Three Anchor Range Position Calculator
Solve a two-dimensional position from three anchor ranges and check whether all entered distances agree with the candidate.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Subtract squared range equations to obtain two linear equations for the candidate coordinates. Recalculate each distance and compare the largest residual with your tolerance.
2(Ai−A0)·P=|Ai|²−|A0|²+r0²−ri²; verify |P−Ai|−ri
Worked example
Anchors (0,0), (6,0), (0,8) with ranges 5,5,5 give P=(3,4), with zero distance residuals.
Assumptions and input details
Coordinates and ranges use the same unit. Exactly three anchors with coordinate magnitudes and ranges up to 1e6; ranges nonnegative. Near-collinear anchor directions with sine below 1e−10 are rejected. Inconsistent ranges yield an algebraic radical-center candidate labelled inconsistent, not a valid position or least-squares fit. The user’s tolerance is an absolute range tolerance, not a statistical confidence region.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Enter two Cartesian points to find their distance, midpoint, coordinate changes and direction. Choose a shared input unit and compare output lengths.
Solve two linear equations in x and y. See determinants, substitution checks and the two lines, including parallel or coincident cases.
Calculate tetrahedron volume, triangular face areas and uniform-solid centroid from four 3D vertices.
Reserved advertising space.