Knowing how to calculate percent or percentage is a useful skill in everyday life. You’ll use percentages to calculate grades, tips, taxes, chance of rain, and car payments. In science, percent finds use in percent error and mass percent calculations. Here is a step-by-step tutorial showing how to find percent and examples of practical applications.

### What Is Percent?

Per cent means “per one hundred.” It expresses the fraction of a number out of a total amount multiplied by 100%. The percent sign (%) or “pct” abbreviation indicate percentage. A percent value may be written as a fraction out of 100 (e.g., 5% is 5/100) or as its decimal equivalent (5/100 is 0.05).

### How to Calculate Percent

**Determine the total amount or number.**- D
**ivide the number you want expressed as a percent by the total.**Usually, you divide the smaller number by the larger number. **Multiply the answer by 100%.**

### Example Percent Calculation: Marbles

You have 9 marbles. 3 of them are blue. What percent of the marble are blue? What percent of the marbles are not blue?

- Start with the total number of marbles. This is 9.
- Divide the number of blue marbles (3) by the total number of marbles (9).

3/9 = 0.333 - Multiply the answer by 100%.

0.333 x 100% = 33.3%

There are two ways to find the percent of marbles that are not blue. The percentages of all the colors of marbles must add up to 100%, so the easiest way is to subtract the percentage of blue marbles from 100%.

Percent of other colors = 100% – 33.3%

Percent of other colors = 66.7%

The other way would be to add up the number of non-blue marbles:

- Again, start with the total number of marbles (9).
- Add up the number of non-blue marbles (6) and divide this value by the total number (9):

6/9 = 0.667 - Multiply the answer by 100%.

0.667 x 100% = 66.7%

### Example: How to Calculate a Tip

You want to give a 15% tip on a meal that cost $18.72. How much do you tip?

Find 15% of $18.72:

x = 0.15 * $18.72

x = $2.808 or $2.81

The easier way to calculate tip doesn’t actually require multiplication. Just move the decimal point one space to the left to get 10%, so a 10% tip on $18.72 would be $1.87. A 5% tip would be half this amount or about 94 cents. Add together the 10% tip and the 5% tip to get the 15% tip ($1.87 + $0.94).

### Example: Calculating Sales Tax

If sale tax is 8.1%, how much will a $12.99 toy cost?

The first step is to find 8.1% of $12.99. Remember, 8.1% is the same as 8.1/100 or 0.081.

x = 0.081 * $12.99

x = $1.05

So, the tax on the toy is $1.05. The total cost is the item price plus the tax:

Total = $12.99 + $1.05 = $14.04

### Example: Calculate a Grade

You need to get at least 60% on the final exam to pass a class. The final has 15 questions that are all worth the same amount. How many do you need to get correct in order to pass?

Calculate what 60% of 15 is. Remember, 60% is the same as the fraction 60/100 or the decimal value 0.60.

x = 0.60 * 15

x = 9

So, you need to get at least 9 questions right to get a 60% on the test.

### References

- Bennett, Jeffrey; Briggs, William (2005).
*Using and Understanding Mathematics / A Quantitative Reasoning Approach*(3rd ed.). Pearson Addison Wesley. ISBN 0-321-22773-5. - Smith, D.E. (1958) [1951].
*History of Mathematics*. 2. Courier Dover Publications. ISBN 0-486-20430-8.