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Grid Convergence Angle Calculator

Computes grid convergence from latitude, longitude and the central meridian for map projections.

100% FreeRuns in your browserIntermediate
How to use this calculator

Inputs

Grid convergence γ between true north and grid north — projection-derived, with the first-order approximation beside it — and grid → true azimuth under a printed sign convention.

Point

Decimal degrees (−31.95), DMS (31 57 0 S) or DDM (31° 57.0′ S).

Decimal degrees (115.86), DMS (115 51 36 E) or DDM (115° 51.6′ E).

Projection

Decimal degrees (115.86), DMS (115 51 36 E) or DDM (115° 51.6′ E).

Bearing (optional)

Decimal degrees (135), DMS (135 0 0) or DDM (135° 0.5′).

Enter the values and press Calculate.

Or load an example to see a worked result.

True north and grid north at your point
Not to scale — γ exaggerated
True north and grid north at your pointTrue north arrow, grid north arrow rotated by the convergence γ, the γ arc and an optional grid bearing ray.True NGrid Nγbearingγ: true N → grid N, clockwise +true az = grid az + γ
If γ is the clockwise angle from true north to grid north, true azimuth = grid azimuth + γ. Always print the convention with the value.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

How the method works

A fixed worked example to explain the method — it is not your result.

Always print the selected convergence sign convention
Illustrative method
Always print the selected convergence sign conventionTrue north arrow, grid north arrow rotated by the convergence γ, the γ arc and an optional grid bearing ray.True NGrid Nγbearingγ: true N → grid N, clockwise +true az = grid az + γ
If γ is the clockwise angle from true north to grid north, true azimuth = grid azimuth + γ. Always print the convention with the value.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the latitude and longitude.
  2. Choose the projection: enter a Transverse Mercator central meridian, or let UTM pick the zone (standard or one you enter).
  3. Optionally enter a grid bearing to convert to a true azimuth.
  4. Press Calculate. The precise and approximate values are shown side by side with their difference.

How it works

Sign convention (always printed with the result): γ is the clockwise angle from true north to grid north, so true azimuth = grid azimuth + γ.

Precise: γ comes from the same Krüger-series Transverse Mercator kernel as the UTM converters. Its sign and size agree with a finite difference of proj4's own projection to about 1×10⁻⁸°. It is offered within 6° of the central meridian and marked unavailable beyond, rather than replaced with the approximation.

Approximation: γ ≈ (λ − λ₀) sin φ. It is exact on the central meridian and at the equator and drifts with distance from the meridian.

Worked example

−31.95°, 116°, central meridian 117°. Approximation +0.529179°, precise +0.529218° (the approximation is 0.141″ smaller). A grid bearing of 100° is a true azimuth of 100.529218°.

Common mistakes

  • Applying γ with the wrong sign. Check the printed convention before adding or subtracting.
  • Using the approximation several degrees from the meridian, where it drifts by arcseconds.
  • Confusing grid convergence with magnetic declination.

Frequently asked questions

Why does grid convergence matter?

Bearings on a map grid differ from true bearings by the convergence angle; surveyors apply it when relating grid and true north.

Does grid convergence change with the date?

No. Grid convergence is pure geometry — it depends only on where you are relative to the central meridian, not on time. The angle that changes with date is magnetic declination (true north vs magnetic north); use the Magnetic Declination Calculator for that.

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Cite this tool

Zerdly. (2026). Grid Convergence Angle Calculator. Retrieved from https://www.zerdly.com/tools/grid-convergence-angle-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.