geoprimsField-grade geospatial math

Antenna height from a slant measurement

The vertical height to the antenna reference point from a slant height measured to the edge of the antenna, its radius, and the mark-to-ARP offset.

Experimental: not yet fully verified. How results are checked

1.7972m

The antenna reference point is 1.7972 m above the mark.

Slant minus vertical
Provenance
Computed by
survey.gnss.antenna-height 1.0.0, core 0.1.0
Model
The slant, the radius, and the vertical make a right triangle: vertical to the measurement point = √(slant² − radius²), plus the vertical offset from that point to the ARP
Accuracy
Exact geometry; as good as the tape and the antenna's published radius and offset
Notes
1 shown with the answer
Cites
NOAA National Geodetic Survey, GPS Antenna Calibration: antenna reference point and slant heights

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

Model: The slant, the radius, and the vertical make a right triangle: vertical to the measurement point = √(slant² − radius²), plus the vertical offset from that point to the ARP

Show your work

  1. Vertical to the measurement point

    (slant2−radius2)

    √(1.8² − 0.1²) = 1.7972 m

  2. Vertical to the ARP

    + offset

    1.7972 + 0 = 1.7972 m

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact geometry; as good as the tape and the antenna's published radius and offset

Worked example: 1.800 m slant to a 0.100 m radius. Source: add-practitioner-essentials antenna scenario: √(1.8² − 0.1²) ≈ 1.7972 m, with the formula shown. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Measurement point to ARP
0 m
Antenna radius
0.100 m
Slant height
1.800 m

You get

Vertical height to the ARP
1.7972 m
Slant minus vertical
0.0028 m

Review: Not yet independently reviewed by a licensed surveyor.

Last verified: 2026-09-22, 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: 5 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Terms

ANTINFO: antenna information
NGS's records of GNSS antenna dimensions, including the radius to the measurement mark and the offset to the ARP. Source: GPS Antenna Calibration: antenna reference point and slant heights
ARP: antenna reference point
The point on a GNSS antenna, usually the bottom of its mount, that antenna heights and calibrations are measured to. Source: GPS Antenna Calibration: antenna reference point and slant heights

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