Description
Calculate residual=firstNumerator*secondDenominator-secondNumerator*firstDenominator and withinTolerance for its inclusive absolute bound.
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.
Calculate residual=firstNumerator*secondDenominator-secondNumerator*firstDenominator and withinTolerance for its inclusive absolute bound.
When to use this tool
Use Ratio Tolerance Cross Product Margin 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 firstNumerator, firstDenominator, secondNumerator, secondDenominator, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual, withinTolerance. Inspect withinTolerance before interpreting the associated values.
Calculate residual=firstNumerator*secondDenominator-secondNumerator*firstDenominator and withinTolerance for its inclusive absolute bound. Require nonzero denominators and nonnegative tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstNumerator | First Numerator | Required. Finite number. |
| firstDenominator | First Denominator | Required. Finite number. |
| secondNumerator | Second Numerator | Required. Finite number. |
| secondDenominator | Second Denominator | Required. Finite number. |
| tolerance | Nonnegative absolute tolerance in the tested quantity, unless a different convention is stated. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Signed discrepancy under the formula stated above. | Required. Finite number. |
| withinTolerance | Within Tolerance | Required. Boolean. |
{
"input": {
"firstNumerator": 2,
"firstDenominator": 3,
"secondNumerator": 4,
"secondDenominator": 6,
"tolerance": 0
},
"output": {
"residual": 0,
"withinTolerance": true
}
}Limitations and assumptions
- Tolerance has cross-product units, not direct ratio-difference units, and changes under scaling of the representations. No rounding, uncertainty estimate, or actual proportion fitting is performed.
- 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 Margin One Input Sensitivity
Differentiate proportional gross margin (revenue-cost)/revenue with respect to both inputs.
- Ratio Component Reversal
Return reversedRatio=denominator/numerator, requiring both original components nonzero.