Percentage Change Calculator

Calculate the percentage increase or decrease between two numbers

Other Titles
Understanding Percentage Change
Percentage change is a simple mathematical concept that represents the degree of change over time. It is used to express the difference between a new value and an old value as a percentage of the old value.

The Formula for Percentage Change

  • The calculator uses a straightforward formula to determine the change between two numbers.
  • The formula is `((V2 - V1) / V1) * 100`.
Percentage change is one of the most common ways to measure a change in a value. A positive result indicates a percentage increase, while a negative result indicates a percentage decrease. This calculator takes the absolute value for the final display and indicates whether it was an increase or decrease separately.
Breaking Down the Formula:

Core Formula

  • Initial Value (V1) = 150
  • Final Value (V2) = 180
  • Change = ((180 - 150) / 150) * 100 = (30 / 150) * 100 = 0.2 * 100 = 20%
  • Result: A 20% increase.

How to Use the Calculator: A Step-by-Step Guide

  • Enter the original value in the 'Initial Value' field.
  • Enter the new value in the 'Final Value' field.
  • Click 'Calculate' to see the percentage change.
Using this tool is simple. You just need to identify which value came first and which came second. The order is very important.

Practical Example

  • Scenario: Last year, a company had 80 employees. This year, it has 100 employees. What is the percentage change?
  • 1. Enter 80 in the 'Initial Value (V1)' field.
  • 2. Enter 100 in the 'Final Value (V2)' field.
  • 3. Click 'Calculate'.
  • 4. Result: A 25% increase in employees.

Applications in Finance, Economics, and Statistics

  • Tracking the rise and fall of stock prices or market indices.
  • Measuring economic growth (e.g., GDP change).
  • Analyzing changes in data points in scientific research or business reports.
Financial Analysis:
Investors and financial analysts use percentage change constantly. If a stock price moves from $200 to $210, the percentage change is ((210 - 200) / 200) * 100 = 5%. This allows for easy comparison of the performance of different assets, regardless of their absolute prices.
Economic Indicators:
Economists use percentage change to report on things like inflation, unemployment rates, and Gross Domestic Product (GDP). Saying that GDP grew by 2.5% last quarter is a clear and standardized way to communicate the health of an economy.

Common Scenarios

  • If your rent increases from $1,500 to $1,575, that's a 5% increase.
  • If a website's daily visitors drop from 5,000 to 4,500, that's a 10% decrease.

Important Distinction: Percentage Change vs. Percentage Points

  • Percentage change refers to the relative change from an initial value.
  • Percentage points refer to the absolute arithmetic difference between two percentages.
Understanding the Difference
Our calculator measures the percentage change, which is the relative change.

Concept Clarification

  • If a mortgage rate goes from 4% to 6%, the change is 2 percentage points.
  • The percentage change in that rate is ((6-4)/4)*100 = 50%.

The Importance of the Base Value (V1)

  • The initial value is the reference point for the entire calculation.
  • A different starting point will produce a different percentage change, even if the absolute difference is the same.
The choice of the initial value (the denominator in the fraction) is critical. A change from 50 to 100 is a 100% increase ((100-50)/50). However, a change from 100 back to 50 is a 50% decrease ((50-100)/100). The absolute change is 50 in both cases, but the percentage change is different because the starting point (the base) is different. This is a key concept in understanding why a 100% gain is wiped out by only a 50% loss.

Asymmetric Changes

  • Gain: $100 -> $150 is a 50% increase.
  • Loss: $150 -> $100 is a 33.3% decrease.