How to Calculate Percentage: Formulas, Examples and Cheat Sheet

To calculate a percentage of a number, divide the percentage by 100 and multiply by the number: 18% of 250 is 0.18 × 250 = 45. To find what percentage one number is of another, divide the part by the whole and multiply by 100: 45 out of 60 is 45 ÷ 60 × 100 = 75%.

“Per cent” means “per hundred”, so every percentage question is really about scaling to 100. Below are the five calculations that cover almost every real situation, the reverse-percentage trick most people get wrong, and a cheat sheet you can keep.

1. Percentage of a number

Example: a restaurant bill is $64 and you want to tip 15%. 0.15 × 64 = $9.60.

Mental shortcut: find 10% by moving the decimal point one place left, then build from there. 10% of 64 is 6.40, half of that (5%) is 3.20, so 15% is 6.40 + 3.20 = 9.60.

Swap trick: x% of y equals y% of x. 8% of 25 is hard; 25% of 8 is easy, and both are 2.

2. What percentage is one number of another?

Example: you scored 45 out of 60 on a test. 45 ÷ 60 = 0.75, × 100 = 75%.

Make sure the “whole” is the right one. If 12 of 30 students in a class are left-handed, 12 ÷ 30 = 40% of the class is left-handed. If 12 of the school’s 400 left-handers are in that class, 12 ÷ 400 = 3% of left-handers are in it. Same 12, different question.

For marks across several weighted assignments, the grade calculator does the weighting for you.

3. Percentage change (increase or decrease)

A positive result is an increase, a negative result is a decrease.

Example: a monthly bill rises from $80 to $92. (92 − 80) ÷ 80 × 100 = 15% increase.

Example: it falls back from $92 to $80. (80 − 92) ÷ 92 × 100 = 13.04% decrease.

Notice that the rise and the fall are not the same size in percentage terms, because the starting value is different. Always divide by the old value.

4. Increase or decrease a number by a percentage

Example: a $45,000 salary with a 4% raise becomes 45,000 × 1.04 = $46,800.

Example: a $250 jacket at 30% off costs 250 × 0.70 = $175.

Using a single multiplier (1.04 or 0.70) is faster and less error-prone than working out the change and then adding or subtracting it.

5. Reverse percentages: finding the original

This is the calculation people get wrong most often. If you know the value after a percentage change, divide by the multiplier to get back to the original.

Example: before a discount. A phone costs $480 after a 20% discount. The original price is 480 ÷ 0.80 = $600.

Example: removing tax. A receipt shows $54.00 including 8% sales tax. The price before tax is 54 ÷ 1.08 = $50.00, so the tax was $4.00.

The common mistake: taking 8% off the total. 54 × 0.92 = $49.68, which is wrong, because the 8% was calculated on $50, not on $54.

Percentage points vs percent

When a percentage itself changes, there are two ways to describe it:

• An interest rate rises from 4% to 5%. That is a rise of 1 percentage point.
• The same rise is a 25% increase in the rate, because (5 − 4) ÷ 4 × 100 = 25%.

Both statements are true. News reports and loan offers mix them up, so check which one is meant.

Successive percentages multiply, they don’t add

Up then down: a price rises 10% and then falls 10%. 100 × 1.10 × 0.90 = 99, so the net change is −1%, not zero.

Stacked discounts: “20% off, plus an extra 10% at checkout” is 0.80 × 0.90 = 0.72 of the price, a total discount of 28%, not 30%.

Growth over years: 5% a year for 3 years is 1.05³ = 1.157625, a 15.76% total rise, not 15%. This is compounding; our guide to compound interest covers it in depth.

Recovering from a loss: after a 50% fall, you need a 100% rise to get back to where you started (50 × 2 = 100).

Percentage difference vs percentage change

Percentage change has a clear “before” and “after”. When you compare two values with no natural starting point, such as two shops’ prices, people often use the percentage difference, which divides by the average:

Example: $40 and $50. |40 − 50| ÷ 45 × 100 = 22.2%. By contrast, $50 is 25% more than $40, and $40 is 20% less than $50. Say which measure you are using.

Cheat sheet

Common fractions as percentages

Formula summary

Common mistakes to avoid

1. Dividing by the wrong base. Percentage change always divides by the starting value.
2. Reversing a percentage by subtracting it. Divide by the multiplier instead.
3. Adding successive percentages. Multiply the factors.
4. Confusing percent with percentage points.
5. Rounding too early. Keep full precision until the final step, especially with money.

If you want to skip the arithmetic, the percentage calculator handles all of these and shows the working. Students converting grade averages to percentages should read our guide on CGPA to percentage, because those conversions use official formulas, not plain percentage maths.

FAQ

How do I calculate a percentage of a total?

Divide the part by the total and multiply by 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.

How do I add a percentage to a number?

Multiply by 1 plus the percentage as a decimal. Adding 15% to 200 is 200 × 1.15 = 230.

How do I find the original price before a discount?

Divide the sale price by 1 minus the discount as a decimal. A $75 item after 25% off was 75 ÷ 0.75 = $100.

Why is a 10% rise followed by a 10% fall not zero?

The fall is taken from a bigger number. 100 rises to 110, and 10% of 110 is 11, so the price ends at 99, a 1% loss overall.