Percentage Calculator

1. X% of Y

   A share of an amount — like tax on a value.

2. X is what % of Y

   A ratio as a percentage — like an effective tax rate.

3. % change

   Movement from an old value to a new one.

4. Increase / decrease

   Apply a percentage up or down to a starting number.

A rate moving from 10% to 12% has risen by two percentage points, but by twenty percent. Both descriptions are correct and they describe the same change. Which one gets quoted usually depends on who is doing the quoting, and the gap between them is where a lot of misleading reporting lives.

When you read that a charge "went up 20%", it is worth establishing which of the two is meant before reacting to it.

A fall and a rise of the same percent do not cancel

Rs 100 losing 20% becomes Rs 80. Adding 20% back to Rs 80 gives Rs 96, not Rs 100 — because the second percentage is taken from a smaller base. Getting back to the original needs a 25% rise.

This is the arithmetic behind a discount that looks better than it is, and behind an investment that is still down after a recovery which matched the fall.

Removing a percentage is not subtracting it

To take an 18% tax out of an inclusive figure, divide by 1.18. Subtracting 18% of the gross removes too much, because the 18% was calculated on the smaller net amount in the first place.

For tax specifically, the sales tax calculator handles both directions.

Where this stops

This is arithmetic, so it is exact. What it cannot tell you is which base a figure you have read elsewhere was calculated on — and that, rather than the calculation, is where most percentage confusion starts.