Calculate straight-line grid distance, coordinate differences, and bearing from two easting/northing points, or find an endpoint from distance and bearing.

Planar geometry only. Use the same projected grid, zone and datum for both points. Numeric eastings/northings only; no latitude/longitude or alphanumeric grid references.

Changing this selection reinterprets all coordinates; it does not convert them.

Related Calculators

Grid Reference Distance Formula

The formula gives planar grid distance from numeric eastings and northings in the same projected coordinate system, zone, datum and unit. Do not enter latitude/longitude or shortened alphanumeric references. Projection scale and convergence mean this is not necessarily ground distance or true/geodesic bearing.

D = โˆš((Eโ‚‚ - Eโ‚)ยฒ + (Nโ‚‚ - Nโ‚)ยฒ)

Variables:

  • D is the distance between the two points
  • Eโ‚ is the Eastings coordinate of the first point
  • Nโ‚ is the Northings coordinate of the first point
  • Eโ‚‚ is the Eastings coordinate of the second point
  • Nโ‚‚ is the Northings coordinate of the second point

To calculate the distance, subtract the Eastings and Northings coordinates of the first point from the corresponding coordinates of the second point. Square the results, sum them, and then take the square root of the sum.

What is a Grid Reference?

A grid reference is a system used to pinpoint a location on a map by using a set of coordinates. These coordinates are typically given as Eastings and Northings, which represent the distance east and north, respectively, from a defined origin point. Grid references are commonly used in mapping and navigation to accurately describe the position of a point on the Earth's surface. They are essential in fields such as geography, cartography, and various engineering disciplines.

How to Calculate Grid Reference Distance?

The following steps outline how to calculate the distance between two points using their grid references.

  1. First, determine the Eastings and Northings coordinates of the first point (Eโ‚, Nโ‚).
  2. Next, determine the Eastings and Northings coordinates of the second point (Eโ‚‚, Nโ‚‚).
  3. Calculate the difference between the Eastings coordinates (Eโ‚‚ - Eโ‚).
  4. Calculate the difference between the Northings coordinates (Nโ‚‚ - Nโ‚).
  5. Square both differences and sum them.
  6. Take the square root of the sum to find the distance (D).
  7. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Eastings 1 (Eโ‚) = 500000

Northings 1 (Nโ‚) = 200000

Eastings 2 (Eโ‚‚) = 500100

Northings 2 (Nโ‚‚) = 200100

With coordinates in meters, ฮ”E=100m and ฮ”N=100m, so distance=141.42135624m and grid bearing=45ยฐ clockwise from grid north. NIST defines the international foot as0.3048m and the legacy US survey foot as1200/3937m; use the unit associated with the source grid.