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How to Work Out Percentage Without Calculator

Reviewed by Calculator Editorial Team

Calculating percentages without a calculator is a valuable skill that can save time and build confidence in your math abilities. Whether you're working on a budget, analyzing data, or simply want to understand percentages better, these methods will help you work through percentage problems efficiently.

Basic Percentage Calculation

Calculating a percentage of a number is one of the most common percentage problems. For example, what is 20% of 50?

Formula

Percentage = (Percentage Value ÷ 100) × Total Amount

Step-by-Step Example

  1. Convert the percentage to a decimal by dividing by 100: 20% ÷ 100 = 0.20
  2. Multiply the decimal by the total amount: 0.20 × 50 = 10
  3. The result is 10, which means 20% of 50 is 10.

Tip

For quick mental calculations, you can use the "rule of 100" method. For example, to find 20% of 50, think of 20% as 20 out of 100, then multiply 20 by 0.5 to get 10.

Calculating Percentage Increase

Determining the percentage increase between two numbers is useful for tracking growth or changes over time.

Formula

Percentage Increase = [(New Value - Original Value) ÷ Original Value] × 100

Example

If a product's price increases from $50 to $75, what is the percentage increase?

  1. Subtract the original value from the new value: $75 - $50 = $25
  2. Divide the difference by the original value: $25 ÷ $50 = 0.5
  3. Multiply by 100 to get the percentage: 0.5 × 100 = 50%
  4. The price increased by 50%.

Calculating Percentage Decrease

Calculating percentage decrease is similar to percentage increase but involves a reduction in value.

Formula

Percentage Decrease = [(Original Value - New Value) ÷ Original Value] × 100

Example

If a stock's value drops from $100 to $70, what is the percentage decrease?

  1. Subtract the new value from the original value: $100 - $70 = $30
  2. Divide the difference by the original value: $30 ÷ $100 = 0.3
  3. Multiply by 100 to get the percentage: 0.3 × 100 = 30%
  4. The stock value decreased by 30%.

Finding What Percentage One Number Is of Another

This calculation determines what percentage a part is of a whole.

Formula

Percentage = (Part ÷ Whole) × 100

Example

If 30 out of 100 students passed an exam, what percentage passed?

  1. Divide the part by the whole: 30 ÷ 100 = 0.3
  2. Multiply by 100 to get the percentage: 0.3 × 100 = 30%
  3. 30% of the students passed the exam.

Calculating Percentage Change

Percentage change measures how much a quantity has increased or decreased over time.

Formula

Percentage Change = [(New Value - Original Value) ÷ Original Value] × 100

Example

If a company's revenue changes from $50,000 to $60,000, what is the percentage change?

  1. Subtract the original value from the new value: $60,000 - $50,000 = $10,000
  2. Divide the difference by the original value: $10,000 ÷ $50,000 = 0.2
  3. Multiply by 100 to get the percentage: 0.2 × 100 = 20%
  4. The revenue increased by 20%.

Frequently Asked Questions

How do I calculate a percentage without a calculator?

To calculate a percentage without a calculator, convert the percentage to a decimal by dividing by 100, then multiply by the total amount. For example, to find 20% of 50, divide 20 by 100 to get 0.20, then multiply by 50 to get 10.

What is the formula for percentage increase?

The formula for percentage increase is: [(New Value - Original Value) ÷ Original Value] × 100. This tells you how much a value has increased in percentage terms.

How do I find what percentage one number is of another?

To find what percentage one number is of another, use the formula: (Part ÷ Whole) × 100. For example, if 30 is the part and 100 is the whole, the calculation is (30 ÷ 100) × 100 = 30%.

What is the difference between percentage increase and decrease?

Percentage increase measures how much a value has grown, while percentage decrease measures how much a value has shrunk. Both use the same formula but apply it to different scenarios.

How can I quickly estimate percentages mentally?

For quick mental calculations, use the "rule of 100" method. For example, to find 20% of 50, think of 20% as 20 out of 100, then multiply 20 by 0.5 to get 10.