Triangulation Calculator

What Is Triangulation?

Triangulation is a surveying method that determines an unknown point by forming a triangle from two known reference points and measuring bearings (angles). It is used in navigation, land surveying, and GPS-free positioning.

See also: Triangle Vertices Calculator and Distance Calculator.

Intersection vs Resection

Intersection finds an unknown landmark by observing it from two known positions with measured bearings.

Resection finds your own position by observing two known landmarks and measuring bearings toward them.

Triangulation Formula

Given points $A(x_1, y_1)$ and $B(x_2, y_2)$ with bearings $\alpha$ and $\beta$:

$$x_3 = \frac{(y_1 - y_2) + x_2 \tan\theta_2 - x_1 \tan\theta_1}{\tan\theta_2 - \tan\theta_1}$$

where $\theta = 90° - \text{bearing}$ converts azimuth to slope angle.

Worked Example

From $A(0, 0)$ with bearing 30° and $B(5, 0)$ with bearing 330°, the landmark is at approximately $(2.5, 4.33)$.