Percentage Increase Calculator
Calculate Percentage Increase
Enter the original and new values to find the percentage increase.
Visualizing the Increase
Understanding the Percentage Increase Calculator
Our Percentage Increase Calculator helps you quickly determine the percentage growth from an original value to a new value. This is useful in various scenarios, from analyzing investment returns to tracking business growth or even understanding price changes.
What is Percentage Increase?
Percentage increase is a measure of how much a value has grown or increased relative to its original value, expressed as a percentage of the original value. It quantifies the relative change between two numbers, indicating the magnitude of growth.
Anyone who needs to compare a new value to an old value and understand the relative change can use a Percentage Increase Calculator. This includes investors, business owners, analysts, students, and consumers.
A common misconception is that percentage increase is the same as the absolute difference. The absolute difference is just the new value minus the old value, while the percentage increase puts this difference into perspective relative to the starting point.
Percentage Increase Calculator Formula and Mathematical Explanation
The formula to calculate the percentage increase is:
Percentage Increase = [(New Value – Original Value) / |Original Value|] * 100%
Where:
- New Value is the final or ending value.
- Original Value is the initial or starting value.
- |Original Value| represents the absolute value of the Original Value, ensuring the denominator is positive, which is standard when the original can be negative, though less common for simple increase contexts where the original is usually positive and non-zero. If the original value is zero, the percentage increase is undefined or infinite if the new value is positive.
Step-by-step derivation:
- Calculate the Difference: Find the absolute increase by subtracting the original value from the new value (New Value – Original Value).
- Divide by the Original Value: Divide the difference by the absolute value of the original value to get the relative increase.
- Multiply by 100: Convert the relative increase into a percentage by multiplying by 100.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Original Value (Voriginal) | The starting value before the change. | Varies (e.g., $, units, count) | Usually > 0 for standard increase, but can be any number. Not zero for this formula. |
| New Value (Vnew) | The ending value after the change. | Varies (e.g., $, units, count) | Any number. |
| Difference (ΔV) | The absolute change between the new and original values (Vnew – Voriginal). | Same as values | Any number |
| Percentage Increase (%) | The relative change expressed as a percentage of the original value. | % | Any number, typically positive for an increase. |
Practical Examples (Real-World Use Cases)
Example 1: Salary Increase
Suppose your salary was $50,000 last year, and this year it increased to $55,000.
- Original Value = 50,000
- New Value = 55,000
- Difference = 55,000 – 50,000 = 5,000
- Percentage Increase = (5,000 / 50,000) * 100 = 0.1 * 100 = 10%
Your salary increased by 10%.
Example 2: Website Traffic Growth
A website had 10,000 visitors last month and 12,500 visitors this month.
- Original Value = 10,000
- New Value = 12,500
- Difference = 12,500 – 10,000 = 2,500
- Percentage Increase = (2,500 / 10,000) * 100 = 0.25 * 100 = 25%
The website traffic increased by 25%. Our Percentage Increase Calculator makes this easy to see.
How to Use This Percentage Increase Calculator
- Enter the Original Value: Input the starting value in the "Original Value" field. This is the value before the increase occurred. It should not be zero.
- Enter the New Value: Input the final value in the "New Value" field. This is the value after the increase.
- View the Results: The calculator will automatically display the percentage increase, the absolute difference, and reiterate the original and new values.
- Reset: Click the "Reset" button to clear the fields and start over with default values.
- Copy: Click "Copy Results" to copy the main result and values to your clipboard.
The primary highlighted result shows the percentage increase. Intermediate values show the absolute difference and the inputs used. Use the Percentage Increase Calculator to quickly understand growth rates in various contexts.
Key Factors That Affect Percentage Increase Results
- Original Value Magnitude: The same absolute difference will result in a smaller percentage increase if the original value is large, and a larger percentage increase if the original value is small. For instance, an increase of 10 from 10 is 100%, but from 100 is only 10%.
- New Value Magnitude: The larger the new value compared to the original, the larger the percentage increase.
- Time Period: While the calculator only looks at two values, the time between these values is crucial for interpreting the increase (e.g., 10% increase per year vs. per month).
- Base for Comparison: Ensure the original value is the correct baseline for the comparison you intend to make.
- Absolute vs. Relative Change: Understand that percentage increase is a relative measure. A small absolute change can be a large percentage increase if the base is small.
- Zero as Original Value: A percentage increase from zero to a positive number is technically infinite or undefined with the standard formula, as division by zero is not allowed. Our Percentage Increase Calculator requires a non-zero original value.
Frequently Asked Questions (FAQ)
- Q1: How do I calculate percentage increase between two numbers?
- A1: Subtract the original number from the new number, divide the result by the absolute value of the original number, and multiply by 100. Our Percentage Increase Calculator does this for you.
- Q2: What if the new value is smaller than the original value?
- A2: If the new value is smaller, it's a percentage decrease. The formula still works, but the result will be negative. You might want to use a percentage change calculator for that.
- Q3: Can the original value be zero?
- A3: Mathematically, you cannot divide by zero, so the percentage increase from zero to a positive number is undefined or considered infinite. This calculator requires a non-zero original value.
- Q4: Can the original value be negative?
- A4: Yes, the formula uses the absolute value of the original value in the denominator, so it can handle negative original values, though it's less common when talking about simple "increase." For example, going from -10 to -5 is a 50% increase relative to the absolute base of 10.
- Q5: What's the difference between percentage increase and percent change?
- A5: Percentage increase specifically measures growth. Percent change can measure both increase (positive result) and decrease (negative result). See our percentage change calculator for more.
- Q6: How do I calculate a 20% increase on a number?
- A6: Multiply the number by 1.20 (which is 1 + 20/100). For example, a 20% increase on 50 is 50 * 1.20 = 60.
- Q7: How do I find the original value if I know the new value and the percentage increase?
- A7: Original Value = New Value / (1 + (Percentage Increase / 100)). For example, if the new value is 120 after a 20% increase, the original was 120 / 1.20 = 100.
- Q8: Is the Percentage Increase Calculator free to use?
- A8: Yes, our Percentage Increase Calculator is completely free to use online.