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Percentage Calculator

Please enter any two values below or adjust the default values as needed, then click the “Calculate” button to find the third value.

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If is %, what is the total?

Percentage Difference Calculator

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Percentage Change Calculator

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What is a Percentage?

In mathematics, a percentage is a way to express a number or ratio as a fraction of 100. It provides a dimensionless relationship between two numbers and can also be represented using ratios, fractions, or decimals. Percentages are typically indicated by the “%” symbol, but can also be written as “percent” or “pct” following the number.

For example: 35 100 is the same as the decimal 0.35.

To calculate a percentage, multiply the ratio by 100. For example, if 25 of 50 students are male, the ratio is:

25 50 = 0.5 Multiplying this by 100 gives: 0.5×100=50

This means that 50% of the students in the classroom are male.

Percentage formula

Although the percentage formula can be expressed in various forms, it is essentially an algebraic equation involving three values:

P × V1 = V2

Here, P represents the percentage, V1 is the initial value to be modified by the percentage, and V2 is the result of applying P to V1. The calculator automatically converts the input percentage into its decimal equivalent to compute the solution. However, when solving for the percentage, the returned value is the actual percentage, not its decimal form.

For example: P × 30 = 1.5

To solve for P = 1.5 30 = 0.05 × 100 = 5 %

When solving manually, it is essential to express the percentage in decimal form first. Once the decimal value of P is calculated, multiply it by 100 to convert it back to a percentage. This is precisely what the calculator does, but it accepts inputs in percent form instead of decimals.

Percentage difference formula

The percentage difference between two values is calculated by dividing the absolute value of their difference by the average of the two values. To express the result as a percentage, multiply it by 100. The formula is as follows:

\[ \text{Percentage Difference} = \frac{|V_1 – V_2|}{\frac{(V_1 + V_2)}{2}} \times 100 \]

For example, if \( V_1 = 10 \) and \( V_2 = 6 \):

\[ |10 – 6| = 4 \]

The average is:

\[ \frac{(10 + 6)}{2} = 8 \]

Dividing the difference by the average:

\[ \frac{4}{8} = 0.5 \]

Finally, multiplying by 100 gives:

\[ 0.5 \times 100 = 50\% \]

This means the percentage difference between 10 and 6 is 50%.

Percentage change formula

Percentage increase and decrease are calculated by finding the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values, dividing the result by the initial value, and calculating how much the initial value has changed.

The percentage increase calculator above determines either an increase or decrease of a specific percentage of the input number. It works by converting the percentage into its decimal equivalent and then either adding (for increase) or subtracting (for decrease) this value from 1. Multiplying the original number by this result gives either the increased or decreased value. Refer to the example below for clarification:

Example:

500 increased by 10%: 500 × ( 1 + 0.1 ) = 550

500 decreased by 10%: 500 × ( 1 0.1 ) = 450

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