How to Work Out What Percent One Number Is of Another

Divide the part by the total, then multiply by 100.

(part ÷ total) × 100

30 out of 150: divide to get 0.2, multiply to get 20%.

The arithmetic is trivial. Identifying which number is which is where it goes wrong.

Finding the total

The total is whatever follows the word “of” in the question.

• “30 is what percent of 150?” → 150 is the total
• “What percent of the class passed?” → the class size is the total
• “The deposit as a percentage of the price” → the price is the total

That word is a reliable signal. When the sentence does not contain it, rephrase until it does — the total will surface.

Getting it backwards

Swap the two and the maths still works, which is exactly the problem. You get an answer, it just describes something else.

30 of 150  → 20%
150 of 30  → 500%

The 500% is not an error message. It is the correct answer to “150 is what percent of 30?”, which is a real question you did not ask.

With numbers this different, the absurd result gives it away. With 45 and 50 you would get 90% or 111% — both plausible, and nothing warns you.

The sanity check: if the part is smaller than the total, the answer must be under 100%. If it comes out above, you have them the wrong way round.

Above 100% is often correct

Results over 100% are not automatically wrong. They mean the part exceeds the total, which happens legitimately all the time:

• 120 units sold against a 100-unit target → 120% of target
• Spending 3,000 against a 2,500 budget → 120% of budget

The check above applies to your intent. If you expected a portion of something and got 340%, you have swapped them. If you were measuring against a target, over 100% is the good outcome.

Making the fraction obvious

For a rough answer, convert the total into something near 100.

18 out of 40: multiply both by 2.5 and you have 45 out of 100 → 45%.

7 out of 20: multiply both by 5 → 35 out of 100 → 35%.

Any total that divides neatly into 100 — 4, 5, 10, 20, 25, 50 — can be scaled up this way, and the answer appears without a calculator.

Where it shows up

This is the same calculation behind test scores, conversion rates, budget usage, market share, attendance, and completion figures. The framing changes and the maths does not.

Whenever you are asked “how much of the thing”, the number after “of” goes on the bottom.