Percentage Formula
Calculate percentages using Percentage = (Part / Whole) × 100.
Includes formulas for percentage increase, decrease, and finding the whole.
The Formula
Percentage: Percentage = (Part / Whole) × 100
Finding the Part: Part = (Percentage / 100) × Whole
Finding the Whole: Whole = Part / (Percentage / 100)
The percentage formula expresses a number as a fraction of 100.
"Percent" literally means "per hundred."
Variables
| Symbol | Meaning |
|---|---|
| Percentage | The result expressed as a value out of 100 |
| Part | The portion or amount you are measuring |
| Whole | The total or full amount |
Percentage Change
- A positive result means a percentage increase
- A negative result means a percentage decrease
Example 1
You scored 42 out of 60 on a test. What is your percentage?
Part = 42, Whole = 60
Percentage = (42 / 60) × 100
Percentage = 0.7 × 100
Percentage = 70%
Example 2
A shirt was $80 and is now $60. What is the percentage decrease?
Old Value = 80, New Value = 60
Percentage Change = ((60 - 80) / 80) × 100
Percentage Change = (-20 / 80) × 100 = -0.25 × 100
Percentage Change = -25% (a 25% decrease)
When to Use It
Use the percentage formula when:
- Calculating test scores, grades, or completion rates
- Figuring out discounts and sale prices
- Measuring percentage increases or decreases (profit, loss, growth)
- Comparing proportions across different totals
Key Notes
- Basic formula: percentage = (part / whole) × 100: The "whole" is the reference quantity. "What percent of 80 is 20?" → (20/80) × 100 = 25%. Always identify which quantity is the base (whole) before calculating.
- Percentage change: ((new − old) / |old|) × 100: Positive = increase, negative = decrease. A price rising from $50 to $60 is a 20% increase; falling to $40 is a 20% decrease. The base is always the original value.
- Percentage point vs relative percent: A rate rising from 10% to 15% is a 5 percentage point increase but a 50% relative increase. These are entirely different — confusing them is a common error in media and data reporting.
- Sequential percentages are multiplicative, not additive: A 10% increase followed by a 10% decrease gives 1.10 × 0.90 = 0.99 — a net 1% decrease, not zero. Never add consecutive percent changes.
- Applications: Percentages appear in tax rates, discounts, investment returns, statistical prevalence, grade calculations, and data analysis. Understanding the base is essential — "20% off" and "20% of the sale price" are not the same discount.