Geodetic to ECEF Coordinate Converter

Description

Convert ellipsoidal geodetic coordinates to right-handed ECEF meter coordinates.

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 ellipsoidal geodetic coordinates to right-handed ECEF meter coordinates.

Geodetic latitude, longitude and ellipsoidal height can be represented as geocentric Cartesian coordinates on an explicit ellipsoid. Changing representation alone does not change a datum or epoch.^[1]

When to use this tool

Use this tool when you need to convert ellipsoidal geodetic coordinates to right-handed ECEF meter coordinates.

How to use the tool and how it works

Enter semiMajorMeters, flattening, latitudeDegrees, longitudeDegrees, ellipsoidalHeightMeters using the definitions below.
Run the operation. Resolve input-format errors before interpreting an output.
Read result.ecefMeters, using the stated boundary, ordering, sign and absence conventions.

Calculate prime-vertical radius N, then X=(N+h)cos(phi)cos(lambda), Y=(N+h)cos(phi)sin(lambda), Z=[N(1−e²)+h]sin(phi). Return [X,Y,Z] meters with a separate exact-pole cosine branch.^[2]

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.
longitudeDegrees	East-positive longitude in degrees from −180 through 180.	Finite numeric value satisfying the stated comparisons.
ellipsoidalHeightMeters	Signed height above the reference ellipsoid in meters; the operation-specific height bounds apply.	Finite numeric value satisfying the stated comparisons.

Output field	Interpretation
result	Object containing the fields below.
result.ecefMeters	Three Cartesian [X,Y,Z] coordinates in meters, in the stated frame.

json

{
  "input": {
    "semiMajorMeters": 10,
    "flattening": 0,
    "latitudeDegrees": 0,
    "longitudeDegrees": 0,
    "ellipsoidalHeightMeters": 0
  },
  "output": {
    "result": {
      "ecefMeters": [
        10,
        0,
        0
      ]
    }
  }
}

Limitations and assumptions

Height magnitude≤10⁹ m and h≥−0.1a; latitude is geodetic and height ellipsoidal. Axis order is X at the zero meridian/equator, Y at 90° east/equator, Z north; no epoch or datum transformation is included.
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

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