Description
Use the normalized half-chord and a rationalized sagitta expression for depthFromSurface to reduce cancellation.
Geometric quantities depend on the coordinate system, the chosen shape, and compatible length units. A component formula can determine a midpoint, signed turn, or area term without validating an entire drawing or physical object.
Use the normalized half-chord and a rationalized sagitta expression for depthFromSurface to reduce cancellation.
When to use this tool
Use Sphere Chord Midpoint Depth when you need one geometric component under the stated shape and orientation convention.
How to use the tool and how it works
- Enter sphereRadius, chordLength. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read depthFromSurface. Use the output convention below.
Require positive sphereRadius and chordLength between zero and the diameter. Use the normalized half-chord and a rationalized sagitta expression for depthFromSurface to reduce cancellation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sphereRadius | Positive circle radius in a common length unit. | Required. Finite number; strictly above 0. |
| chordLength | Chord length in the radius unit; the supported formula returns the minor sagitta. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| depthFromSurface | Minor sagitta in the same length unit as sphereRadius and chordLength. | Required. Finite number. |
{
"input": {
"sphereRadius": 5,
"chordLength": 6
},
"output": {
"depthFromSurface": 1
}
}Limitations and assumptions
- This is the minor circular-section depth from surface to chord midpoint, not sphere volume or arc length; ideal spherical geometry and coherent units are assumed.
- 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
Check the complete geometry and use a suitable geometric model for intersections, tolerances, and construction details.
References
Similar or alternative tools
- Cylinder Annulus Cross Section Thickness
Return their difference as radialThickness and π × difference × sum as annularArea.
- Banquet Round Table Seat Arc
Divide 360 degrees and the circular perimeter 2πr by seat count for angle and perimeter arc per seat.