﻿ Calculate distance between two OS National Grid Reference points Movable Type Scripts

Calculate distance and bearing between two OS National Grid Reference points

Enter the Ordnance Survey grid references (6- or 8-digit) into the text boxes:

Ref1:
Ref2: — Distance: Bearing:

The distance calculation is simple pythagoras trigonometry, √(x² + y²) – the involved part is transforming OS grid references into regular co-ordinates in order to apply the maths (see the OS National Grid site for an explanation of the grid references).

6-digit references resolve to 100m squares; 8-digit references resolve to 10m squares (10-digit references can also be used, giving 1m squares).

For greater or lesser precision, change the number of decimals in the toFixed() methods.

If you also use latitude/longitude points, I have implemented a script for converting between Lat/Long & OS Grid References. If you want distances between latitude/longitude points, see my Lat/Long page.

JavaScript functions are shown below; use ‘View Source’ to see the full JavaScript implementation. I offer these formulæ & scripts for free use and adaptation as my contribution to the open-source info-sphere from which I have received so much. You are welcome to re-use these scripts [under a simple attribution license, without any warranty express or implied] provided solely that you retain my copyright notice and a link to this page.

If you would like to show your appreciation, I would most gratefully accept donations.

If you need any advice or development work done, I am available for consultancy.

If you have any queries or find any problems, contact me at ku.oc.epyt-elbavom@oeg-stpircs.

function gridDistance(ref1, ref2) {
// ref1 & ref2 may be 6- or 8-digit references eg SU387148 or SU38714856

// convert to fully numeric references
var p1 = gridrefNumeric(ref1);
var p2 = gridrefNumeric(ref2);

// get E/N distances between ref1 & ref2
var deltaE = p2-p1;
var deltaN = p2-p1;

// and pythagoras gives us the distance between the points
var dist = Math.sqrt(deltaE*deltaE + deltaN*deltaN);

return (dist/1000).toFixed(2); // return result in km, 2 decimals
}

function gridBearing(ref1, ref2) {
// split numeric references into arrays
var p1 = gridrefNumeric(ref1);
var p2 = gridrefNumeric(ref2);

// get E/N distances between ref1 & ref2
var deltaE = p2-p1;
var deltaN = p2-p1;

// arctan gives us the bearing, just need to convert -pi..+pi to 0..360 deg
var deg = (90-(Math.atan2(deltaN, deltaE)/Math.PI*180)+360) % 360;

return deg.toFixed(0);  // return result in degrees, no decimals
}

/*
* convert standard grid reference ('SU387148') to fully numeric ref ([438700,114800])
*
*   note that northern-most grid squares will give 5-digit northings
*   no error-checking is done on gridref (bad input will give bad results or NaN)
*/
function gridrefNumeric(gridref) {
// get numeric values of letter references, mapping A->0, B->1, C->2, etc:
var letE = gridref.toUpperCase().charCodeAt(0) - 'A'.charCodeAt(0);
var letN = gridref.toUpperCase().charCodeAt(1) - 'A'.charCodeAt(0);
// shuffle down letters after 'I' since 'I' is not used in grid:
if (letE > 7) letE -= 1;
if (letN > 7) letN -= 1;

// convert grid letters into 100km-square indexes from false origin (grid square SV):
var e = ((letE+3)%5)*5 + (letN%5);
var n = (19-Math.floor(letE/5)*5) - Math.floor(letN/5);

// skip grid letters to get numeric part of ref, stripping any spaces:
gridref = gridref.slice(2).replace(/ /g,'');

// append numeric part of references to grid index:
e += gridref.slice(0, gridref.length/2);
n += gridref.slice(gridref.length/2);

// normalise to 1m grid:
switch (gridref.length) {
case 6: e += '00'; n += '00'; break;
case 8: e += '0'; n += '0'; break;
// 10-digit refs are already 1m
}

return [e, n];
}