Grid Convergence Angle Calculator
Compute the convergence angle between true north and grid north at any location in a transverse Mercator projection (UTM, state plane).
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About grid convergence
In a projected coordinate system like UTM or state plane, grid north (parallel to grid Y axis) does not generally align with true north (parallel to the local meridian). The angle between them is the grid convergence, which is zero on the central meridian of the zone and increases east or west of it. Azimuths measured on the ground must be corrected by this angle to convert between "grid" and "true" bearings.
The simple approximation γ ≈ (λ - λ₀) · sin(φ) is accurate to about 1 arcminute near the central meridian. For precision work and larger distances from the central meridian, a higher-order expansion is used. This tool shows both the simple and the higher-order correction. Convergence is small (<1°) for most projects but can reach several degrees at high latitudes far from the central meridian.
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Practical use cases
Converting total station azimuths from field observations to grid azimuths for coordinate computation.
Preparing setout sheets that reconcile compass/true bearings with project grid bearings.
Computing geodetic azimuths from GNSS-derived grid azimuths for long baselines.
Educational: understanding how projection distorts the relationship between true and grid directions.
Frequently asked questions
When is grid convergence zero?
On the central meridian of the projection zone, and at the equator for any longitude. At every other point it is non-zero.
How big can convergence get?
At 45°N and 3° from the central meridian, convergence ≈ 2.1°. At 60°N and 3°: ≈ 2.6°. At 75°N and 3°: ≈ 2.9°. Tropical latitudes have smaller values.
Does this apply only to UTM?
It applies to any transverse Mercator projection, including UTM and most state/country plane coordinate systems. The formula is the same, only the central meridian differs per zone.
How accurate is the simple formula vs the higher-order?
For distances <200 km from the central meridian, the simple formula is accurate to arcseconds. Beyond that, use the higher-order correction (also shown by this tool).
Related tools
Use with our coordinate converter for UTM projection and bearing-azimuth converter for field azimuth reductions.