Two Percentage Calculations Everyone Needs (And How to Do Them)
Almost every percentage question in ordinary life is one of two calculations, and confusing them is behind most of the mistakes. The Percentage Calculator does both directions.
The two sums
What is X per cent of Y? Multiply Y by X and divide by a hundred. Twenty per cent of 60 is 12. This is the one for tips, discounts, tax and commission.
X is what per cent of Y? Divide X by Y and multiply by a hundred. 12 out of 60 is twenty per cent. This is the one for conversion rates, test scores and shares of a total.
They are inverses of each other, and the giveaway is what you already know. If you know the percentage and want an amount, it is the first. If you know two amounts and want the relationship, it is the second.
Getting the base right
This is where the real errors live. A percentage is always a percentage of something, and that something is the base. Change the base and the answer changes.
A price goes from 50 to 60. Is that a twenty per cent rise or a sixteen point seven per cent one? It is twenty per cent of the original, which is the correct way round - percentage change is always measured against where you started. The 16.7 figure uses the new price as the base and answers a different question.
The same trap appears in reverse. Something that falls from 60 to 50 has fallen by 16.7 per cent, not twenty, because the base is now 60. A rise and a fall of the same percentage do not cancel out, and that single fact explains a great deal of misleading statistics.
Taking a percentage off, and putting it back
A thirty per cent discount leaves you paying seventy per cent, so multiplying by 0.7 is quicker than working out the discount and subtracting it.
Going the other way needs division, not multiplication. If a price after a twenty per cent discount is 80, the original was 80 divided by 0.8, which is 100 - not 80 plus twenty per cent, which gives 96. This is the sum people get wrong when working backwards from a total that includes tax, and the Sales Tax Calculator handles that case specifically.
Percentage points are a different thing
If an interest rate moves from 2 per cent to 3 per cent, that is a rise of one percentage point and a rise of fifty per cent. Both are true and they mean different things, which is why the distinction exists.
Common questions
How do I calculate a tip quickly?
Ten per cent is moving the decimal point one place. Halve it for five, double it for twenty.
What is the percentage difference between two numbers?
Divide the gap by the original and multiply by a hundred. Which number is "the original" decides the answer, so say which you mean.
Can a percentage be over a hundred?
Yes, whenever something more than doubles. A rise from 10 to 30 is a 200 per cent increase.
Got a percentage to work out?