Percentage Formulas

Master percentage calculations with our comprehensive formula reference. From basic percentages to complex percentage changes, find all the mathematical expressions you need.

1Basic Percentage

The fundamental formula to convert a fraction to a percentage.

Example:

Find what percentage 25 is of 100

Variables:

  • Part: The portion being measured
  • Whole: The total or reference value
  • Percentage: Result as a percentage

2Finding X% of a Number

Calculate what a given percentage of a number equals.

or equivalently:

Example:

What is 25% of 80?

Variables:

  • X: The percentage value
  • N: The number
  • Result: X% of N

3Percentage Change

Calculate the percentage increase or decrease between two values.

Types of Change:

Percentage Increase:

When New Value > Original Value, result is positive

Percentage Decrease:

When New Value < Original Value, result is negative

Example:

Price changed from $50 to $65

The price increased by 30%

4Finding Original Value

Determine the original value when you know the final value and percentage change.

After Percentage Increase:

Example: Final value is $130 after a 30% increase

After Percentage Decrease:

Example: Final value is $70 after a 30% decrease

5Compound Percentages

Handle multiple percentage changes applied successively.

Multiple Increases:

For consecutive increases of p₁%, p₂%, etc.

Example:

$100 increased by 10%, then by 20%

Note: This is not the same as a 30% increase!

6Percentage Points vs Percentages

Understanding the difference between percentage points and percentage changes.

Percentage Points

Absolute difference between percentages

Example: Interest rate changed from 5% to 7%
Difference: 7 - 5 = 2 percentage points

Percentage Change

Relative change between percentages

Same Example: 5% to 7%
increase

7Common Percentage Calculations

Discount and Markup

Discount Price

Markup Price

Tax Calculations

Tip Calculations

Quick Reference

Common Conversions

50%=0.5 = 1/2
25%=0.25 = 1/4
20%=0.2 = 1/5
10%=0.1 = 1/10

Key Relationships