Quick answer
Percentage change = (new − old) ÷ |old| × 100. Going from 80 to 100 is a 25% change, a difference of 20.
Enter the old and new values. The calculator returns the percentage change and the difference.
Related tools: Percent Difference Calculator: Symmetric percent difference between two values. Percentage Calculator: Calculate a percentage of a number, what percent one number is of another, or the whole from a part. Percent Increase Calculator: Percentage increase between two values.
How to use the Percentage Change Calculator
- Enter old value.
- Enter new value.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Old value | A number | — |
| New value | A number | — |
Formula and method
Formula
change % = (new − old) ÷ |old| × 100
IEEE-754 double precision; shown to at most 6 decimal places.
The difference is divided by the absolute starting value, so a rise from a negative base is reported as an increase.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Old value = 80; New value = 100.
| Result | Value |
|---|---|
| Percentage change | 25 % |
| Difference | 20 |
Example 2
Inputs: Old value = 100; New value = 80.
| Result | Value |
|---|---|
| Percentage change | -20 % |
| Difference | -20 |
Example 3
Inputs: Old value = 50; New value = 50.
| Result | Value |
|---|---|
| Percentage change | 0 % |
| Difference | 0 |
The first line is the headline result (percentage change). Below it the percentage Change Calculator lists difference, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Direction
A positive result is an increase and a negative result a decrease. From 100 to 80 the change is −20%. The result can exceed 100% or be below −100% when values cross zero.
Where this estimate stops applying
An old value of 0 is undefined. For comparing two values with no baseline, use percent difference. Compounding successive changes multiplies the factors: +25% then −20% returns to the start (1.25 × 0.8 = 1).
How the result changes with old value
Holding every other input at the first worked example, this table changes only old value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Old value | Percentage change | Difference |
|---|---|---|
| 40 | 150 % | 60 |
| 80 | 25 % | 20 |
| 160 | -37.5 % | -60 |
| 320 | -68.75 % | -220 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Old value: entering "0" shows "Percentage change is undefined when the old value is 0." beside that field and no result.
Choosing between the Percentage Change Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Percent Difference Calculator](/math/percent-difference-calculator/) | value 1 and value 2 | Percent difference |
| [Percentage Calculator](/math/percentage-calculator/) | what do you want to find?, a and b | 15% of 200 |
| [Percent Increase Calculator](/math/percent-increase-calculator/) | original value and new value | Percentage increase |
| [Percent Decrease Calculator](/math/percent-decrease-calculator/) | original value and new value | Percentage decrease |
| [Percentage of a Percentage Calculator](/math/percentage-of-a-percentage-calculator/) | x and y | Result |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Old value 0 is undefined
- Result can exceed 100% or be below −100%
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for old value to confirm this.
Frequently asked questions
What is the change from 50 to 40?
From 50 to 40 the change is (40 − 50) ÷ 50 = −20%.
Is it symmetric?
No, it depends on the base.
How do I apply a change?
Multiply by (1 + change/100).
What does the Percentage Change Calculator calculate?
Find the percentage increase or decrease from an old value to a new value. It returns Percentage change and Difference.
What formula does the Percentage Change Calculator use?
change % = (new − old) ÷ |old| × 100. The difference is divided by the absolute starting value, so a rise from a negative base is reported as an increase.
What do I need to enter in the percentage Change Calculator?
You enter Old value and New value.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Old value 0 is undefined.
What are the limits of this calculator?
Old value 0 is undefined. Result can exceed 100% or be below −100%.
What is an example of a percentage Change result?
With old value 80 and new value 100, the percentage change is 25 %.
Related calculators
- Percent Difference Calculator — Symmetric percent difference between two values.
- Percentage Calculator — Calculate a percentage of a number, what percent one number is of another, or the whole from a part.
- Percent Increase Calculator — Percentage increase between two values.
- Percent Decrease Calculator — Percentage decrease between two values.
- Percentage of a Percentage Calculator — Find X% of Y%, optionally applied to a base amount.
- Ratio Percentage Calculator — Percentage share of each part of a ratio.
- Reverse Percentage Calculator — Work backwards from a final amount to the original value before a percentage increase or decrease.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.