📍 Triangulation Calculator
Find position from distances to three known points
Known Points
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Point 3 (x₃, y₃)
Distances from Unknown Point
How to Use This Calculator
Enter Three Known Points
Input coordinates (x₁, y₁), (x₂, y₂), and (x₃, y₃) of three known reference points.
Enter Distances
Input distances d₁, d₂, and d₃ from the unknown point to each reference point.
Calculate
Press "Calculate Position" to find the unknown point's coordinates using triangulation.
Formula
Circle equations:
(x - x₁)² + (y - y₁)² = d₁²
(x - x₂)² + (y - y₂)² = d₂²
(x - x₃)² + (y - y₃)² = d₃²
Solving system gives the intersection point
Method: Triangulation (trilateration) solves the system of three circle equations to find the intersection point where all three circles meet.
Requirements: Three non-collinear points and three distances. The three circles must intersect at a single point for a unique solution.
About Triangulation Calculator
The Triangulation Calculator (trilateration) finds the position of an unknown point from its distances to three known reference points. It solves the system of three circle equations.
When to Use This Calculator
- GPS: Calculate position from distances to satellites
- Navigation: Determine location from beacon distances
- Surveying: Find positions from reference points
- Engineering: Locate objects from measured distances
- Robotics: Localize robots using landmarks
Frequently Asked Questions
What is triangulation?
Triangulation (trilateration) is a method to determine position from distances to three known points. It solves the intersection of three circles.
Why do I need three points?
Three points are needed to uniquely determine a 2D position. Two circles typically intersect at two points; the third circle eliminates ambiguity.
What if there's no solution?
If the three circles don't intersect at a single point (due to measurement errors or invalid configuration), there's no solution. Points must be non-collinear for a valid solution.