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Resection Calculation
Determine an unknown survey station from observations to known control points using the three-point resection method, with coordinate and residual checks.
Three-Point Resection
Enter three known control-point coordinates and the observed horizontal angles at the unknown station. The calculator solves the station coordinates using a nonlinear least-squares refinement and reports the angular residuals.
Control Point A
Control Point B
Control Point C
Observed Angles at Unknown Station P
Enter the smaller horizontal angle between each consecutive pair of observed directions. Values should normally be between 0° and 180°.
Solution Settings
Enter three control points and two observed angles to calculate the unknown station.
Distance Resection Check
Use measured distances from the unknown station to three known control points to compute the station by trilateration. This provides an independent coordinate solution and closure check.
Control Points
Enter three known points and their measured distances from P.
Resection Formula Reference
Definitions and checks used by this calculator.
ResectionFind the coordinates of an occupied station from observations to known control points.
Angular observationFor points i and j, θᵢⱼ = |atan2(Nⱼ−N, Eⱼ−E) − atan2(Nᵢ−N, Eᵢ−E)|, reduced to the smaller angle.
ResidualAngular residual = observed angle − computed angle, after reducing to the principal angular difference.
TrilaterationSubtract squared-distance equations to obtain a linear system, then solve for the unknown coordinates.
Important: Three-point angular resection can have ambiguous configurations. The calculator uses the supplied approximate coordinate as an optional starting value; when omitted, it uses the control-point centroid as the starting point and reports the achieved residuals so the surveyor can assess the solution.