Our triangulation calculator will find the coordinates of an unknown point based on two known locations and the bearing measured either to or from those locations. It is a compact surveying toolkit for anyone working with maps, sightings, and coordinate geometry.
With the calculator you can either:
- Calculate the position of a landmark (an intersection) by observing it from two known stations; or
- Calculate your own position (a resection) by observing two landmarks with known coordinates.
If you don't know what triangulation is or the formula for triangulation, worry not! Keep reading to learn the definition of triangulation, how to use the triangulation calculator, and the difference between triangulation and trilateration in surveying.
What is triangulation in surveying? — Triangulation definition
Triangulation, when related to geometry or surveying, is a method of determining the location of an unknown point by forming a triangle (or triangles) to it from known points. Instead of measuring distances directly, you measure angles (bearings) and use them together with a known baseline to fix the unknown position.
There are two general types of triangulation:
- Intersection — you triangulate an unknown landmark by making observations from two different known locations; and
- Resection — you determine your own position by observing two known landmarks from a single location.
Triangulation formula to find the location of a landmark (intersection)
Let A(x₁, y₁) and B(x₂, y₂) be the two observation points, with bearings toward the landmark of α and β, respectively. If C(x₃, y₃) is the location of the landmark, the points A, B, and C form the vertices of a triangle.
A bearing is measured clockwise from North, so a line of sight at bearing θ points in the direction (sin θ, cos θ). Writing the two lines of sight and solving for their intersection gives:
x₃ = x₁ + t·sinα
y₃ = y₁ + t·cosα
where:
- α is the bearing from A to the landmark;
- β is the bearing from B to the landmark; and
- t is the distance from A to the landmark along the line of sight.
💡 If sin(β − α) = 0, the two lines of sight are parallel and never meet — there is no unique fix. Choose stations whose bearings differ by a healthy angle (ideally close to 90°) for the most accurate result.
Triangulation formula to determine your position (resection)
Resection flips the problem around. Now A and B are the two known landmarks, and you stand at the unknown point P, measuring the bearing from your position to each landmark. Because a line of sight is the same line whether you look forward or backward along it, the unknown point still lies on both bearing lines — so the very same intersection formula returns your coordinates. This calculator handles the bookkeeping for you: just pick the Resection mode and enter the landmark coordinates and the bearings you measured toward them.
How to use the triangulation calculator?
- Choose the method: Intersection (find a landmark) or Resection (find your own position).
- Select your measurement system — metric (meters) or US/Imperial (feet). Coordinates and distances are reported in that unit.
- Enter the coordinates of the two known points and the bearing associated with each (clockwise from North, 0°–360°).
- Read off the coordinates of the unknown point, the distances to it, the baseline, and the interior angles of the triangle.
The calculator also reports a 16-point compass direction for every bearing and the bearing of the baseline between your two known points, so you can sanity-check your fieldwork at a glance.
Triangulation vs. trilateration
Triangulation and trilateration both fix an unknown point using a triangle, but they measure different things:
- Triangulation uses angles (bearings) from known points, together with a known baseline, to locate the unknown point. It was the backbone of classical land surveying, when measuring angles with a theodolite was far easier than measuring long distances.
- Trilateration uses distances from known points instead of angles. Modern GPS is a form of trilateration: your receiver measures its distance to several satellites and solves for its position. If you need the distance-based approach, try our distance and coordinate calculators instead.
FAQs
What is triangulation used for?
Triangulation is used in land surveying, navigation, astronomy, cartography, and search-and-rescue to locate a point that can't be reached directly — using only angle measurements from two or more known positions.
How do I triangulate my position from two landmarks?
Measure the bearing from your position to each of two landmarks with known coordinates, switch this calculator to Resection mode, and enter the landmark coordinates and the two bearings. The tool returns your coordinates where the two back-bearing lines cross.
Why should the two bearings be well separated?
When the two lines of sight cross at a shallow angle, a small error in either bearing shifts the intersection a long way. Bearings that differ by roughly 90° give the strongest, most reliable fix; bearings that are nearly parallel give a weak one (and, if exactly parallel, no fix at all).
Is triangulation the same as GPS?
No. GPS uses trilateration (measuring distances to satellites), while triangulation uses angles to known points. They are complementary methods for the same goal: pinpointing a location.