What is grid convergence?

Grid convergence (also called meridian convergence) is the angle between true north (toward the geographic pole) and grid north (the northing direction on a projected map like UTM). It is positive east of the central meridian and negative west of it.

How is grid convergence different from magnetic declination?

Magnetic declination is the angle between magnetic north and true north — caused by Earth's magnetic field. Grid convergence is purely geometric, the angle between true north and the projection's grid north. A full bearing correction may need both values.

What formula does this calculator use?

The simplified UTM formula: γ ≈ (λ − λ₀) × sin(φ), where λ is your longitude, λ₀ is the zone central meridian (6° × zone − 183°), and φ is your latitude. This is accurate to within arc-seconds for most practical survey work away from the poles.

Is positive convergence east or west?

By the standard surveying convention used here, a positive angle means grid north lies east of true north — i.e., your location is east of the central meridian. A negative angle means grid north is west of true north.

What UTM zone should I use?

Each UTM zone is 6° wide. Zone 1 covers 180°W–174°W. Use the auto-detect button or compute your zone as: floor((longitude + 180) / 6) + 1. Most GPS receivers and GIS software display the zone alongside UTM coordinates.

Grid Convergence Calculator

Name: Grid Convergence Calculator
Availability: InStock
Author: Nham Vu

Calculate the grid convergence angle between true north and grid north for any longitude and UTM zone.

Location & Zone

Longitude (decimal degrees)

Negative = west hemisphere

Latitude (decimal degrees)

Negative = southern hemisphere (valid range −80° to +84°)

UTM Zone number (1–60)

Leave blank and click Auto-detect to derive from longitude.

Result

Enter coordinates and click Calculate.

Sample Calculations

Location	Longitude	Latitude	Zone	Convergence
Central meridian	−87°	45°	16	0° 00′ 00″
East of CM	−83°	45°	17	+2° 49′ 42″
Hanoi, Vietnam	105.84°	21.02°	48	+0° 51′ 06″

Click any row to load those values into the calculator.

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Summary

Calculate the grid convergence angle between true north and grid north for any longitude and UTM zone.

How it works

Enter the longitude of your location in decimal degrees (negative for west).
Enter the latitude in decimal degrees (negative for south).
Select the UTM zone number (1–60) or let the calculator detect it automatically.
The calculator applies the standard UTM grid convergence formula using the angular difference from the zone's central meridian.
Results show the convergence angle in degrees, minutes, and seconds, plus practical guidance on applying the correction.

Use cases

Correct a compass bearing from true north to grid north when plotting on a UTM map.
Verify map orientation during land surveying in the field.
Apply gyrotheodolite readings to grid-referenced survey control networks.
Understand grid vs. magnetic north corrections for orienteering or military land navigation.
Compute the central meridian offset for custom grid projections.
Cross-check GIS software output when debugging coordinate transformations.

Frequently Asked Questions

Last updated: 2026-06-24 · Reviewed by Nham Vu