Percentage Calculator

About Percentage Calculator

A percentage is a way of expressing a quantity as a fraction of 100. The word "percent" literally means "per hundred," which is why the percentage symbol (%) represents a ratio whose reference base is 100. For example, 25% is equivalent to 25/100, 0.25, and one quarter. Percentages provide a convenient way to compare quantities even when the numbers themselves have different scales.

Percentages are used throughout mathematics and everyday life. They appear in discounts, taxes, grades, statistics, interest rates, population changes, business reports, measurements, probability, scientific data, financial calculations, and comparisons between quantities. Because percentages describe a relationship rather than simply an absolute amount, the same percentage can represent very different numerical values depending on the reference quantity.

This Percentage Calculator combines three common percentage problems in one tool. It can calculate a percentage of a number, determine what percentage one number represents of another number, and calculate the percentage change between an original value and a new value. These calculations are related, but they answer different mathematical questions and therefore use different formulas.

What Is a Percentage?

A percentage represents a ratio out of 100. For example, 40% means 40 parts out of every 100 parts. It can be converted to a decimal by dividing by 100:

Likewise, a decimal can be converted into a percentage by multiplying it by 100:

Fractions can also be expressed as percentages. For example:

What Is a Percentage of a Number?

The first calculation determines how much a particular percentage represents of a given number. To calculate P% of a value V, convert the percentage to a decimal and multiply it by the value.

For example, to calculate 20% of 150:

Therefore, 20% of 150 is 30. This type of calculation is commonly used when determining discounts, taxes, commissions, portions of a total, statistical proportions, and other quantities based on a percentage.

What Percentage Is One Number of Another?

The second calculation answers a different question: given a part and a whole, what percentage does the part represent? The part is divided by the whole and the result is multiplied by 100.

For example, if 30 is part of a total of 60:

Therefore, 30 is 50% of 60. The order of the numbers matters. Asking what percentage 30 is of 60 is not the same as asking what percentage 60 is of 30.

Percentage Change

Percentage change measures how much a value has changed relative to its original value. It is especially useful when comparing a starting measurement with a later measurement. The calculation uses the difference between the new and original values and compares that difference with the original value.

For example, if a value increases from 50 to 75, the absolute change is 25. Relative to the original value of 50:

The result is a 50% increase. If the new value were smaller than the original value, the percentage change would be negative, indicating a decrease.

Percentage Increase and Decrease

A percentage increase changes an original value by adding a specified percentage of that original value. A percentage decrease subtracts a specified percentage of the original value.

For example, increasing 500 by 10% gives:

Decreasing 500 by 10% gives:

Percentage Change vs. Percentage Difference

Percentage change and percentage difference are not the same calculation. Percentage change normally compares a new value with a designated original or starting value. Percentage difference, on the other hand, compares two values without treating either one as the starting point. It uses the average of the two values as the reference.

This distinction is important when interpreting results. If one value is explicitly the original measurement and the other is the new measurement, percentage change is generally the appropriate calculation. If two measurements are simply being compared without a designated starting point, percentage difference may be more appropriate.

Why the Reference Value Matters

A percentage is always relative to some reference quantity. This is why the same numerical difference can produce different percentage changes. For example, an increase of 10 from 50 to 60 represents a 20% increase, while an increase of 10 from 100 to 110 represents only a 10% increase. The absolute change is identical, but the original values are different.

Successive Percentage Changes

Percentage increases and decreases applied one after another should not generally be added together. Each new percentage change is applied to the value produced by the previous change.

For example, increasing a value by 20% and then decreasing the resulting value by 20% does not return it to its starting value:

The final value is 96 rather than 100. This happens because the second 20% is calculated from 120 rather than from the original 100.

Percentage Calculation Formulas

Example

Suppose a product originally costs $80 and its price increases to $100. The absolute increase is $20. The percentage change is calculated using the original $80 as the reference:

The price therefore increased by 25%. Notice that calculating the change relative to the original value is essential; using the new value as the denominator would answer a different mathematical question.

Using This Percentage Calculator

Enter the values for the three percentage calculations shown above. The calculator evaluates each section independently and provides the numerical result together with the formula, substitution, intermediate calculation, and interpretation of the result. If a calculation would require division by zero, the calculator identifies that condition instead of returning an invalid numerical result.