Description
Return cosine latitude times that angular width.
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 cosine latitude times that angular width.
When to use this tool
Use Latitude Cell Cosine Weight when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter latitudeRadians, longitudeWidthRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weight. Use the output convention below.
Require latitudeRadians within ±π/2 and nonnegative longitudeWidthRadians. Return cosine latitude times that angular width.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeRadians | Latitude Radians | Required. Finite number. |
| longitudeWidthRadians | Longitude Width Radians | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weight | cos(latitude) times longitude width; dimensionless and not complete cell area. | Required. Finite number. |
{
"input": {
"latitudeRadians": 0,
"longitudeWidthRadians": 2
},
"output": {
"weight": 2
}
}Limitations and assumptions
- This is a dimensionless spherical weighting factor; a complete area also requires the relevant radius-squared and latitude-integration terms. Longitude width is not capped at a full turn by the tool.
- 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.
- Spherical Cap Latitude Area Fraction
Return the north-cap whole-sphere area fraction (1-sin latitude)/2 and its south-cap complement.