Description
Return z equal to radius times sine latitude.
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 z equal to radius times sine latitude.
When to use this tool
Use Geocentric Axis Z Component Sphere when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter radius, latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read z. Use the output convention below.
Require nonnegative radius and latitudeRadians within ±π/2. Return z equal to radius times sine latitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; minimum 0. |
| latitudeRadians | Latitude Radians | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| z | Z | Required. Finite number. |
{
"input": {
"radius": 5,
"latitudeRadians": 1.5707963267948966
},
"output": {
"z": 5
}
}Limitations and assumptions
- Latitude is spherical/geocentric for this formula, and z uses the radius length unit. Geodetic latitude on an ellipsoid requires a different model; a full three-dimensional position is not constructed.
- 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
- Latitude Height Radius Approximation
Return their sum and height divided by surfaceRadius as relativeChange.
- Ellipsoid Prime Vertical Radius Term
Return semimajor divided by the square root of 1 minus eccentricitySquared times sine-squared latitude.