Equatorial Horizontal Coordinates

Transform geometric hour angle and declination to altitude and azimuth north-through-east; no refraction or time-to-hour-angle conversion is inferred.

Description

Geometric hour angle and declination map to local altitude and azimuth at a supplied latitude.

Geometric hour angle and declination map to local altitude and azimuth at a supplied latitude. Azimuth here runs from north through east, while refraction and clock-to-hour-angle conversion are separate operations.^[1]

Transform geometric hour angle and declination to altitude and azimuth north-through-east; no refraction or time-to-hour-angle conversion is inferred.

When to use Equatorial Horizontal Coordinates

Use this tool to transform geometric hour angle and declination to altitude and azimuth north-through-east; no refraction or time-to-hour-angle conversion is inferred.

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.

How to use Equatorial Horizontal Coordinates and understand its results

Prepare the source, detector or coordinate measurements. Confirm frame, epoch, angular units, axis directions and the stated RA proper-motion convention before entering values.
Enter latitudeDegrees, declinationDegrees, hourAngleDegrees using the field table and calculation rules, then run the tool.
Read altitudeDegrees, azimuthDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
latitudeDegrees	Latitude degrees	number	Required
declinationDegrees	Declination degrees	number	Required
hourAngleDegrees	Hour angle degrees	number	Required

Enter latitude/declination within ±90 and finite hour angle in degrees. The tool constructs east, north and up components, clips the altitude sine for roundoff and returns degree angles. It rejects horizontal-component norm below 10⁻¹⁴ at zenith/nadir because azimuth is undefined.

altitude=asin(up); azimuth=wrap[atan2(east,north)]

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
altitudeDegrees	Altitude degrees	number
azimuthDegrees	Azimuth degrees	number

json

{
  "input": {
    "latitudeDegrees": 45,
    "declinationDegrees": 0,
    "hourAngleDegrees": 0
  },
  "output": {
    "altitudeDegrees": 45.00000000000001,
    "azimuthDegrees": 180
  }
}

Limitations and assumptions

No refraction, terrain horizon, sidereal time or observing-date conversion is applied. All values are geometric; a successful direction is not an observability or telescope-limit check.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Declination Altitude Visibility: Compute geometric daily altitude extrema and visibility relative to a supplied horizon boundary, including both circumpolar and never-rising cases; refraction is excluded. For a complementary task, use Bennett Observed Altitude Refraction: Apply Bennett refraction to observed altitude, with caller pressure and temperature; anomalous atmospheric structure is not modeled.

References

Equatorial Horizontal Coordinates — tool.io

Similar or alternative tools

Declination Altitude Visibility
Compute geometric daily altitude extrema and visibility relative to a supplied horizon boundary, including both circumpolar and never-rising cases; refraction is excluded.
Bennett Observed Altitude Refraction
Apply Bennett refraction to observed altitude, with caller pressure and temperature; anomalous atmospheric structure is not modeled.