Percentages express an amount as a part of one hundred. They appear in discounts, price increases, taxes, statistics, comparisons, interest rates and many everyday situations.
Although the operations are usually simple, it is common to confuse a percentage of an amount, percentage change, percentage difference and the percentage required to return to an original value.
What does percentage mean?
Percentage literally means “per one hundred.” For example, 25% represents 25 parts out of a total of 100.
A percentage can be written in three equivalent forms:
To convert a percentage to a decimal, divide it by 100:
How to calculate a percentage of an amount
To calculate a percentage of a number, multiply the amount by the percentage and divide by 100.
Example: calculate 15% of 200
Therefore, 15% of 200 is 30.
Example: calculate 21% of 1,000
Twenty-one percent of 1,000 is 210.
How to find what percentage one value represents
When you know a partial value and the total, divide the partial value by the total and multiply by 100.
Example: 30 is what percentage of 200?
Therefore, 30 represents 15% of 200.
Example: 45 correct answers out of 60
The correct answers represent 75% of the total.
How to calculate a percentage increase
To increase a value by a percentage, calculate the percentage amount and add it to the original value.
You can also use a direct formula:
Example: increase 100 by 21%
The final value after a 21% increase is 121.
Example: increase a price of 800 by 12%
The new price is 896.
How to calculate discounts and decreases
To apply a discount, calculate the percentage of the original price and subtract it.
You can also obtain the final price directly:
Example: 20% discount on 500
The discount is 100 and the final price is 400.
Example: 35% discount on 1,200
The final price is 780.
How to calculate percentage change
Percentage change shows how much a value increased or decreased relative to its original value.
Increase example: from 100 to 125
The value increased by 25%.
Decrease example: from 200 to 150
The negative result represents a 25% decrease.
Percentage change versus percentage difference
These calculations look similar, but they answer different questions.
| Operation | When it is used | Reference |
|---|---|---|
| Percentage change | When there is an original value and a new value | The original value |
| Percentage difference | When two equivalent values are compared | The average of both values |
Percentage difference uses the absolute difference between the values and divides it by their average.
Example: compare 80 and 100
The percentage difference between 80 and 100 is approximately 22.22%.
How to find the original value
Sometimes you know the final price after an increase or discount but need to recover the original value.
Original value after an increase
If the final value is 121 after a 21% increase:
Original value after a discount
If an item costs 400 after a 20% discount:
The original price was 500.
Successive percentages are not added directly
When multiple percentages are applied one after another, every percentage is calculated using the previous result.
Two 20% discounts
Assume an original price of 100:
The final price is 64. The total discount is 36%, not 40%.
A 20% increase followed by a 20% decrease
The final result is 96. Applying +20% and then −20% does not restore the original value.
Percentage points versus percentage change
Percentage points compare two percentage values directly.
If a rate moves from 20% to 25%, it increased by:
- 5 percentage points.
- 25% in relative terms, because 5 is 25% of 20.
Common percentage calculation mistakes
Using the wrong reference value
In percentage change, the denominator must be the original value. Changing the denominator changes the result.
Adding successive discounts
Successive discounts are applied one after another. They should not be added as though both were applied directly to the original price.
Confusing percentages with percentage points
A change between two rates can be expressed as a point difference or as a relative percentage change. They are different measurements.
Dividing by zero
It is not possible to calculate what percentage a number represents of zero. Conventional percentage change is also undefined when the original value is zero.
Rounding too early
Keep several decimal places during the calculation and round only the final result.
Calculate percentages automatically
Use the SWS Universe calculator to calculate percentages, increases, discounts, changes and differences without writing the formulas manually.