus $2.40 is $7.20.

Is "20% of 50" the same as "50% of 20"?

Yes — both are 10. Percentages are commutative, so you can swap the two numbers whenever it makes the arithmetic easier. Working out 50% of 20 in your head is far quicker than 20% of 50.

How do I calculate percentage in Excel or Google Sheets?

Use a plain division and let the cell format do the rest: =B2/C2 with the cell formatted as a percentage. For a percentage of a number, =A2*0.2 gives 20% of A2.

How do I calculate the percentage of marks for multiple subjects?

Add up all the marks you scored, add up all the marks available, then divide one by the other and multiply by 100. Averaging the individual subject percentages gives a different answer whenever the papers have different totals.