Percentage Change Calculator | Measure Increase or Decrease

Calculate percentage increase or decrease between values with our percentage change calculator. Perfect for financial analysis, statistics, and data comparison.

Percentage Calculator

Calculate percentages, changes, and differences

Percentage Calculation Results

Based on your input values

25% of 100 is:

25.00

Formula: (25 ÷ 100) × 100

Visual Representation

25% of 100 = 25

What This Means

This calculation finds a specified percentage of a value. You've calculated 25% of 100, which means 0.25 times 100.

Applications

Calculate discounts (e.g., 20% off a $100 item)
Determine taxes (e.g., 7% sales tax on a purchase)
Figure out tips (e.g., 15% tip on a restaurant bill)

Understanding Percentage Calculations

Learn more about various percentage calculations and their applications

Understanding Percentages

The word "percentage" comes from "per centum" which means "per hundred" in Latin. A percentage is a way to express a number as a fraction of 100, making it easier to compare relative values.

Basic Concepts

100% represents the whole or total amount
50% is half of the total
25% is one quarter of the total
1% is one hundredth of the total
200% is twice the total

Converting Between Formats

Percentage	Decimal	Fraction
100%	1.0	1
75%	0.75	3/4
50%	0.5	1/2
25%	0.25	1/4
20%	0.2	1/5
10%	0.1	1/10
1%	0.01	1/100

Common Calculations

Finding a Percentage of a Number

To find X% of Y:

X% of Y = (X ÷ 100) × Y

Example: What is 25% of 80?

Write the percentage as a decimal: 25% = 25 ÷ 100 = 0.25
Multiply by the number: 0.25 × 80 = 20
Result: 25% of 80 is 20

Finding What Percentage One Number is of Another

To find what percentage X is of Y:

X is (X ÷ Y) × 100% of Y

Example: 20 is what percentage of 80?

Divide the first number by the second: 20 ÷ 80 = 0.25
Multiply by 100 to convert to a percentage: 0.25 × 100 = 25%
Result: 20 is 25% of 80

Calculating Percentage Change

To find the percentage change from X to Y:

Percentage Change = ((Y - X) ÷ X) × 100%

Example: What is the percentage change from 80 to 100?

Find the difference: 100 - 80 = 20
Divide by the original value: 20 ÷ 80 = 0.25
Multiply by 100: 0.25 × 100 = 25%
Result: The percentage change from 80 to 100 is a 25% increase

Finding Percentage Difference

To find the percentage difference between X and Y:

Percentage Difference = (|X - Y| ÷ ((X + Y) ÷ 2)) × 100%

Example: What is the percentage difference between 80 and 100?

Find the absolute difference: |80 - 100| = 20
Find the average: (80 + 100) ÷ 2 = 90
Divide the difference by the average: 20 ÷ 90 = 0.222...
Multiply by 100: 0.222... × 100 = 22.22...%
Result: The percentage difference between 80 and 100 is 22.22...%

Note: Unlike percentage change, percentage difference is always positive and treats both values equally.

Real-World Applications

Finance and Business

Discounts and Sales: "20% off" means the price is reduced by 20% of the original price
Interest Rates: Banks express interest as a percentage of the principal amount
Tax Calculations: Sales tax, income tax, and other taxes are calculated as percentages
Growth Rates: Business metrics like revenue growth are expressed as percentage changes
Profit Margins: The percentage of revenue that becomes profit

Education

Grading: Test scores are often expressed as percentages (90% = A, 80% = B, etc.)
Class Rankings: Students might be in the "top 10%" of their class
Attendance Rates: Schools track attendance as a percentage of total school days
Improvement Metrics: Student progress is often measured as a percentage improvement

Science and Statistics

Chemical Concentrations: Solutions are often described by percentage concentration
Statistical Significance: Results are considered significant at certain percentage thresholds
Experimental Error: Margin of error in experiments is expressed as a percentage
Probability: The chance of an event occurring can be expressed as a percentage

Health and Fitness

Body Fat Percentage: The proportion of body mass that is fat
Nutritional Information: Daily values on food labels are shown as percentages
Heart Rate Zones: Training zones are often calculated as percentages of maximum heart rate
Weight Loss Goals: Often specified as a percentage of starting weight

Tips and Common Mistakes

Tips for Working with Percentages

Convert percentages to decimals by dividing by 100 (e.g., 25% = 0.25)
For a percentage increase, multiply by (1 + percentage/100) (e.g., 20% increase: multiply by 1.2)
For a percentage decrease, multiply by (1 - percentage/100) (e.g., 20% decrease: multiply by 0.8)
To find the original value after a percentage change, divide by (1 + percentage change/100)
Percentage points and percentages are different concepts, especially in finance and statistics

Calculation Shortcuts

Finding 10%: Just move the decimal point one place to the left (e.g., 10% of 250 = 25)
Finding 1%: Move the decimal point two places to the left (e.g., 1% of 250 = 2.5)
Finding 5%: Find 10% and divide by 2 (e.g., 5% of 250 = 25 ÷ 2 = 12.5)
Finding 20%: Find 10% and multiply by 2 (e.g., 20% of 250 = 25 × 2 = 50)
Finding 25%: Divide by 4 (e.g., 25% of 250 = 250 ÷ 4 = 62.5)
Finding 50%: Divide by 2 (e.g., 50% of 250 = 250 ÷ 2 = 125)
Finding 33.33%: Divide by 3 (e.g., 33.33% of 250 = 250 ÷ 3 = 83.33)