Download your Word document
Two-Circle Triangulation Calculator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Two-Circle Triangulation Calculator — result sheet
Find the two possible planar intersection points from a baseline and two distances, exposing mirror-image ambiguity and the tangent case.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Place A=(0,0) and B=(L,0). The intersection x-coordinate is (rₐ²−rᵦ²+L²)/(2L), and y=±√(rₐ²−x²).
Two measured distances locate the target at the intersection of two circles, but reflection across the baseline usually produces two equally valid points. The calculator reports both instead of silently choosing one side.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Distance between reference points — length units; minimum 1.0E-6; maximum 1000000000
- Distance from point A — length units; minimum 1.0E-6; maximum 1000000000
- Distance from point B — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Distance between reference points | 10 |
| Distance from point A | 6 |
| Distance from point B | 8 |
x = 3.6; y = ±4.8; the two possible points are (3.6, 4.8) and (3.6, −4.8).
Assumptions and limits
- The reference points lie on a straight baseline and the target is represented in a flat Euclidean plane.
- Distances are positive and use one consistent unit.
- The triangle inequality must hold; incompatible distances have no real intersection.
- When the circles are tangent, the two mirror solutions merge into one point on the baseline.
- The orientation of the real target is not known, so both positive and negative y solutions are returned.
- Measurement error, map projection, altitude, and sensor calibration are not modeled.
- This is a two-distance geometry result, not a complete GPS, radio, or navigation solution.
- For field work, use redundant observations and an appropriate adjustment or error model.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.