Percentage Calculator

Calculate percentages, percentage changes, and reverse percentage calculations with ease. Perfect for students, professionals, and anyone who needs to work with percentages.

How It Works

Basic Percentage Calculation

Formula: Percentage = (Part ÷ Whole) × 100

Calculate what percentage one number is of another. For example, if you have 25 out of 100, the percentage is 25%.

Percentage Change

Formula: Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100

Calculate the percentage increase or decrease between two values. Positive results indicate an increase, negative results indicate a decrease.

Reverse Percentage

Formula: Original Value = Result ÷ (Percentage ÷ 100)

Find the original value when you know the percentage and the result. For example, if 80 is 20% of a number, the original number is 400.

Common Uses

• Academic: Grade calculations, test scores, assignment weights
• Business: Sales growth, profit margins, market share
• Finance: Interest rates, investment returns, loan calculations
• Statistics: Data analysis, survey results, population studies
• Shopping: Discounts, tax calculations, tip calculations

Examples

Basic Percentage

• 25 is what percentage of 200? Answer: 12.5%
• 150 is what percentage of 300? Answer: 50%

Percentage Change

• Price increased from $100 to $120. Change: +20%
• Temperature dropped from 80°F to 60°F. Change: -25%

Reverse Percentage

• If 80 is 20% of a number, what's the original? Answer: 400
• If 150 is 75% of a number, what's the original? Answer: 200

Mathematical Principles

Source: Standard mathematical formulas taught in mathematics education worldwide.

Accuracy: All calculations use precise mathematical formulas with proper rounding to 2 decimal places.

Validation: Results are verified against standard mathematical principles and educational standards.

Important Notes

• Division by Zero: Cannot calculate percentage when the whole value is zero
• Negative Values: Percentage change can be negative (indicating decrease)
• Precision: Results are rounded to 2 decimal places for practical use
• Units: Percentages are dimensionless ratios expressed as percentages

Sources:

• National Council of Teachers of Mathematics (NCTM)
• Mathematical Association of America (MAA)
• Standard mathematics textbooks and educational resources

Disclaimer: This calculator is for educational and informational purposes. For critical calculations, always verify results through multiple methods.