StringMash.com

Waypoint projection calculator

Go a distance on a bearing from a coordinate, or measure between two.

Conversion

A projection runs out from a start point. To measure between two points instead, pick Two points → Distance and bearing.

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Updates as you type
DDMN 32° 42.169 W 117° 09.306
DD32.702821, -117.155095
DMSN 32° 42' 10.16" W 117° 09' 18.34"

These send the coordinates to that app or site, and only when you follow one.

Show the steps
NESW70.0°250 mStart in the middle, not to scale
  1. Start: 32.70205, -117.1576.
  2. Distance: 250 m.
  3. Bearing: 70.0° clockwise from true north.
  4. Solved on the WGS84 ellipsoid, the shape GPS uses, with Vincenty's direct formula.
  5. Arriving, the line is heading 70.0°. On a curved Earth that differs from the starting bearing over long distances.
  6. The bearing is from true north. A magnetic compass points to magnetic north, which can be several degrees away.

Using the calculator

Type the start coordinate in any format, then set the distance, its unit and the bearing in degrees from true north. The projected point appears in all three coordinate formats, with a copy button for each and links to open it in a map. Show the steps draws the projection and gives the bearing you'd be heading on arrival.

To work backwards, switch to Two points → Distance and bearing and put one coordinate on each line. You get the distance in metres, kilometres, feet and miles, the bearing from the first point to the second, and the bearing back.

Why the shape of the Earth matters

The Earth is slightly squashed: the WGS84 ellipsoid that GPS uses is 6,378.137 km from centre to equator and about 6,356.752 km to the poles, a difference of 21 km. A calculator that treats the Earth as a perfect sphere can be out by up to about 0.5% of the distance, a couple of metres on a 500 m projection.

This one solves the problem on the ellipsoid, with Thaddeus Vincenty's formulae, which are accurate to within half a millimetre. Every result in our tests is checked against GeographicLib, the reference library, and has to land within 10 cm of it.

True north, not compass north

Bearings here, and in almost every puzzle that asks for a projection, are measured from true north, the direction of the North Pole. A magnetic compass points at magnetic north, which can be several degrees away and drifts year by year. To walk a projection with a compass, look up the declination for where you are, from NOAA's calculator or your GPS, and correct for it.

The bearing back from the second point isn't quite the first bearing plus 180°. The shortest path over a curved surface bends, so its direction changes along the way. Over a few hundred metres the difference is a fraction of a degree; over an ocean it's tens of degrees.

Written for a desk calculator

Vincenty published his method in Survey Review in April 1975. His aim was the shortest possible programme, because he was running it on a Wang 720 desk calculator with a few kilobytes of memory. The result is accurate to within half a millimetre, and it has one known weakness. For two points almost exactly opposite each other on the globe, the inverse calculation can fail to settle, and rather than guess, this page says so. The standard example is the pair 0°, 0° and 0.5° N, 179.7° E.

Questions

What does a bearing of 360 mean?

The same as 0: due north. Bearings run clockwise, so 90 is east, 180 south and 270 west.

The puzzle gives feet. Do I need to convert?

No. Pick feet in the Unit setting. Miles and kilometres are there too.

How accurate is the result?

The maths is accurate to well under a millimetre on the WGS84 ellipsoid. In practice your GPS receiver is the limit, at a few metres.

Can I project from a point given in decimal degrees?

Yes. The start point can be in any of the three formats, and the result comes back in all three.

Not affiliated

Not affiliated with or endorsed by Geocaching HQ / Groundspeak. Geocaching is a registered trademark of its owner.

Sources

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