Grid variation (grivation)

Model: Grid variation G = D − γ: the model's declination D minus the grid convergence γ (the bearing of grid north from true north) of the UTM or UPS zone, both east positive

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1. Grid convergence

   bearing of grid north from true north

   UPS north = 45°

2. Grid variation

   $$G=D-\gamma$$

   45.32° − 45° = 0.32°

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

Accuracy: As good as the declination (WMM2025: about 0.3° to a few degrees near the poles); the convergence is exact

When to use this: Use this when you are navigating on a grid rather than on meridians -- a military map, a polar route, anything working in UTM or UPS bearings. Grivation is the angle from grid north to magnetic north, so it is what turns a compass reading into a grid bearing, and it is not the declination unless you happen to be on the zone's central meridian.

Limitations: Three norths, and mixing them is the danger this tool exists to remove: grivation is measured from GRID north, so it is not interchangeable with the declination except on a central meridian, where the convergence is zero. Its accuracy is the declination's -- about half a degree from the model, more near the poles -- since the convergence is exact. And the grid matters: the same point has a different grivation in UTM and in UPS, so the grid used is reported with the answer rather than assumed.

Worked example: At 86° N, 45° E in UPS north. Source: add-geodesy-suite grivation scenario: WMM2025 declination minus the UPS convergence.

Review: Not yet independently reviewed by a geodesist.

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

Sources

• The US/UK World Magnetic Model for 2025-2030: Technical Report, NOAA National Centers for Environmental Information and British Geological Survey, WMM2025, NESDIS/NCEI (December 2024). Section 1.2 (equations 1-25: synthesis, secular variation, and elements) and Section 3 (uncertainty, blackout and caution zones).
• International Geomagnetic Reference Field: the fourteenth generation, International Association of Geomagnetism and Aeronomy (IAGA), Working Group V-MOD, IGRF-14 (igrf14coeffs.txt). Coefficient table, 1900.0-2025.0 main field and 2025-2030 secular variation.
• The Universal Grids and the Transverse Mercator and Polar Stereographic Map Projections, NGA.SIG.0012, National Geospatial-Intelligence Agency, NGA.SIG.0012_2.0.0_UTMUPS. Sections 3 (UTM zones, Norway and Svalbard exceptions) and 4 (UPS).

Terms

UPS: Universal Polar Stereographic

The polar companion to UTM, covering the areas north of 84° N and south of 80° S. Source: NGA.SIG.0012 UTM and UPS

UTM: Universal Transverse Mercator

A grid of 60 zones, each 6° of longitude wide, that turns latitude and longitude into eastings and northings in meters. Source: NGA.SIG.0012 UTM and UPS

WGS: World Geodetic System

The US Department of Defense global reference frame and ellipsoid that GPS uses; the current version is WGS 84. Source: Department of Defense World Geodetic System 1984