Percentage Calculator
Your all-in-one tool to calculate percentages, percentage change, sale discounts, tips, and grades, all with clear, step-by-step solutions.
Solve for any part of the percentage sentence:
Percentage Change Solver
Grade Percentage Calculator
Sale & Discount Calculator
Tip Calculator
Practice Problems
Test your knowledge by solving for the unknown value.
Common Percentage Mistakes to Avoid
Using the Wrong Base
When calculating percentage change, always divide by the original value, not the new one. The formula is (New - Old) / Old. Our "Change" calculator handles this 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
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
The Core Formula
This is the fundamental relationship used in most percentage problems. Our "Basic" calculator can solve for any of the three parts.
Formula: Part = (Percentage / 100) * Whole
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
Discounts & Savings
Calculate how much you save during a sale and the final price you pay.
Savings: Price * (Discount % / 100)
Final Price: Price - Savings
How to Use the Percentage Calculator
1. Select a Calculator
Choose from Basic, Change, Discount, Tip, or Grade using the tabs at the top of the tool.
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
Click "Calculate" to see your answer, the formula used, and a clear, step-by-step solution to help you understand the process.
What Makes Our Calculator Different?
Solve Any Problem
Our 'Basic' calculator isn't just for "What is X% of Y?". You can fill in any two boxes to solve for the missing piece, whether it's the part, the whole, or the percentage.
Real-World Scenarios
Go beyond abstract math. Instantly solve common, everyday problems with dedicated calculators for store discounts and restaurant tips.
Visual Learning
Don't just get a number—understand it. We use waffle charts and bar graphs to give you a visual representation of the percentages, making the concepts easier to grasp.
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'.
Interactive Practice
Test your knowledge with randomly generated problems. Get instant feedback, step-by-step explanations, and fun animations for correct answers to make learning engaging.
Real-World Examples
Calculating a Stock Price Increase
Scenario: A stock goes from $150 to $180. What is the percentage increase?
How to solve: In the "Change" tab, enter `150` in "Original Value" and `180` in "New Value". The calculator will show a **20% increase**.
Finding the Original Price Before a Sale
Scenario: A jacket is $75 after a 25% discount. What was the original price?
How to solve: In the "Discount" tab, enter `75` in "Final Price" and `25` in "Discount %". The calculator will find the "Original Price" 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 "Tip" tab, enter `80` in "Bill Amount" and `20` in "Tip %". The calculator will show the tip is **$16** and the total is **$96**.
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 "Grade" tab, enter `45` in "Correct Answers" and `50` in "Total Questions". The calculator will show your score is **90%**.