Description
Calculate Albers equal-area conic construction constants with tangent-limit and degeneracy handling.
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.
Calculate Albers equal-area conic construction constants with tangent-limit and degeneracy handling.
When to use this tool
Use this tool when you need to calculate Albers equal-area conic construction constants with tangent-limit and degeneracy handling.
How to use the tool and how it works
- Enter semiMajorMeters, flattening, firstParallelDegrees, secondParallelDegrees using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.n, result.c, result.firstParallelQ, result.secondParallelQ, result.degenerate, using the stated boundary, ordering, sign and absence conventions.
Calculate m for both standard parallels and authalic q for each. For distinct parallels use n=(m1²−m2²)/(q2−q1); for equal parallels use n=sin(phi1). Return c=m1²+n q1, both q values and abs(n)<10⁻¹² degeneracy.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. |
| firstParallelDegrees | First geodetic standard parallel in degrees, magnitude≤89.9999°. | Finite numeric value satisfying the stated comparisons. |
| secondParallelDegrees | Second geodetic standard parallel in degrees, magnitude≤89.9999°. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.n | Dimensionless Lambert/Albers cone constant under the stated tangent/secant rule. |
| result.c | Dimensionless Albers construction constant m1²+n q1. |
| result.firstParallelQ | Dimensionless authalic q at the first standard parallel. |
| result.secondParallelQ | Dimensionless authalic q at the second standard parallel. |
| result.degenerate | Operation-specific degenerate case: near-zero cone constant or zero isotropic sigma, as described above. |
{
"input": {
"semiMajorMeters": 10,
"flattening": 0,
"firstParallelDegrees": 30,
"secondParallelDegrees": 30
},
"output": {
"result": {
"n": 0.49999999999999994,
"c": 1.25,
"firstParallelQ": 0.9999999999999999,
"secondParallelQ": 0.9999999999999999,
"degenerate": false
}
}
}Limitations and assumptions
- Parallels exclude the poles and the ellipsoid is explicit. These are Albers construction constants, not a sum of user weights, full projected coordinates or an automatic repair of degenerate symmetric parallels.
- 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
- Lambert Conformal Conic Constant n Solver from Two Parallels
Calculate a Lambert conformal-conic cone constant with tangent/secant branches and degeneracy evidence.
- Authalic Latitude Equal-Area Converter
Convert geodetic latitude to equal-area authalic latitude using the ellipsoidal q function.