The five calculations
- X% of Y — multiply Y by X divided by 100. 20% of 250 is 250 × 0.2 = 50.
- X is what percent of Y — divide X by Y and multiply by 100. 50 out of 250 is 20%.
- Percentage change — subtract the old value from the new, divide by the old value, multiply by 100. From 250 to 300 is (300−250)/250 = 20% increase.
- Add or subtract a percentage — multiply by (1 + X/100) or (1 − X/100).
- Reverse a percentage — divide by (1 + X/100) to recover the value before an increase.
The mistake almost everyone makes
A 20% fall followed by a 20% rise does not return you to where you started. Take 100: a 20% fall gives 80, and a 20% rise on 80 gives 96, not 100. The percentages are applied to different bases, so they do not cancel.
The same trap appears with discounts and tax. If a price includes 20% tax, the tax portion is not 20% of the displayed price — it is the displayed price divided by 1.2, subtracted from the displayed price. That is what the reverse calculation above is for.
Percentage points are not percent
If a rate rises from 4% to 6%, that is a rise of two percentage points, but a 50% increase. Both statements are true and they describe the same change. Reports that mix the two are a common source of confusion, and occasionally of deliberate misdirection.
Working with margins and markups
Markup is calculated on cost; margin is calculated on the selling price. An item costing 100 sold for 150 carries a 50% markup but a 33.3% margin. Confusing the two is one of the more expensive arithmetic errors in small business, because it quietly overstates profitability on every sale.
Frequently asked questions
How do I calculate X percent of a number?
Multiply the number by the percentage divided by 100. For example, 20% of 250 is 250 x 0.2, which is 50.
How do I calculate percentage increase?
Subtract the old value from the new value, divide the result by the old value, then multiply by 100. Dividing by the old value rather than the new one is the step people most often get wrong.
Does a 20% decrease followed by a 20% increase return the original number?
No. Each percentage applies to a different starting figure. 100 falls to 80, and a 20% rise on 80 gives 96.
What is the difference between percent and percentage points?
A move from 4% to 6% is two percentage points, and also a 50% increase. Both describe the same change but measure it differently.
What is the difference between margin and markup?
Markup is measured against cost and margin against the selling price. An item costing 100 and sold for 150 has a 50% markup but a 33.3% margin.