Zerdly

AER (Azimuth/Elevation/Range) to ECEF Converter

Converts azimuth, elevation and range line-of-sight to a target into ECEF coordinates via ENU.

100% FreeRuns in your browserProfessional
How to use this calculator

Inputs

A line-of-sight observation (azimuth, elevation or zenith angle, slant range) from a known origin → ENU, ΔXYZ and the absolute ECEF target.

Origin

Decimal degrees (−31.95), DMS (31 57 0 S) or DDM (31° 57.0′ S).

Decimal degrees (115.86), DMS (115 51 36 E) or DDM (115° 51.6′ E).

Ellipsoidal height h — not AHD or sea level.

Observation

Decimal degrees (135), DMS (135 0 0) or DDM (135° 0.5′).

Decimal degrees (135), DMS (135 0 0) or DDM (135° 0.5′).

Ellipsoid

A shape only — choosing one does not transform between datums or epochs.

More options

Printed with the result so the numbers never travel without their reference. It is a label only: nothing is transformed.

Enter the values and press Calculate.

Or load an example to see a worked result.

Line of sight in the origin's local frame
Not to scale
Line of sight in the origin's local frameOblique sketch of the east, north and up axes at the origin with the displacement vector and its three components.E (east)N (north)U (up)OriginENUTarget = origin + R·[E, N, U]
East, north and up axes at the origin; the local displacement is rotated into ECEF and added to the origin.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

How the method works

A fixed worked example to explain the method — it is not your result.

A local displacement is rotated, then added to the origin
Illustrative method
A local displacement is rotated, then added to the originOblique sketch of the east, north and up axes at the origin with the displacement vector and its three components.E (east)N (north)U (up)OriginENUTarget = origin + R·[E, N, U]
East, north and up axes at the origin; the local displacement is rotated into ECEF and added to the origin.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the origin latitude, longitude and ellipsoidal height, and choose the ellipsoid.
  2. Enter the azimuth, clockwise from geodetic north.
  3. Choose elevation above horizontal (−90° to 90°) or zenith angle (0° to 180°), then enter the angle and the slant range in metres.
  4. Press Calculate and read ENU, ΔXYZ, the target XYZ and the target position.

How it works

E = r cos(el) sin(az), N = r cos(el) cos(az), U = r sin(el); a zenith angle z is converted with el = 90° − z.

The ENU vector is rotated into ECEF with the same matrix as the ENU converter and added to the origin.

The target's latitude, longitude and height come from the iterated inverse, so the chain is exact in both directions.

This is pure geometry in the origin's tangent frame: no refraction, Earth-curvature or deflection-of-the-vertical correction is applied.

Worked example

Origin −31.95°, 115.86°, 50 m; az 45°, el 10°, 1,000 m. E = N = 696.364 m and U = 173.648 m. The target is X −2,363,620.391, Y 4,874,748.607, Z −3,355,255.782 m — about −31.94372°, 115.86736° at 223.724 m ellipsoidal height. The height gain exceeds U because the ellipsoid curves away under a level line of sight.

Common mistakes

  • Entering a zenith angle as an elevation (or the reverse): 80° zenith is 10° elevation.
  • Using a magnetic or grid bearing as the azimuth. The formula needs azimuth from geodetic (true) north.
  • Expecting a refracted field observation to be reduced. Apply refraction and instrument corrections before using this tool.

Frequently asked questions

What is AER used for?

Radar, theodolite and antenna pointing express a target as azimuth, elevation and range from an observer.

What happens at zero range?

The target is the origin and the azimuth no longer matters; the tool returns the origin's coordinates exactly.

Related tools

Explore more in Surveying, Coordinates, GIS & CAD.

Cite this tool

Zerdly. (2026). AER (Azimuth/Elevation/Range) to ECEF Converter. Retrieved from https://www.zerdly.com/tools/aer-azimuth-elevation-range-to-ecef-converter/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.