Description
Return uncapped=total*fraction, capped=min(uncapped,cap), and boundaryExcess=max(0,uncapped-cap).
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.
Return uncapped=total*fraction, capped=min(uncapped,cap), and boundaryExcess=max(0,uncapped-cap).
When to use this tool
Use Proportional Cap Boundary Mass 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 total, fraction, cap. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read uncapped, capped, boundaryExcess. Use the output convention below.
Return uncapped=total*fraction, capped=min(uncapped,cap), and boundaryExcess=max(0,uncapped-cap). Require nonnegative total and cap and fraction within zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| total | Total | Required. Finite number; minimum 0. |
| fraction | Dimensionless fraction under the stated basis. | Required. Finite number; minimum 0; maximum 1. |
| cap | Cap | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| uncapped | Uncapped | Required. Finite number. |
| capped | Capped | Required. Finite number. |
| boundaryExcess | Boundary Excess | Required. Finite number. |
{
"input": {
"total": 100,
"fraction": 0.6,
"cap": 50
},
"output": {
"uncapped": 60,
"capped": 50,
"boundaryExcess": 10
}
}Limitations and assumptions
- The cap can reduce the allocation to zero. This reports one supplied cap calculation without redistributing excess, selecting an applicable rule, or updating an allocation.
- 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
- Diluted Mixture Displacement Mass Balance
Remove a homogeneous portion from initialMass, add addedMass at addedFraction, and return positive finalMass, soluteMass, and fraction.
- Proportional Cost Fixedfee Base
Calculate variable=quantity*unitCost and total=variable+fixedFee.