Library / Foundations: Maths / FMA-01
Foundations: Maths
Percentage change
Increase or decrease from a start value, as a percentage.
- Ref
- FMA-01
- Rev
- v1
- Field
- Foundations: Maths
- Result
- Δ% [%]
A is the starting value and B the final value. A negative result means a decrease. Always divide by the original value.
Percentage change compares how much a value has moved with where it started. Divide the change by the original value, then multiply by 100.
Calculator
- Multiplier B/A1.15
- Absolute change12
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A rise of 20% then a fall of 20% does not return to the start, because the second change is a percentage of a different value.
- The multiplier B/A is the quickest route for reverse and repeated changes.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (%) | Local step | Change in result |
|---|---|---|---|---|---|---|
| A Starting value | 10 to 500 | −81.6 | 820 | 901.6 | +10% | −10.5 pp |
| B Final value | 10 to 500 | −87.5 | 525 | 612.5 | +10% | +11.5 pp |
Sweep of Final value
| Final value | Percentage change (%) |
|---|---|
| 10 | −87.5 |
| 16.31 | −79.62 |
| 26.59 | −66.76 |
| 43.36 | −45.8 |
| 70.71 | −11.61 |
| 115.3 | 44.13 |
| 188 | 135 |
| 306.6 | 283.3 |
| 500 | 525 |
Sweep one variable
Variables and how each one contributes
Percentage change
What the equation gives you. Everything else feeds it.
Starting value
The original value. Inversely related: a bigger start means the same change is a smaller percentage.
Final value
The value after the change. Directly raises the percentage change.
Worked example with the values above
- Change: B − A = 92 − 80 = 12.
- Divide by the original: 12 / 80 = 0.15.
- Multiply by 100: 15 %.
Assumptions and limits
- The starting value is not zero.
- Both values are in the same units.
Common mistakes
- Dividing by the new value instead of the original.
- Forgetting that a decrease gives a negative answer.
Statistics and uncertainty
If A and B are measured with independent relative errors, the error in B/A is about √[(δA/A)² + (δB/B)²], and it is magnified when the change is small compared with the values.
Where it is used
- Rates of change in cost, mass or fuel use.
- Comparing measurements before and after a modification.
Maths you need
- Fractions and decimals: a percentage is a fraction of 100
- Subtraction: change = final − original