Percentage Calculator

Understanding Percentage Calculations

Basic Percentage Formula

The fundamental percentage formula is:

Percentage = (Part / Whole) × 100

This converts a fraction into a percentage by multiplying by 100.

Converting Between Formats

• Percentage to Decimal: Divide by 100 (25% = 0.25)
• Decimal to Percentage: Multiply by 100 (0.75 = 75%)
• Percentage to Fraction: Put over 100 and simplify (40% = 40/100 = 2/5)
• Fraction to Percentage: Divide and multiply by 100 (3/4 = 0.75 = 75%)

Common Percentage Formulas

Finding X% of Y:

Result = (X / 100) × Y

Example: 20% of 500 = (20/100) × 500 = 100

Finding What % X is of Y:

Percentage = (X / Y) × 100

Example: 25 is what % of 200? = (25/200) × 100 = 12.5%

Finding the Whole (X is Y% of what?):

Whole = X / (Y / 100)

Example: 50 is 25% of what? = 50 / (25/100) = 200

Percentage Increase:

New Value = Original × (1 + Percentage/100)

Example: 100 increased by 20% = 100 × (1 + 20/100) = 120

Percentage Decrease:

New Value = Original × (1 - Percentage/100)

Example: 100 decreased by 20% = 100 × (1 - 20/100) = 80

Percentage Change:

Change = ((New - Old) / Old) × 100

Example: Change from 50 to 75 = ((75-50)/50) × 100 = +50%

Reverse Percentage (After Increase):

Original = Final / (1 + Percentage/100)

Example: $120 after 20% increase, original = 120/(1+0.20) = $100

Reverse Percentage (After Decrease):

Original = Final / (1 - Percentage/100)

Example: $80 after 20% discount, original = 80/(1-0.20) = $100

Percentage vs Percentage Points

Important Distinction:

• Percentage Change: Relative change. If something goes from 10% to 15%, that is a 50% increase.
• Percentage Points: Absolute change. If something goes from 10% to 15%, that is a 5 percentage point increase.