Percentage Calculator
Calculate percent of a number, percent change, or reverse percentage.
About This Calculator
How to Use
- Select the calculation mode from the dropdown (What is P% of X, Percent change, or Reverse)
- Enter the required values in the input fields that appear
- Click Calculate to see your result with detailed explanation
- Switch modes to perform different types of percentage calculations
- Results show both the answer and the calculation method used
Understanding Percentages
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere in daily life—from calculating discounts and tax rates to measuring growth rates and test scores.
Key Percentage Concepts:
- Percentage (%): A number expressed as a fraction of 100 (50% = 50/100 = 0.5)
- Base Value: The original or total amount (the "whole")
- Part Value: The portion of the base (a piece of the "whole")
- Percentage Change: The relative change between two values
- Percentage Point: The absolute difference between two percentages
Understanding percentages is essential for financial literacy, data analysis, academic success, and making informed everyday decisions.
Percentage Formulas
Three main percentage calculations:
Result = (P / 100) × X
Example: What is 15% of 200?
Result = (15 / 100) × 200 = 0.15 × 200 = 30
Change% = [(B - A) / A] × 100
Example: From 120 to 150?
Change = [(150 - 120) / 120] × 100 = (30 / 120) × 100 = 25% increase
Original = X / (P / 100)
Example: 30 is 15% of what?
Original = 30 / (15 / 100) = 30 / 0.15 = 200
Common Percentage Conversions
Quick reference for frequently used percentages:
| Percentage | Decimal | Fraction | Example |
|---|---|---|---|
| 10% | 0.10 | 1/10 | 10% of 100 = 10 |
| 25% | 0.25 | 1/4 | 25% of 100 = 25 |
| 50% | 0.50 | 1/2 | 50% of 100 = 50 |
| 75% | 0.75 | 3/4 | 75% of 100 = 75 |
| 100% | 1.00 | 1/1 | 100% of 100 = 100 |
Practical Use Cases
- Shopping & Sales: Calculate discounts, sale prices, and savings (30% off $50 = $15 savings)
- Finance & Investing: Calculate interest rates, returns on investment, and portfolio changes
- Grades & Academics: Convert test scores to percentages (45/50 = 90%)
- Business & Economics: Calculate profit margins, markups, tax rates, and commissions
- Health & Fitness: Track weight loss/gain, body fat percentage changes
- Statistics & Data: Express proportions, growth rates, and comparative data
- Tips & Gratuity: Calculate restaurant tips (15% or 20% of bill)
- Real Estate: Calculate down payments, commission rates, and price changes
Frequently Asked Questions
How do I convert a percentage to a decimal?
Divide the percentage by 100. For example: 25% = 25 ÷ 100 = 0.25. Alternatively, move the decimal point two places to the left (25% → 0.25).
What's the difference between percentage and percentage points?
Percentage is relative change: from 20% to 30% is a 50% increase [(30-20)/20 × 100]. Percentage points is absolute difference: from 20% to 30% is a 10 percentage point increase (30 - 20 = 10).
How do I calculate a percentage increase or decrease?
Use the formula: [(New Value - Old Value) / Old Value] × 100. Positive result = increase, negative = decrease. Example: from $100 to $120 is [(120-100)/100] × 100 = 20% increase.
Can percentages exceed 100%?
Yes! Percentages can be any value. 150% means 1.5 times the original value. 200% means double. This is common when measuring growth (sales increased 300% = quadrupled).
How do I add or subtract percentages?
You cannot simply add percentages unless they're from the same base. Example: 10% of 100 (=10) + 20% of 100 (=20) = 30, but this is NOT 30% of 100 unless you're working with the same base value. Calculate each separately, then combine.