Description
Calculate a circle's minor sagitta and the difference between major and minor sagittas.
Planar orientation and geometric projections depend on the direction of axes and vectors as well as length units. Signed area and height retain side information, while chord sagitta and cone slant angles use specific ideal shapes. Finite-precision formulas and degenerate boundary cases require explicit interpretation.
Calculate a circle's minor sagitta and the difference between major and minor sagittas.
When to use this tool
Use Circle Chord Sagitta Difference when checking the stated oriented vector, ideal cone or circle convention.
How to use the tool and how it works
- Enter radius, halfChord. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minorSagitta, majorMinusMinorSagitta. Use the output convention below.
Require radius>0 and halfChord in [0,radius]. Let q=halfChord/radius and r=sqrt((1-q)*(1+q)); return minorSagitta=halfChord*q/(1+r) and major-minus-minor=2*radius*r.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number; strictly above 0. |
| halfChord | Half of the full chord length, within [0,radius]. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minorSagitta | Minor Sagitta | Required. Finite number. |
| majorMinusMinorSagitta | Major Minus Minor Sagitta | Required. Finite number. |
{
"input": {
"radius": 5,
"halfChord": 3
},
"output": {
"minorSagitta": 0.9999999999999999,
"majorMinusMinorSagitta": 8
}
}Limitations and assumptions
- The ratio-based expression avoids subtracting nearly equal radii; it still uses floating point and does not infer a measured arc or uncertainty.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use complete geometry and appropriate robust predicates or uncertainty analysis for near-degenerate inputs and physical design conclusions.
References
Similar or alternative tools
- geometry/chord-length
Compute the chord length subtended by a central angle in a circle.
- geometry/circle-arc-length
Compute the arc length of a circular segment from its central angle and radius.