Description
Invert a strictly positive closed ratio interval; no decimal display rounding.
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.
Invert a strictly positive closed ratio interval; no decimal display rounding.
When to use this tool
Use Reciprocal Ratio Rounding Envelope 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 ratio, absoluteError. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read reciprocalLower, reciprocalUpper. Use the output convention below.
Return reciprocalLower=1/(ratio+absoluteError) and reciprocalUpper=1/(ratio-absoluteError). Require nonnegative error and ratio strictly above that error.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ratio | Ratio under the stated units and direction. | Required. Finite number. |
| absoluteError | Absolute Error | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| reciprocalLower | Reciprocal Lower | Required. Finite number. |
| reciprocalUpper | Reciprocal Upper | Required. Finite number. |
{
"input": {
"ratio": 2,
"absoluteError": 0.5
},
"output": {
"reciprocalLower": 0.4,
"reciprocalUpper": 0.6666666666666666
}
}Limitations and assumptions
- The original interval must remain positive. This is a deterministic reciprocal bound, not a confidence interval, uncertainty estimate, or rounding-policy verification.
- 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
- Ratio Preserving Integer Rounding Residual
Return crossResidual=roundedNumerator*denominator-numerator*roundedDenominator, requiring nonzero original and rounded denominators and integer rounded components.
- Reciprocal Ratio Spread
Return ratio=first/second, reciprocal=second/first, and signedSpread=ratio-reciprocal, requiring both scalars nonzero.