How to Calculate Percentage: 6 Everyday Methods With Examples
Percentages are everywhere: discounts, marks, interest, tax and tips. The word simply means "per hundred", so 15% is 15 out of every 100. Most percentage questions fit one of six patterns, and once you know which pattern you have, the sum is easy.
1. Find a percentage of a number
Part = Number × Percentage ÷ 100
What is 15% of 2,400? 2,400 × 15 ÷ 100 = 360.
Mental shortcut: 10% is the number with the decimal point moved one place left, and 5% is half of that. So 15% of 2,400 is 240 + 120 = 360.
2. Find what percentage one number is of another
Percentage = Part ÷ Whole × 100
You scored 72 out of 90. 72 ÷ 90 × 100 = 80%.
3. Percentage increase and decrease
Change % = (New − Old) ÷ Old × 100
A phone goes from 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. A negative answer means a decrease.
Notice that going back down is not the same percentage. From 100 down to 80 is a drop of 20 out of 100, which is a 20% decrease. The base for the change is always the starting value, so the two directions give different percentages.
4. Add or subtract a percentage (discounts and markups)
To add a percentage, multiply by (1 + p/100). To subtract it, multiply by (1 − p/100).
- A shirt costs 1,500 with a 20% discount: 1,500 × 0.80 = 1,200.
- A bill of 800 with a 10% service charge: 800 × 1.10 = 880.
5. Reverse percentage: find the original
You know the final price after a percentage was added or removed, and you want the original. Divide by the same factor.
A jacket is on sale for 1,600 after a 20% discount. The sale price is 80% of the original, so original = 1,600 ÷ 0.80 = 2,000. This is the same idea that lets you take GST out of a tax-inclusive price, which you can see in How to Calculate GST.
6. Percentage points versus percent
If an interest rate moves from 8% to 10%, it has gone up by 2 percentage points, but it has risen by 25 percent (2 ÷ 8 × 100). News reports often mix these up, so watch which one is meant.
Successive percentages do not simply add
A price rises 10% and then falls 10%. It does not return to where it began. Starting at 100, the rise gives 110, and 10% off 110 is 99. In the same way, a 20% discount followed by another 10% discount is not 30% off. It is 100 × 0.80 × 0.90 = 72, which is 28% off in total.
Common mistakes
- Using the wrong base. "Percent more than" uses the smaller original as its base; "percent less than" uses the larger original.
- Subtracting a percentage from a total that already includes it, instead of dividing by the factor.
- Rounding too early. Keep the full number until the last step.
Practice and check
Try your own numbers in the Percentage Calculator. It handles all the patterns above, shows the formula it used, and helps you check your own working. Practise with prices you see while shopping and you will soon do the common cases in your head.