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Zenith Angle from Altitude Complement Calculator

Convert signed horizon altitude in [-90,90] degrees to zenith angle [0,180] degrees; same apparent/geometric convention must be retained.

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Description

Convert signed horizon altitude to its complementary zenith angle in degrees.

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 signed horizon altitude to its complementary zenith angle in degrees.

When to use this tool

Use this tool when you need to convert signed horizon altitude to its complementary zenith angle in degrees.

How to use the tool and how it works

  1. Enter altitudeDegrees using the definitions below.
  2. Run the operation. Resolve input-format errors before interpreting an output.
  3. Read result.zenithDegrees, using the stated boundary, ordering, sign and absence conventions.

Return 90−altitudeDegrees. Altitude is measured from the local horizontal and zenith angle from the upward vertical, so a negative altitude gives a zenith angle above 90°.1

Input fieldMeaning and unitsAccepted input
altitudeDegreesSigned elevation above the local horizontal in degrees, from −90 through 90.Finite numeric value satisfying the stated comparisons.
Output fieldInterpretation
resultObject containing the fields below.
result.zenithDegreesComplementary angle from the upward vertical, in degrees.
json
{
  "input": {
    "altitudeDegrees": -10
  },
  "output": {
    "result": {
      "zenithDegrees": 100
    }
  }
}

Limitations and assumptions

  • Altitude lies from −90° through 90°, producing a zenith angle from zero through 180°. This complement does not add refraction or determine an observed horizon.
  • 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

  1. Tool behavior and example: Zenith Angle from Altitude Complement Calculator — tool.io

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