Description
Differentiate proportional gross margin (revenue-cost)/revenue with respect to both inputs.
A ratio compares quantities under a stated numerator and denominator. Fractions, percentage numerals, and percentage-point changes use different conventions, and changing a part can also change its whole. Unit consistency, zero denominators, rounding, and the order of adjustments determine the result.
Differentiate proportional gross margin (revenue-cost)/revenue with respect to both inputs.
When to use this tool
Use Proportional Margin One Input Sensitivity when you need this specific ratio, allocation, transformation, interval, or adjustment-order calculation with an explicit base.
How to use the tool and how it works
- Enter revenue, cost. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read revenueDerivative, costDerivative. Use the output convention below.
Return revenueDerivative=cost/revenue² and costDerivative=-1/revenue, requiring nonzero revenue.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| revenue | Revenue | Required. Finite number. |
| cost | Cost | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| revenueDerivative | Local derivative of (revenue-cost)/revenue with respect to revenue. | Required. Finite number. |
| costDerivative | Cost Derivative | Required. Finite number. |
{
"input": {
"revenue": 100,
"cost": 60
},
"output": {
"revenueDerivative": 0.006,
"costDerivative": -0.01
}
}Limitations and assumptions
- These are local derivatives of (revenue-cost)/revenue with the other input fixed. Signed values are accepted, and no actual margin, accounting treatment, uncertainty, or financial recommendation is computed.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Check numerator, denominator, units, and adjustment order before comparing results. Use a complete allocation or physical mixture model when a single arithmetic term leaves relevant constraints unspecified.
References
Similar or alternative tools
- Proportional Cap Boundary Mass
Return uncapped=total*fraction, capped=min(uncapped,cap), and boundaryExcess=max(0,uncapped-cap).
- Proportional Cost Fixedfee Base
Calculate variable=quantity*unitCost and total=variable+fixedFee.