Triangulation Calculator

Triangulation is a method of determining the location of an unknown point by forming a triangle between that point and two other known points. By measuring the angles from each known point toward the unknown one, you can calculate its exact coordinates using trigonometry. It is one of the oldest and most reliable techniques in land surveying and navigation.

The basic principle is that if you know the position of two points and can measure the bearing (angle) from each to a third unknown point, the lines of sight from both known points will intersect at the unknown location. This intersection gives you the exact coordinates of the target. The more accurate your angle measurements, the more precise the result.

Intersection (also called forward triangulation) is used to find the position of an unknown landmark — you stand at two known points and observe the unknown target. Resection (also called reverse triangulation) is the opposite — you are at an unknown location and observe two landmarks with known coordinates to determine your own position. This calculator supports both approaches by using the same mathematical framework.

Triangulation uses angle measurements from known points to find an unknown location, while trilateration uses distance measurements. GPS technology primarily uses trilateration, measuring distances from multiple satellites. Triangulation is more commonly used in traditional surveying where measuring angles with a theodolite is more practical than measuring distances directly.

You need the X and Z (or X and Y) coordinates of two known points, plus the bearing angle observed from each of those points toward the unknown location. The angles can be entered in degrees or radians. Make sure both bearing angles actually converge — parallel or near-parallel lines of sight will produce inaccurate or undefined results.

If the two lines of sight are parallel or nearly parallel, they do not intersect at a well-defined point. This causes the calculation to fail or produce extremely large, unreliable coordinates. To get accurate results, ensure that the angle between the two lines of sight (the intersection angle) is ideally between 30° and 150°. Angles close to 0° or 180° lead to poor accuracy.

Triangulation is used in land surveying, mapping, navigation, military positioning, wildlife tracking, and even mobile phone network localization. Historically, it was used to create highly accurate national maps before GPS existed. Today it still plays a role in scenarios where GPS is unavailable or insufficient, such as underground surveying or forensic site mapping.

A bearing angle is measured clockwise from north (or from a reference axis) and indicates the direction from a known point toward the target. In this calculator, angles are treated as azimuths — measured from the positive Z-axis (or north) clockwise. Entering the correct bearing is critical: even a small angular error at a long distance can shift the calculated position significantly.