What is a percentage?
A percentage is a way of expressing a number as a part of 100. The word "percent" literally means "per hundred." The percent symbol is %. For example, 25% means 25 parts out of 100, while 50% means 50 parts out of 100.
Percentages are used everywhere in everyday life. You may see them when comparing prices, calculating discounts, checking grades, measuring changes in a budget, reviewing interest rates, analyzing statistics, or working out how much one number represents compared with another.
Because percentage calculations can take several different forms, this calculator provides four common calculations in one place. You can find a percentage of a number, determine what percentage one number is of another, calculate a percentage increase or decrease, and work out a discount and final price.
How to calculate a percentage
The basic percentage formula is:
Percentage = (Part ÷ Whole) × 100
Suppose you scored 45 points out of a possible 60 points. To find your percentage, divide 45 by 60 and multiply the result by 100. The result is 75%.
Another common question is "What is 20% of 150?" In that case, convert 20% to a decimal by dividing it by 100, then multiply it by 150. The result is 30.
Common percentage calculations
Percentage of a number
To calculate X% of Y, multiply Y by X divided by 100.
Formula: (X ÷ 100) × Y
What percent is X of Y?
Divide X by Y and multiply the result by 100.
Formula: (X ÷ Y) × 100
Percentage change
Compare the difference between a new value and the original value.
Formula: ((New − Original) ÷ Original) × 100
Percentage discount
Calculate the amount saved from an original price and discount rate.
Discount = Price × Rate ÷ 100
Percentage increase and decrease
Percentage change tells you how much a value has changed relative to its original value. The original number is important because it provides the baseline for the comparison.
Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
If a price goes from $100 to $125, the difference is $25. Dividing $25 by the original $100 gives 0.25. Multiplying by 100 gives a 25% increase.
If a price falls from $100 to $80, the difference is -$20. Relative to the original $100, that represents a 20% decrease. The same formula works for both increases and decreases; the sign of the result tells you the direction of the change.
How to calculate a discount
Percentage discounts are especially common when shopping. To calculate a discount, multiply the original price by the discount percentage expressed as a decimal.
For example, imagine an item costs $80 and has a 25% discount. Twenty-five percent of $80 is $20, so the discount saves you $20. Subtracting $20 from the original $80 gives a final price of $60.
Final Price = Original Price − Discount Amount
This calculator separates the discount amount from the final price so you can see both numbers clearly.
Where percentages are used
Percentages are useful far beyond school math. They are a basic part of many everyday calculations.
- Shopping: Calculate sale prices, discounts, and savings.
- School: Convert test scores and grades into percentages.
- Business: Compare changes in sales, expenses, revenue, or other figures.
- Finance: Work with rates, returns, changes, and other percentage-based values.
- Statistics: Express proportions and comparisons as percentages.
- Daily planning: Compare budgets, quantities, targets, and changes over time.
Why percentage changes can be confusing
One common source of confusion is that percentage increases and decreases are based on the starting value. A 50% increase followed by a 50% decrease does not return a number to its original value.
For example, start with 100. A 50% increase brings the value to 150. A 50% decrease from 150 is 75, not 100. The reason is that the second 50% is calculated using 150 as the new starting point.
This is why it is important to identify the original or reference value before calculating a percentage change.
Percentage calculator examples
| Question | Calculation | Answer |
|---|---|---|
| What is 20% of 150? | 0.20 × 150 | 30 |
| 50 is what percent of 200? | (50 ÷ 200) × 100 | 25% |
| Increase from 100 to 120 | (20 ÷ 100) × 100 | 20% increase |
| 20% off $100 | $100 × 0.20 | $20 saved |
Frequently asked questions
How do I calculate a percentage?
To find what percentage one number is of another, divide the first number by the second number and multiply by 100. For example, 25 divided by 100 times 100 equals 25%.
What is 10% of 200?
Ten percent of 200 is 20. You can calculate it by multiplying 200 by 0.10.
How do I calculate percentage increase?
Subtract the original value from the new value, divide that difference by the original value, and multiply by 100. The result is the percentage increase when the new value is greater than the original.
How do I calculate percentage decrease?
Subtract the new value from the original value, divide the difference by the original value, and multiply by 100. The result is the percentage decrease when the new value is lower than the original.
How do I calculate 20% off a price?
Multiply the original price by 0.20 to find the discount amount. Then subtract the discount from the original price to get the final price.
Can a percentage be greater than 100%?
Yes. A percentage can be greater than 100% when the value being compared is larger than the reference value. For example, 150 is 150% of 100.
What is the difference between percentage and percentage change?
A percentage can describe a part of a whole, while percentage change measures how much a value has increased or decreased relative to an original value.
Does this percentage calculator store my numbers?
The calculations on this page are performed directly in your browser. The calculator does not need to send your entered numbers to a server to perform these calculations.
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More About Percentages
For additional background on percentages and related mathematical concepts, you can also explore these educational references: