How to Calculate Percentages

To calculate a percentage, divide the part by the whole and multiply the result by 100. That single formula answers almost every percentage question you'll ever run into, whether you're splitting a restaurant bill, checking a discount, or figuring out a test score. The tricky part isn't the math itself, it's knowing which number is the "part" and which is the "whole" in a given problem.

If you'd rather skip the arithmetic entirely, the Percentage Calculator handles all three core percentage questions instantly. But understanding the formula is worth five minutes, because it makes every percentage problem you encounter — at work, at the store, or in a spreadsheet — obvious instead of confusing.

The Percentage Formula

There are really only three questions people ask about percentages, and each one rearranges the same basic formula:

What is X% of Y? → (X ÷ 100) × Y
X is what percent of Y? → (X ÷ Y) × 100
X is Y% of what number? → X ÷ (Y ÷ 100)

Once you can spot which of these three shapes a problem fits, the calculation is just plugging in numbers.

Worked Examples

Percentage of a number

Question: What is 20% of 150?

Convert 20% to a decimal (20 ÷ 100 = 0.2), then multiply by 150.

0.2 × 150 = 30

So 20% of 150 is 30.

What percent is X of Y

Question: 45 is what percent of 180?

Divide the part by the whole, then multiply by 100.

(45 ÷ 180) × 100 = 25

So 45 is 25% of 180.

Percentage increase and decrease

Percentage change problems trip more people up because there are two extra steps: find the difference, then compare it to the original number, not the new one.

Increase example: A product's price goes from $80 to $92. The increase is $12. Divide that by the original price: 12 ÷ 80 = 0.15, or 15%. The price increased by 15%.

Decrease example: A city's population drops from 50,000 to 46,500. The decrease is 3,500. Divide by the original: 3,500 ÷ 50,000 = 0.07, or 7%. The population decreased by 7%.

The formula for a percentage increase is:

((New Value − Original Value) ÷ Original Value) × 100

If the result is negative, you've calculated a decrease. The dedicated percentage increase calculator does this automatically if you'd rather not track the sign yourself, and it's especially handy when you're comparing several changes at once, like quarterly revenue or year-over-year growth.

Common Real-World Uses

Tips

To leave an 18% tip on a $64 bill: 0.18 × 64 = 11.52, so you'd add about $11.52, bringing the total to roughly $75.52. Most people round the tip up or down to a whole number for simplicity.

Discounts

A $120 jacket marked 30% off: the discount amount is 0.3 × 120 = 36. Subtract that from the original price: 120 − 36 = 84. You pay $84. A common shortcut is to calculate what you'll actually pay directly — multiply by (1 − discount rate), so 120 × 0.7 = 84 in one step.

Grades

If you scored 42 out of 50 on a test, your percentage grade is (42 ÷ 50) × 100 = 84%. This is the same "what percent is X of Y" formula from above — grades, test scores, and completion rates all use this exact structure.

Mistakes to Avoid

Comparing to the wrong base. Percentage change is always calculated against the original number, not the new one. Going from 100 to 150 is a 50% increase, but going from 150 back to 100 is a 33.3% decrease, not 50%, because the base changed.
Forgetting to convert the percent to a decimal. 20% is 0.2, not 20, when you're multiplying. Skipping this step is the single most common source of errors.
Adding percentages instead of compounding them. A 10% increase followed by another 10% increase is not a 20% increase overall. $100 up 10% is $110; up another 10% is $121, an actual increase of 21%.
Rounding too early. If a calculation has multiple steps, round only the final answer. Rounding intermediate results can shift your final number noticeably, especially with larger amounts.
Mixing up percentage change and percentage difference. Percentage change assumes one value is the "before" and one is the "after." Percentage difference, used when comparing two values with no clear starting point, divides by the average of the two numbers instead of one specific original value.

Frequently asked questions

How do I calculate a percentage of a number?

Convert the percentage to a decimal by dividing it by 100, then multiply that decimal by the number. For example, to find 15% of 200, calculate 0.15 × 200 = 30. This is the most common percentage calculation and the one worth memorizing first, since the other two formulas are just rearrangements of it.

How do I calculate percentage increase?

Subtract the original value from the new value to get the amount of change, then divide that change by the original value and multiply by 100. Going from 40 to 50 is a change of 10; 10 ÷ 40 = 0.25, so that's a 25% increase. Always divide by the starting number, not the ending one.

What is the percentage difference between two numbers?

Percentage difference compares two values without treating either one as the "original." Take the absolute difference between the two numbers, divide by the average of the two numbers, and multiply by 100. For 40 and 50, the difference is 10, the average is 45, and 10 ÷ 45 × 100 ≈ 22.2%. This differs from percentage change, which would give a different answer depending on which number you treat as the starting point.

How do I work out a percentage in reverse?

This is the "X is Y% of what number" problem: you know a value and what percentage it represents, and you need the original total. Divide the known value by the percentage expressed as a decimal. For example, if $45 is 30% of an unknown total, calculate 45 ÷ 0.3 = 150. This shows up often with taxes and discounts, such as figuring out the pre-tax price when you only know the tax amount and rate.