Everyday math
How to Calculate Percentages
Percentages show a number as part of 100. That makes them useful for discounts, grades, tips, price increases, savings rates, taxes, fees, and comparison math. The formulas are simple, but the wording can be confusing because "20% of 150," "20% more than 150," and "150 is 20% of what?" are three different questions.
The safest way to handle percentage math is to identify which value is the part, which value is the whole, and whether you are moving forward or backward. The calculator handles the arithmetic, but understanding the pattern helps you catch obvious input mistakes.
Percent of a number
To find a percent of a number, divide the percent by 100 and multiply by the number. For example, 20% of 150 is 0.20 times 150, which equals 30. This is the most common percentage question for tips, fees, taxes, and partial amounts.
Formula: percent divided by 100 times number.
Part as a percent of the whole
To find what percent one number is of another, divide the part by the whole and multiply by 100. If 30 out of 150 items are complete, 30 divided by 150 is 0.20, or 20%. This pattern works for completion rates, score percentages, budget share, and survey results.
Formula: part divided by whole times 100.
Percentage change
Percentage change compares an old value with a new value. Subtract the original value from the new value, divide by the original value, then multiply by 100. If a price rises from 100 to 125, the change is 25 divided by 100, or a 25% increase.
Use percentage change when one value is clearly the starting point. Use percent difference when neither value is the obvious starting value.
Add or subtract a percentage
Adding a percentage means multiplying by 1 plus the percentage as a decimal. Adding 15% to 200 means 200 times 1.15, which equals 230. Subtracting a percentage means multiplying by 1 minus the percentage as a decimal. Subtracting 15% from 200 means 200 times 0.85, which equals 170.
This is useful for sale tax, markups, discounts, price increases, and fee estimates.
Reverse percentages
Reverse percentage questions work backward from a final value. If an item costs 80 after a 20% discount, the final price is 80% of the original price. Divide 80 by 0.80 to get the original price of 100. If a value is 120 after a 20% increase, divide 120 by 1.20 to get the original value of 100.
The common mistake is subtracting 20 from 80 or adding 20 back to 80. A percent change is based on the original value, so the reverse calculation needs division.
Grade percentages
A grade percentage is points earned divided by points possible, multiplied by 100. If you earned 42 points out of 50, the score is 42 divided by 50, or 84%. If an assignment is weighted, the grade percentage may need to be multiplied by the assignment weight before it is added to the course average.
For course planning, use the GPA Calculator after you know the final course grades and credits.
Fractions and decimals
Fractions, decimals, and percentages are different ways to describe the same relationship. Three eighths is 3 divided by 8, or 0.375. Multiply by 100 and it becomes 37.5%. To turn a percentage into a decimal, divide by 100. To turn a decimal into a percentage, multiply by 100.
Percentage FAQ
Why is a 50% increase followed by a 50% decrease not the same number?
Because the second percentage is based on the new value, not the original value. Starting at 100, a 50% increase gives 150. A 50% decrease from 150 gives 75.
What is the difference between percent change and percent difference?
Percent change uses an original value as the baseline. Percent difference uses the average of two values as the baseline, which is useful when neither value is clearly first.
How do I calculate a discount quickly?
Find the discount amount by multiplying the price by the discount percent, then subtract it from the price. Or multiply the price by 1 minus the discount decimal.