Finance
Percentage Increase Calculator
Compare an old value and a new value to see the percentage change.
Your details
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Your result
Based on the values you enter
Useful next checks
- Compare a few scenarios before making a decision.
- Check rates, fees, tax, and timing outside the estimate.
- Use the explanation below to understand the formula.
Intro
Use this percentage increase calculator to compare an original value and a new value. It shows increases, decreases and the numerical change between the two values.
How it works
Enter a non-zero original value and a new value. The percentage result compares the signed difference with the magnitude of the starting value. The result detail labeled "Absolute change" is new value - original value: it keeps the sign of the difference and can be negative.
Formula
This calculator uses percentage change = (new value - original value) / abs(original value) x 100.
abs(original value) is the absolute value, or magnitude, of the original value. For example, abs(-100) = 100. The numerator keeps its sign; only the denominator uses the starting magnitude. When the original value is positive, this is the usual change-divided-by-original formula.
Example calculation
If a value rises from 80 to 100, the numerical change is 20 and the percentage increase is 25%: (100 - 80) / 80 x 100 = 25%.
| Original value | New value | Numerical change | Percentage change |
|---|---|---|---|
| 80 | 100 | 20 | 25% |
| 100 | 80 | -20 | -20% |
| -100 | -50 | 50 | 50% |
| -100 | -150 | -50 | -50% |
| 100 | 0 | -100 | -100% |
For -100 to -50, the difference is +50 and the starting magnitude is 100, giving +50%. Dividing by the signed original value of -100 would give -50% instead. The calculator uses the magnitude-based convention shown here.
How to interpret the result
A positive result means the new number is higher; a negative result means it is lower. An unchanged non-zero value gives 0%. "Higher" does not necessarily mean better: the meaning depends on the quantity being compared.
With a negative starting value or a comparison that crosses zero, the result is signed change relative to the starting magnitude. Do not treat it as a universal growth-rate or investment-return definition. Use the convention appropriate to the dataset and consider the numerical change alongside the percentage.
Assumptions and limitations
- An original value of zero is rejected because abs(0) is zero and division by zero is undefined.
- A new value of zero is allowed when the original value is non-zero. From 100 to 0 the result is -100%; from -100 to 0 it is +100% under this convention.
- Negative inputs are allowed; the absolute-value denominator does not make the result itself always positive.
- A starting value close to zero can produce a very large percentage.
- Results are rounded for display. This is a single before-and-after comparison, not an annualized or compounded return.
Sources and method
OpenStax's explanation of absolute value supports the meaning of magnitude. The BLS percentage-change example illustrates the familiar earlier-value denominator with positive index values. These references do not certify this tool's negative-baseline convention as a universal growth calculation; the examples above explain its existing behavior.
Frequently asked questions
Can it show a decrease?
Yes. If the new value is lower, new minus original is negative, so the result is negative even when the original value is below zero.
What if the original value is zero?
A percentage change from zero is undefined because abs(0) is zero. The calculator requires a non-zero original value.
How are negative starting values handled?
The formula is (new - original) / abs(original) x 100. From -100 to -50 it returns +50%; from -100 to -150 it returns -50%. Interpret this as signed change relative to the starting magnitude, not a universal growth-rate definition.
Can the new value be zero?
Yes, provided the original value is non-zero. From 100 to 0 the result is -100%, while from -100 to 0 it is +100% under this calculator's convention.