Percentage Calculator

Online calculator and formula to calculate percentage from the ratio of percentage value to base value

Percentage Calculator

Percentage Calculation

This function calculates the percentage that a specified percentage value represents relative to a base value. Determine what percentage one number is of another.

Input Values
The value to calculate the percentage for
The reference or total value
Result precision
Percentage Result
Percentage:
Understanding Percentages

A percentage shows what portion or share one number represents of another. Formula: (Percentage Value / Base Value) × 100. Example: 20 out of 150 = 13.33%

Percentage Visualization

Percentage represents a part of a whole. Divide the percentage value by the base value and multiply by 100.
Percentage = (Value / Base) × 100

Calculation Process
Percentage Value
20
÷ Base Value
Base Value
150
× 100
Result (Percentage)
13.33%


What is a Percentage?

Percentage expresses a proportion or ratio as a fraction of 100:

  • Definition: Part of a whole expressed as a value out of 100
  • Symbol: % represents "per hundred"
  • Scale: 0% = none, 100% = all, 200% = double
  • Standardized: Makes different ratios comparable
  • Universal: Used across business, science, and daily life
  • Flexible: Can represent any ratio or proportion

Mathematical Foundations

The percentage calculation is based on simple ratio and multiplication:

Percentage Formula
P = (V / B) × 100

Divide the percentage value by the base value and multiply by 100 to express as a percentage.

Terminology and Variables

Variables
  • P = Percentage (result)
  • V = Percentage Value (what we're measuring)
  • B = Base Value (the reference or total)
  • 100 = Conversion factor for percentage
Key Concepts
  • Ratio: Comparison between two values
  • Proportion: Part of a whole
  • Per Centum: Latin for "for each hundred"
  • Scaling: Expressing on 0-100 scale
Important Notes
  • Any percentage can be expressed as a decimal (e.g., 50% = 0.5)
  • Percentages over 100% indicate values greater than the base
  • The base value should always be positive (use absolute value if needed)
  • Order matters: 20 of 150 is different from 150 of 20

Applications of Percentages

Percentage calculations are fundamental in many fields:

Business & Finance
  • Market share analysis
  • Profit margin calculations
  • Discount and tax rates
  • Budget allocation percentages
Education
  • Grade calculations
  • Test score percentages
  • Class participation ratios
  • Completion rates
Science & Research
  • Concentration calculations
  • Yield percentages
  • Population composition
  • Error rates
Daily Life
  • Sales and discounts
  • Tips and gratuities
  • Survey responses
  • Nutritional information

Calculation Examples

Example 1: Basic Percentage
Given

What percentage is 20 of 150?

Question: Calculate the percentage.

Solution
\[P = \frac{V}{B} \times 100\] \[P = \frac{20}{150} \times 100\] \[P = 0.1333 \times 100 = 13.33\%\]
Result

The value 20 represents 13.33% of 150.

Example 2: Percentage Over 100%
Given

By what percentage must a base value of 850 increase to reach 1000?

Question: What percentage is 1000 of 850?

Solution
\[P = \frac{1000}{850} \times 100\] \[P = 1.1765 \times 100 = 117.65\%\]
Result

The value 1000 represents 117.65% of 850.

An increase of 117.65% - 100% = 17.65% is required to reach 1000 from 850.

Example 3: Market Share
Given

A company has sales of $250,000 in a market totaling $1,200,000.

Question: What is the company's market share percentage?

Solution
\[P = \frac{250000}{1200000} \times 100\] \[P = 0.2083 \times 100 = 20.83\%\]
Interpretation

The company controls 20.83% of the market. This helps assess competitive position and market dominance.

Key Points About Percentages

Core Concepts
  • Universal Scale: 0-100 scale for easy comparison
  • Flexible: Can exceed 100% for comparisons greater than base
  • Standardized: Same calculation method everywhere
  • Proportional: Shows relationship between parts and whole
Practical Tips
  • Always divide the part by the whole
  • Multiply by 100 to express as percentage
  • Order matters: division is not commutative
  • Base value must be appropriate context
Summary

Percentage calculation is one of the most fundamental mathematical tools. Whether analyzing market share, evaluating test scores, understanding financial returns, or comparing survey results, this simple formula—(Value / Base) × 100—provides a standardized way to express any ratio on a universal 0-100 scale. Mastering percentage calculations enables clear communication of proportions, comparisons, and insights across all domains from business to science to daily life.