Description
Compute base radius from height × (2r-height), using alternate scaled forms when needed, then divide by sphere radius.
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Compute base radius from height × (2r-height), using alternate scaled forms when needed, then divide by sphere radius.
When to use this tool
Use Sphere Cap Base Radius Ratio when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter sphereRadius, capHeight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read baseRadius, radiusRatio. Use the output convention below.
Require positive sphereRadius and capHeight from zero through twice radius. Compute base radius from height × (2r-height), using alternate scaled forms when needed, then divide by sphere radius.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sphereRadius | Sphere Radius | Required. Finite number; strictly above 0. |
| capHeight | Cap Height | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| baseRadius | Base Radius | Required. Finite number. |
| radiusRatio | Radius Ratio | Required. Finite number. |
{
"input": {
"sphereRadius": 5,
"capHeight": 1
},
"output": {
"baseRadius": 3,
"radiusRatio": 0.6
}
}Limitations and assumptions
- Height is measured from the cap apex to its plane; endpoints yield zero base radius and output does not validate an actual solid or a manufactured part.
- 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
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Sphere Section Circle Radius Gap
Return sqrt((radius-offset)(radius+offset)) and tangent for equality.
- Geometry: Circle Tangent Radius Dot Check
Dot their separately normalized components and compare its absolute value inclusively with tolerance inside result.