Description
Convert geodetic latitude to equal-area authalic latitude using the ellipsoidal q function.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Convert geodetic latitude to equal-area authalic latitude using the ellipsoidal q function.
When to use this tool
Use this tool when you need to convert geodetic latitude to equal-area authalic latitude using the ellipsoidal q function.
How to use the tool and how it works
- Enter semiMajorMeters, flattening, latitudeDegrees using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.authalicLatitudeDegrees, using the stated boundary, ordering, sign and absence conventions.
Calculate authalic q(phi)=(1−e²)[sin(phi)/(1−e²sin²(phi))+atanh(e sin(phi))/e], using q=2sin(phi) for a sphere. Divide by polar q, clamp numerical drift to [−1,1], take arcsine and convert to degrees.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semiMajorMeters | Equatorial semiaxis a in meters, 1–10⁸. It is a radius, not a diameter. | Finite numeric value satisfying the stated comparisons. |
| flattening | Dimensionless ordinary flattening f=(a-b)/a, from zero through 0.02; supply f rather than inverse flattening. | Finite numeric value satisfying the stated comparisons. |
| latitudeDegrees | Geodetic latitude in degrees, north positive; the operation’s pole restrictions apply. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.authalicLatitudeDegrees | Equal-area auxiliary latitude in degrees. |
{
"input": {
"semiMajorMeters": 10,
"flattening": 0,
"latitudeDegrees": 30
},
"output": {
"result": {
"authalicLatitudeDegrees": 29.999999999999996
}
}
}Limitations and assumptions
- Authalic latitude is an equal-area auxiliary latitude on the chosen ellipsoid. It differs from reduced, geocentric and conformal latitude; the clamp only contains floating-point endpoint drift.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
- Authalic Radius R2 from Axes Calculator
Calculate the equal-surface-area authalic sphere radius from explicit semiaxes.
- Conformal Latitude Gauss Computation Calculator
Convert geodetic latitude to Gauss conformal latitude on an explicit ellipsoid.