Percentage Calculator

What is a Percentage?

In mathematics, a percentage is a way of expressing a ratio as a part of 100. It is one of the most common methods of showing proportions, alongside fractions, ratios, and decimals. The percentage symbol “%” is generally used, but you may also see “percent” or “pct.” written after a number. For instance, 35% is equal to the decimal 0.35 or the fraction 35/100.

To find a percentage, take the ratio and multiply it by 100.

Example:

If 25 out of 50 students in a class are male:

\[ \frac{25}{50} = 0.5 \] \[ 0.5 \times 100 = 50\% \]

This means 50% of the class are male students.

Percentage Formula

The general equation for percentage is:

\[ P \times V_1 = V_2 \]

• P = Percentage
• V1 = Base value
• V2 = Result after applying the percentage

Example:

\[ P \times 30 = 1.5 \] \[ P = \frac{1.5}{30} \times 100 = 5\% \]

When solving manually, percentages are expressed as decimals during the calculation, and then multiplied by 100 to return to percent form. Our percentage calculator handles this automatically.

Percentage Difference Formula

The percentage difference between two values compares their difference to the average of the two.

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

Example:

\[ \frac{|10 - 6|}{\frac{10 + 6}{2}} = \frac{4}{8} = 0.5 = 50\% \]

So, the difference between 10 and 6 equals 50%.

Percentage Change Formula

Percentage change measures the increase or decrease of a value compared to its original.

\[ \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100 \]

Examples:

\[ 500 \times (1 + 0.1) = 550 \quad (\text{10% increase}) \] \[ 500 \times (1 - 0.1) = 450 \quad (\text{10% decrease}) \]

Thus, a 10% increase of 500 is 550, while a 10% decrease of 500 is 450.