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How to Calculate Percentage of a Number: Complete Guide

Learn how to find what percentage one number is of another with formulas, examples, and step-by-step instructions

Calculating what percentage one number is of another is a fundamental mathematical skill used in everyday life, from determining test scores and calculating tips to analyzing business data and understanding statistics. This comprehensive guide will teach you multiple methods to find percentages, complete with examples and practical applications.

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Basic Percentage Formula

Standard Formula

Percentage = (Part ÷ Whole) × 100%

Where "Part" is the number you want to find the percentage of, and "Whole" is the total or reference number

Formula Components:

  • Part: The number you're comparing
  • Whole: The total or reference number
  • ÷: Division operation
  • × 100%: Convert decimal to percentage

Alternative Expressions:

Percentage = Part/Whole × 100

% = (A/B) × 100

Step-by-Step Calculation Process

1

Identify the Part and Whole

Determine which number is the "part" (the number you want to find the percentage of) and which is the "whole" (the total or reference number).

2

Divide Part by Whole

Divide the part by the whole to get a decimal value: Part ÷ Whole

3

Convert to Percentage

Multiply the decimal result by 100 to convert it to a percentage, or move the decimal point two places to the right.

Worked Examples

Example 1: Test Score

Problem:

A student scored 85 points out of 100 possible points on a test. What percentage did they score?

Given:
  • Part = 85 points
  • Whole = 100 points

Solution:

Step 1: Part = 85, Whole = 100

Step 2: 85 ÷ 100 = 0.85

Step 3: 0.85 × 100% = 85%

Answer: The student scored 85%

Example 2: Sales Commission

Problem:

A salesperson earned $1,200 in commission from $40,000 in total sales. What percentage commission did they earn?

Given:
  • Part = $1,200 (commission)
  • Whole = $40,000 (total sales)

Solution:

Step 1: Part = 1,200, Whole = 40,000

Step 2: 1,200 ÷ 40,000 = 0.03

Step 3: 0.03 × 100% = 3%

Answer: The commission rate is 3%

Example 3: Survey Results

Problem:

In a survey of 250 people, 175 said they prefer coffee over tea. What percentage of respondents prefer coffee?

Given:
  • Part = 175 people (prefer coffee)
  • Whole = 250 people (total surveyed)

Solution:

Step 1: Part = 175, Whole = 250

Step 2: 175 ÷ 250 = 0.7

Step 3: 0.7 × 100% = 70%

Answer: 70% of respondents prefer coffee

Alternative Calculation Methods

Cross Multiplication Method

Part/Whole = x/100

Steps:

  1. Set up the proportion: Part/Whole = x/100
  2. Cross multiply: Part × 100 = Whole × x
  3. Solve for x: x = (Part × 100) ÷ Whole

Example: 25 out of 80
25/80 = x/100
x = (25 × 100) ÷ 80 = 31.25%

Fraction to Percentage Method

Fraction = Part/Whole → Percentage

Steps:

  1. Write as a fraction: Part/Whole
  2. Convert to decimal by dividing
  3. Multiply by 100 for percentage

Example: 3 out of 8
3/8 = 0.375
0.375 × 100 = 37.5%

Real-World Applications

Education

  • • Test scores and grades
  • • Attendance rates
  • • Assignment completion
  • • Class participation
  • • Graduation rates

Business

  • • Sales commission rates
  • • Market share analysis
  • • Employee performance
  • • Budget allocation
  • • Profit margins

Finance

  • • Interest rates
  • • Investment returns
  • • Tax calculations
  • • Loan payments
  • • Portfolio allocation

Health & Fitness

  • • Body fat percentage
  • • Workout completion
  • • Nutrition tracking
  • • Recovery rates
  • • Goal achievement

Statistics

  • • Survey results
  • • Population studies
  • • Research data
  • • Quality control
  • • Success rates

Daily Life

  • • Tip calculations
  • • Discount shopping
  • • Recipe scaling
  • • Time management
  • • Progress tracking

Common Mistakes to Avoid

×

Confusing Part and Whole

Always identify which number is the part (what you're finding the percentage of) and which is the whole (the total or reference).

×

Forgetting to Multiply by 100

Remember to convert the decimal result to a percentage by multiplying by 100 or moving the decimal point two places right.

×

Using Wrong Units

Ensure both numbers are in the same units before calculating (e.g., both in dollars, both in minutes).

×

Rounding Too Early

Keep full precision during calculations and round only the final result to avoid accumulating errors.

Tips and Tricks

Quick Mental Math

  • • 1/2 = 50%
  • • 1/4 = 25%
  • • 1/5 = 20%
  • • 1/10 = 10%
  • • 3/4 = 75%
  • • 2/3 ≈ 66.67%

Calculation Tips

  • • Use a calculator for complex numbers
  • • Double-check by working backwards
  • • Estimate first to verify reasonableness
  • • Practice with common fractions
  • • Keep track of decimal places

Frequently Asked Questions

How do I know which number is the "part" and which is the "whole"?

The "part" is the number you want to find the percentage of, and the "whole" is the total or reference number. Ask yourself: "What percentage is [part] of [whole]?" The part is usually smaller than the whole, but not always.

Can a percentage be greater than 100%?

Yes! If the "part" is larger than the "whole," the percentage will be greater than 100%. For example, if someone scores 110 points out of 100 possible points (with bonus questions), they scored 110%.

What's the difference between "percentage of" and "percentage increase"?

"Percentage of" finds what percentage one number is of another (static comparison). "Percentage increase" measures how much a value has grown from an original amount (change over time). They use different formulas.

How many decimal places should I include in my answer?

This depends on the context and required precision. For most practical purposes, 1-2 decimal places are sufficient (e.g., 75.5% or 75.25%). For scientific or financial calculations, you might need more precision.

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