Description
Return derivative equal to 2π times cosine 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 derivative equal to 2π times cosine latitude.
When to use this tool
Use Latitude Parallel Circumference Radius Sensitivity when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Require latitudeRadians within ±π/2. Return derivative equal to 2π times cosine latitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeRadians | Latitude Radians | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Local sensitivity with respect to the stated variable, holding other model inputs fixed. | Required. Finite number. |
{
"input": {
"latitudeRadians": 0
},
"output": {
"derivative": 6.283185307179586
}
}Limitations and assumptions
- This is the sensitivity of spherical parallel circumference to sphere radius, with latitude held fixed. Its unit is length per length, and no radius, ellipsoid, or latitude derivative is used.
- 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
- Spherical Latitude Band Area Latitude Sensitivity
Return 2π times radius squared times cosine latitude, with positive sign for an upper boundary and negative sign for a lower boundary.
- Meridian Distance Latitude Sensitivity
Return signed meridian distance radius times latitude and derivative equal to radius.