Formula
Percentage change = ((new value − original value) ÷ |original value|) × 100.
Math
Percentage Change Calculator
Find the percentage increase or decrease between an original value and a new value, with baseline sensitivity, visual proof and a printable comparison record.
Calculator
Working calculator
Live result25.00% increaseChange of 20.00 from baseline 80.00
Formula used
Percentage change = ((new value − original value) ÷ |original value|) × 100.
This is the method behind the answer, so the result can be checked rather than simply trusted.What-if check
Baseline sensitivity
The same new value can tell a different story when the baseline changes. This table keeps the percentage tied to the original value instead of treating the percent as a standalone fact.
| Baseline used | Percent change | Meaning |
|---|---|---|
| 40.00 | 150.00% | increase |
| 80.00 | 25.00% | increase |
| 160.00 | 37.50% | decrease |
Visual proof
Original vs new value
Blue is the original baseline. Gold is the new value. The formula divides the change by the absolute original value, so a zero baseline has no standard percentage-change result.
Visual grid
This number is one point on a larger pattern
Percentage Change is not just a final answer. It is a step on a line: before and after, input and output, assumption and result.
Micro-timehours, minutes, shiftsHuman scaledays, weeks, projectsMacro-timemonths, years, calendars
InputFormulaResult
25.00% increaseCalculationTime keeps the path visible: the input, the method and the final number belong together.
CalculationTime
Percentage Change Calculation Report
25.00% increaseChange of 20.00 from baseline 80.00
Inputs
- Original value
- 80
- New value
- 100
Method
Percentage change = ((new value − original value) ÷ |original value|) × 100.
- Original value 80 and new value 100 gives a change of 20. Divide 20 by 80 to get 0.25, then multiply by 100. The result is a 25% increase.
Assumptions
- The original value is the baseline for the comparison.
- A positive result is an increase; a negative result is a decrease.
- When the original value is zero, ordinary percentage change is undefined because division by zero is not valid.
- The formula uses the absolute original value so comparisons from negative baselines keep a stable percent magnitude.
Notes
Use this space on the printed report for client, supplier, classroom, job-location, measurement, quote or approval notes.
Worked example
Original value 80 and new value 100 gives a change of 20. Divide 20 by 80 to get 0.25, then multiply by 100. The result is a 25% increase.
Professional note
Master’s Tip: percentage change can sound larger or smaller depending on the chosen baseline. A rise from 1 to 2 is a 100% increase, but a fall from 2 to 1 is a 50% decrease. Always state the original value when sharing a result.
Regional and unit assumptions
The calculator displays percent to two decimal places and keeps the original and new values unit-neutral, so it can be used for prices, counts, measurements or index values.
Assumptions and limitations
- The original value is the baseline for the comparison.
- A positive result is an increase; a negative result is a decrease.
- When the original value is zero, ordinary percentage change is undefined because division by zero is not valid.
- The formula uses the absolute original value so comparisons from negative baselines keep a stable percent magnitude.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
Percentage change = ((new value − original value) ÷ |original value|) × 100.
Standard or basis
The calculator displays percent to two decimal places and keeps the original and new values unit-neutral, so it can be used for prices, counts, measurements or index values.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: percentage change can sound larger or smaller depending on the chosen baseline. A rise from 1 to 2 is a 100% increase, but a fall from 2 to 1 is a 50% decrease. Always state the original value when sharing a result.
Related calculators
Questions
How do you calculate percentage change?
Subtract the original value from the new value, divide by the original value, then multiply by 100.
What does a negative percentage change mean?
A negative result means the new value is lower than the original value, so the change is a decrease.
Can percentage change be calculated from zero?
No. Standard percentage change from an original value of zero is undefined because the formula would divide by zero.
Is percentage change the same as percentage point change?
No. Percentage change is relative to a baseline. Percentage point change is the simple difference between two percentages, such as 5% to 7% being a 2-point move.
Calculation note
Percentages make unlike quantities easier to compare because they express change against a common scale of one hundred. That simplicity is useful in classrooms, finance, trade quotes, scientific measurements and everyday price checks.
Percent means a comparison to one hundred
Britannica describes a percentage as a relative value based on hundredth parts of a quantity. That is why the final step in this calculator multiplies by 100: it turns the relative change into a percent that can be read as parts per hundred.
The baseline controls the story
Percentage change is not symmetrical. Moving from 50 to 100 is a 100% increase, but moving from 100 back to 50 is a 50% decrease. The arithmetic is correct in both directions because each comparison uses a different original value.
Use percentage points for rate-to-rate comparisons
When both numbers are already percentages, the simple difference is often clearer. For example, a rate moving from 4% to 6% is a 2 percentage point move, while the relative percentage change is 50%. Reports should name which convention they use.
Sources and further readingBritannica: Percentage