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
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
Something look off?
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
- Instrument Flying Handbook, FAA-H-8083-15B, Federal Aviation Administration, FAA-H-8083-15B. Chapter 9 (navigation systems: DME slant range, time and distance to a station from a bearing change, DME arcs).
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