Knowing how to calculate percentage of a number is a skill needed constantly—whether for discounts, tips, exam results, salary raises, or an increase in your electricity bill. The calculator below covers the three most common ways to calculate percentage of a number, and this page also explains the corresponding calculation method so you can perform the operation on paper if necessary. Simply select a mode and enter the two numbers: the result appears instantly as you type.
How to Calculate Percentage of a Number
“Percent” means “per hundred.” When calculating 15% of a number, you are essentially taking fifteen-hundredths of that number. This fundamental principle applies to all percentage problems you encounter; the only difference lies in the specific value you are trying to determine. The NIST guide to SI units puts it precisely: the % symbol represents the number 0.01.
Multiply the number by the percentage and then divide the result by 100. Alternatively, you can first convert the percentage into a decimal and perform a single multiplication. Example for 15% of 200: 15 ÷ 100 equals 0.15, and 0.15 × 200 equals 30. Example for 20% of 850: 0.20 × 850 equals 170.
The decimal method is faster once mastered: simply move the decimal point two places to the left and perform the multiplication.
The Mental Shortcut Worth Knowing
To find 10% of a number, simply move the decimal point one place to the left. For example, 10% of 850 is 85. From there, you can determine common percentages without a calculator: 5% is half that value, 20% is double it, and 15% is found by adding the 10% and 5% figures. Therefore, to calculate 15% of 850, you do the following: 85 + 42.5 = 127.5. This is very practical for calculating tips and discounts quickly.
The 3 Ways to Calculate Percentage of a Number
Almost every percentage question is one of three shapes. The calculator has a mode for each.
1. What is X% of Y?
This is the standard method; it is the one most people refer to when talking about how to calculate percentage of a number. Both the percentage and the total value are known, and the goal is to determine the partial value.
Divide the percentage by 100 and multiply the result by the total value. 15% of 200 equals 30. For a 25% discount on an item valued at 80, 20 is deducted, resulting in 60.
2. X is What Percent of Y?
This involves two numbers whose relationship is to be determined. This calculation is used for test results, survey results, and any matter relating to the “proportion of a total value.”
Divide the part by the total and then multiply the result by 100. For example, if you obtained 45 points out of a total of 180: 45 ÷ 180 = 0.25 and 0.25 × 100 = 25%. If 30 people out of a total of 200 participated in a survey, this equates to 15%.
3. Percentage Change from X to Y
Use this method when a value has changed and you want to know the magnitude of that variation as a percentage—for example, for prices, wages, traffic figures, or weights.
Subtract the old value from the new one, divide the result by the old value, and multiply by 100. Example: an increase from 40 to 55; the difference is 15, and 15 ÷ 40 × 100 yields a 37.5% increase. Example: a drop from 250 to 200; the difference is −50, and −50 ÷ 250 × 100 yields a 20% decrease.
The old value is placed in the denominator (at the bottom). Swapping these terms is by far the most common error in percentage calculations; this is precisely why an increase from 80 to 100 represents a 25% rise, whereas a drop from 100 to 80 represents a 20% fall: even though the figures are the same, the starting point differs.
Where Percentages Turn Up
- Shopping — Discounts, markdowns, taxes added at checkout
- Salary — Salary increase, bonus based on base salary, deductions
- Education — Grades as a percentage of total points, grading thresholds, attendance
- Money — Interest rates, savings yield, change in value over time
- Health and fitness — Body fat percentage, proportion of daily caloric intake
- Comparisons — Current month vs. previous month, comparison of two options
Related Calculators
- Discount Calculator — work out what you actually pay after a percentage off.
- Salary Hike Calculator — a raise expressed as a percentage increase.
- Compound Interest Calculator — what happens when a percentage is applied repeatedly.
- Body Fat Calculator — a percentage of a different kind.
- Flat vs Reducing Rate Calculator — the same rate meaning two different things.
How do you calculate the percentage of a number?
Divide the percentage by 100 to convert it into a decimal, then multiply it by the number in question. To calculate 15% of 200: 0.15 × 200 = 30. The calculator above performs this operation in its first mode.
How do you find what percent one number is of another?
Divide the smaller number by the larger number and multiply the result by 100. 45 out of 180 equals 45 ÷ 180 × 100 = 25%.
How do you calculate percentage increase?
Subtract the initial value from the new value, divide the result by the initial value, and then multiply by 100. The increase from 40 to 55 corresponds to 37.5%.
What is the difference between percentage change and percentage difference?
In the case of a percentage change, there are well-defined initial and final states, such that the original value serves as the reference. In contrast, percentage difference compares two values without a natural order; therefore, the average of the two values is used as the reference.
Why is a 20% fall not cancelled out by a 20% rise?
Indeed, each value is calculated from a different initial figure. If 100 is reduced by 20%, the result is 80; if 80 is increased by 20%, the result is 96, not 100. The second percentage is calculated based on the smaller figure.
How do I turn a percentage into a decimal?
Divide by 100; this is equivalent to moving the decimal point two places to the left. 15% becomes 0.15, 7.5% becomes 0.075, and 120% becomes 1.2.