Triangulation Calculator

Find a target position from two known observation points and measured angles using trigonometric triangulation.

Enter Known Values

Point A (Observer 1)
Point B (Observer 2)

Target Position

Target Coordinates
--
units
Distance from A to Target --
Distance from B to Target --
Baseline Distance (A to B) --
Angle at Target (C) --

Step-by-Step Solution

Using Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

What is Triangulation?

Triangulation is a technique for determining the location of an unknown point by measuring angles from two known reference points. It forms the basis of surveying, navigation, and many positioning systems.

How It Works

Baseline

The known distance between two observation points A and B.

d = sqrt((Bx-Ax)^2 + (By-Ay)^2)

Law of Sines

Relates sides and angles of the triangle formed by A, B, and the target.

a/sin(A) = b/sin(B) = c/sin(C)

Target Position

Computed from the baseline direction, angle, and distance.

T = A + dA * (cos(theta), sin(theta))

Applications

Triangulation is used in land surveying, GPS systems, cell tower positioning, astronomy (stellar parallax), and search-and-rescue operations. The method has been used for centuries to create accurate maps.

Limitations

  • The two angles plus the angle at the target must sum to 180 degrees.
  • If both angles are too small or too large, the result becomes inaccurate.
  • The method assumes a flat plane; for large distances, curvature must be considered.
  • Measurement errors in angles are amplified when the target is far away.