geoprimsField-grade geospatial math

DME slant range to ground distance

The distance over the ground to a station from the DME reading and your height above the station, and how much the reading overstates it.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

4.902NM

You are 4.902 NM from the station over the ground; the DME reads 0.098 NM long.

Slant-range error
Angle up to you from the station
Provenance
Computed by
aviation.ifr.dme-slant-range 1.0.0, core 0.1.0
Model
DME measures the straight-line (slant) distance; over flat ground the horizontal distance is √(DME² − h²) with h the height above the station in nautical miles (6,076.1 ft each). Error is largest close in and high up (Instrument Flying Handbook, ch. 9)
Accuracy
Exact geometry; ignores the Earth's curvature, which is under 0.01 NM inside 60 NM at 10,000 ft
Notes
1 shown with the answer
Cites
Federal Aviation Administration, Instrument Flying Handbook, FAA-H-8083-15B

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How we got thisFormula, worked example, sources, and proof

Model: DME measures the straight-line (slant) distance; over flat ground the horizontal distance is √(DME² − h²) with h the height above the station in nautical miles (6,076.1 ft each). Error is largest close in and high up (Instrument Flying Handbook, ch. 9)

Accuracy: Exact geometry; ignores the Earth's curvature, which is under 0.01 NM inside 60 NM at 10,000 ft

Worked example: DME 5.0 at 6,000 ft above the station. Source: add-practitioner-essentials slant-range scenario (4.902 NM). It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

DME reading
5.0 NM
Height above the station
6000 ft

You get

Ground distance
4.902 NM
Slant-range error
0.098 NM
Angle up to you from the station
11.4°

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 7 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Terms

DME: distance measuring equipment
A radio aid that shows the straight-line distance from the aircraft to a ground station, in nautical miles. Up high and close in, that slant distance is longer than the distance over the ground. Source: Instrument Flying Handbook

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

DME — distance measuring equipment

A radio aid that shows the straight-line distance from the aircraft to a ground station, in nautical miles. Up high and close in, that slant distance is longer than the distance over the ground.

Source: Instrument Flying Handbook