Triangulation: How to Find Your Position from Bearings
You can see a church spire, a radio mast and a hilltop, and you can find all three on the map. Three compass bearings later, you know exactly where you are standing.
Three words for one family of ideas
In everyday speech, triangulation means working out a position from angles to things you already know. Map readers are usually more precise about it. Resection is fixing your own position by taking bearings to two or three landmarks you can identify on the map. Intersection is the reverse: from two known positions you take bearings to one unknown object, such as a fire on a distant hill, and plot where the lines cross.
Strictly, triangulation is the surveyor's method of mapping a whole country by measuring a chain of triangles between hilltop stations. The Great Trigonometrical Survey of India and Britain's concrete trig pillars both came from it. The geometry underneath all three is the same: a direction from a known point is a line, and two lines cross at one place.
How to find your position by resection
You need a map, a compass, and at least two landmarks you can see and can also find on the map.
- Pick your landmarks Choose two, preferably three, features you can identify both in front of you and on the map: a spire, a mast, a summit, a lake shore. Spread them out, ideally 60 to 120 degrees apart.
- Take a bearing to each Point the compass at the first landmark, turn the housing until the needle sits in the orienting arrow, and read the bearing. Repeat for the others.
- Correct for declination Convert each magnetic bearing to a map bearing: subtract a westerly declination, add an easterly one. This is the reverse of the correction used when walking a bearing taken from the map.
- Turn them into back bearings Add 180 degrees to each bearing, or subtract 180 if it is 180 or more. The back bearing is the direction from the landmark to you.
- Draw the lines On the map, draw a line from each landmark along its back bearing, towards where you think you are.
- Read where they cross Two lines cross at your position. Three lines usually make a small triangle, the cocked hat, and you are inside it.
Worked example: two bearings
After correcting for declination, the church is at 300 degrees from you and the radio mast is at 059 degrees. Which lines do you draw?
- Church: 300 is 180 or more, so subtract 180: 300 - 180 = 120
- Mast: 059 is less than 180, so add 180: 059 + 180 = 239
- Draw a line from the church at 120 degrees and a line from the mast at 239 degrees
You are where the two lines cross. A bearing to a third landmark, drawn the same way, confirms it.
Why three bearings beat two
Two lines always cross somewhere, so two bearings give you a position whether you took them carefully or not. A third bearing is a check. If all three lines meet in a tiny triangle, your bearings were good. If they make a large triangle, at least one bearing was wrong, or one landmark was misidentified, and you should take them again.
The angles matter as well. Lines that cross at close to a right angle give a sharp fix. Lines from two landmarks that lie in almost the same direction cross at a shallow angle, and a one-degree error in either one slides the crossing point a long way along the line.
Resection at world scale: GeoAzimuth
The GeoAzimuth game is resection with cities. The arrows tell you the bearing from the hidden city to several cities you know, exactly the bearings you would take if you stood there with a compass. Picture a line running back from each known city along its back bearing, and the hidden city is where they meet. Over thousands of kilometres the lines are great circles rather than straight lines, but the reasoning is the same.
Check what you learned
Five questions on finding your position from bearings. Pass at 70% or better to complete the lesson.
Practice with Games
Ready to test what you learned? Jump into a game and put it into practice.
Triangulation, in one paragraph
To triangulate your position with a map and compass, a method properly called resection, pick two or three landmarks you can see and can also find on the map, ideally 60 to 120 degrees apart. Take a compass bearing to each, correct it for magnetic declination, and convert it to a back bearing by adding or subtracting 180 degrees, because the line you draw runs from the landmark back towards you. Draw a line from each landmark along its back bearing: two lines cross at your position, and three lines usually form a small triangle called the cocked hat, with you inside it. A large cocked hat means a bearing was wrong or a landmark was misidentified. Intersection is the reverse technique, locating an unknown object from two known positions, and surveyors' triangulation maps whole countries from networks of measured triangles. GPS, by contrast, uses trilateration, measuring distances rather than angles.
Common questions about triangulation
How do you triangulate your position with a compass?
Take bearings to two or three landmarks you can find on the map, correct them for declination, and turn each into a back bearing by adding or subtracting 180 degrees. Draw a line from each landmark along its back bearing. Where the lines cross is your position.
What is the difference between resection and intersection?
Resection finds your own unknown position from bearings to known landmarks. Intersection finds the position of an unknown object, such as a distant fire or a peak, by taking bearings to it from two or more known positions and plotting where the lines cross.
How many landmarks do I need?
Two is the minimum, because two lines cross at one point. Three is better, because the third line shows whether your bearings agree. If all three meet in a small triangle, the fix is good.
What is a cocked hat in navigation?
It is the small triangle formed when three position lines do not meet at exactly one point, because every real bearing has a little error. You are most likely inside it. A large cocked hat is a warning that one bearing is wrong.
Do phones triangulate your location?
Not in the compass sense. Satellite positioning uses trilateration, measuring distances to satellites from signal travel times. Phones also estimate position from nearby Wi-Fi networks and mobile masts, which is often loosely called triangulation even though it mostly relies on signal strength and timing.