Description
Return radius times sine of the angle for the small-circle radius and radius times cosine for its signed plane offset.
Spherical geography models Earth with one radius and angular coordinates. Surface arcs, polar heights, circle radii, and area fractions are different derived quantities; an ideal spherical result does not include ellipsoid or terrain effects.
Return radius times sine of the angle for the small-circle radius and radius times cosine for its signed plane offset.
When to use this tool
Use Spherical Small Circle Radius Factor when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter angularRadius, sphereRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read circleRadius, planeOffset. Use the output convention below.
Require a positive sphere radius and angularRadius in radians from zero through π. Return radius times sine of the angle for the small-circle radius and radius times cosine for its signed plane offset.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angularRadius | Angular Radius | Required. Finite number; minimum 0. |
| sphereRadius | Sphere Radius | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| circleRadius | Circle Radius | Required. Finite number. |
| planeOffset | Plane Offset | Required. Finite number. |
{
"input": {
"angularRadius": 1.5707963267948966,
"sphereRadius": 4
},
"output": {
"circleRadius": 4,
"planeOffset": 2.4492935982947064e-16
}
}Limitations and assumptions
- Both outputs use the radius length unit; plane offset changes sign beyond a hemisphere. Small-circle radius differs from surface distance R times angle, and floating point may leave a tiny endpoint residue.
- 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 ellipsoidal geodesy or a suitable terrain model when spherical assumptions are inadequate. Keep angular units, physical length units, latitude definition, and reference radius explicit.
References
Similar or alternative tools
- Geography: Spherical Cap Latitude Height
Return radius times one minus signed sine latitude for cap height inside result.
- Sphere Section Circle Radius Gap
Return sqrt((radius-offset)(radius+offset)) and tangent for equality.