Description
Return 2π times radius squared times cosine latitude, with positive sign for an upper boundary and negative sign for a lower boundary.
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 2π times radius squared times cosine latitude, with positive sign for an upper boundary and negative sign for a lower boundary.
When to use this tool
Use Spherical Latitude Band Area Latitude Sensitivity when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter radius, latitudeRadians, upperBoundary. 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 positive radius and latitudeRadians within ±π/2. Return 2π times radius squared times cosine latitude, with positive sign for an upper boundary and negative sign for a lower boundary.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| latitudeRadians | Latitude Radians | Required. Finite number. |
| upperBoundary | Upper Boundary | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Local sensitivity with respect to the stated variable, holding other model inputs fixed. | Required. Finite number. |
{
"input": {
"radius": 2,
"latitudeRadians": 0,
"upperBoundary": true
},
"output": {
"derivative": 25.132741228718345
}
}Limitations and assumptions
- This is spherical band-area sensitivity per radian of boundary motion, not a complete area or an ellipsoidal correction.
- 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 Cap Latitude Area Fraction
Return the north-cap whole-sphere area fraction (1-sin latitude)/2 and its south-cap complement.
- Latitude Parallel Circumference Radius Sensitivity
Return derivative equal to 2π times cosine latitude.