Percentage Change Calculator
Your all-in-one tool to calculate percentage change, increases, decreases, and basic percentages with clear, step-by-step solutions.
Percentage Change Solver
Solves for any missing value. Leave one field blank to calculate.
Basic Percentage Solver
Solves for any missing value. Leave one field blank to calculate.
Common Mistakes to Avoid
Using the Wrong Base
The most common error is dividing by the new value instead of the original value. The formula is always (New - Old) / Old. Our calculator handles this correctly for you.
Confusing Percentage Change and Percent Of
A 25% increase from 100 is 125. But 125 is not 25% of 100; it's 125% of 100. Our two calculator tabs help you solve for the right problem every time.
Forgetting the Order of Operations
When calculating manually, always perform the subtraction (New - Old) before you divide. This ensures you are calculating the change relative to the correct starting point.
Frequently Asked Questions
How do you calculate a percentage increase?
To calculate a percentage increase, subtract the original number from the new number, divide that difference by the original number, and then multiply by 100. For example, to find the increase from 80 to 100: (100 - 80) / 80 = 0.25, then 0.25 * 100 = 25% increase.
How do you find the original price after a percentage increase?
To find the original price, divide the new price by (1 + percentage increase as a decimal). For example, if an item costs $120 after a 20% increase, the original price was $120 / (1 + 0.20) = $100. Our calculator can solve this for you by leaving the "Old Value" field blank.
What is the difference between percentage change and percent difference?
Percentage change measures the change from an old value to a new value, making the direction (increase or decrease) important. Percent difference, on the other hand, measures the difference between two numbers relative to their average, and it doesn't have a positive or negative direction.
Is this calculator free to use?
Yes, this tool is completely free and private. All calculations are done in your browser, and no data is ever sent to our servers. You can use it as much as you need without any limits or registration.
Understanding the Concepts
Percentage Change
This measures the difference between two values as a percentage of the original value. It's used to describe growth, decline, or change over time.
Formula: ((New Value - Old Value) / Old Value) * 100
The Core Percentage Formula
This is the fundamental relationship used in most percentage problems. Our "Percentage Of" calculator can solve for any of the three parts.
Formula: Part = (Percentage / 100) * Whole
What is a Percentage?
A percentage is a number or ratio expressed as a fraction of 100 (from the Latin "per centum," meaning "by the hundred"). It's a standardized way to represent a part of a whole, making comparisons easier.
Example: 50% = 50 / 100 = 0.5
How to Use the Percentage Solver
1. Choose Your Calculator
Select either "Percentage Change" for increases/decreases or "Percentage Of" for basic percentage problems using the tabs.
2. Leave One Field Blank
Our smart calculator is designed to solve for any unknown. Fill in the two values you know, and leave the field you want to calculate empty.
3. Get Instant Results
The answer is calculated in real-time as you type, complete with a step-by-step formula breakdown and a helpful visual chart.
What Makes Our Calculator Different?
Solve for Any Variable
Most calculators only find the result. Ours is a true problem-solver. Leave any field blank—Old Value, New Value, or % Change—and we'll find the missing piece for you.
Instant Visual Feedback
Don't just get a number. Our bar charts and waffle charts give you an immediate visual understanding of the relationship between the numbers, making the concepts easier to grasp.
Plain English Interpretation
We translate the math into a clear, human-readable sentence, like "This is a 25% increase, representing a change of $50." This helps you understand the real-world meaning of the result.
Learn with Step-by-Step Solutions
Every calculation comes with a detailed, step-by-step explanation of the exact formula used. It's a great way to learn the 'why' behind the math, not just the 'what'.
Real-World Examples
Calculating a Stock Price Increase
Scenario: You bought a stock at $150 and it's now worth $180. What is the percentage increase?
How to solve: In the "Percentage Change" tab, enter `150` in "Old Value" and `180` in "New Value". The calculator will instantly show a **20% increase**.
Finding the Original Price Before a Sale
Scenario: You bought a jacket for $75, which was on sale for 25% off. What was the original price?
How to solve: In the "Percentage Change" tab, enter `75` in "New Value" and `-25` in "% change". The calculator will find the "Old Value" was **$100**.
Calculating a Tip
Scenario: Your dinner bill is $80 and you want to leave a 20% tip. How much is the tip?
How to solve: In the "Percentage Of" tab, enter `20` in the "%" field and `80` in the "Total" field. The calculator will show the tip amount is **$16**.
Finding Your Test Score
Scenario: You answered 45 questions correctly out of a total of 50. What is your percentage score?
How to solve: In the "Percentage Of" tab, enter `45` in the "Value" field and `50` in the "Total" field. The calculator will show your score is **90%**.