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Percentage of a Total

Give two numbers and see what share the first is of the second — the reverse of the everyday percentage question.

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Per cent and percentage points are not the same thing

This is the question behind marks, market share, turnout and every "what proportion of" sentence: 30 out of 200 is 15%. Divide the part by the total and multiply by 100.

The trap arrives when the numbers are themselves percentages. If unemployment goes from 4% to 5%, that is a rise of one percentage point and of twenty-five per cent. Both statements are true and they sound wildly different — which is exactly why they get swapped, deliberately and accidentally, in reporting about interest rates, taxes and polls.

A share above 100% is not an error. If this month you sold 200 units and last month 30, this month is 666.7% of last month. Any calculator that refuses to go above 100% has assumed the part must sit inside the total, which is true for votes and false for growth.

Frequently asked questions

What percentage of Y is X?

Divide X by Y and multiply by 100. 30 out of 200 is 30 ÷ 200 × 100 = 15%. If the answer is above 100, X is larger than Y — which is a perfectly ordinary thing for it to be.

What is a percentage point?

The plain arithmetic difference between two percentages. From 40% to 44% is four percentage points. The same move is a ten per cent increase, because four is ten per cent of forty. Use "points" when comparing two rates and "per cent" when describing how much one changed.

Why does my total not add up to 100%?

Usually rounding. Three equal shares are 33.3% each, which sums to 99.9%. Published tables often adjust one figure to make the column reach 100 — a footnote reading "figures may not sum due to rounding" is doing exactly that.

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