Percentage Calculator

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. It helps compare values in a standard format, alongside other methods like fractions, decimals, and ratios. Percentages are represented by the % symbol, or written as "percent" or "pct." For example, 35% is the same as 0.35 or 35 out of 100.

To calculate a percentage, you multiply the ratio by 100.

• Example:
  If 25 out of 50 students are male:
  25 ÷ 50 = 0.5
  0.5 × 100 = 50%
  So, 50% of the students are male.

Percentage Formula

The general formula for calculating percentages is:

P × V₁ = V₂

• P is the percentage (in decimal form)
• V₁ is the base value
• V₂ is the result

To find the percentage when V₁ and V₂ are known, rearrange the formula:

P = V₂ ÷ V₁
Then multiply by 100 to convert to a percentage.

• Example:
  P × 30 = 1.5
  P = 1.5 ÷ 30 = 0.05
  0.05 × 100 = 5%

Percentage Difference Formula

To compare two values, use the percentage difference formula:

Percentage Difference = [V₁ – V₂] ÷ [(V₁ + V₂) ÷ 2] × 100

• Example:
  [10 – 6] ÷ [(10 + 6) ÷ 2] = 4 ÷ 8 = 0.5
  0.5 × 100 = 50%

Percentage Change Formula (Increase or Decrease)

To calculate a percentage increase or decrease:

(New Value – Original Value) ÷ Original Value × 100

• Example - Increase:
  500 increased by 10%
  10% = 0.10
  500 × (1 + 0.10) = 550

• ‍Example - Decrease:
  500 decreased by 10%
  500 × (1 – 0.10) = 450