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Coordinate Transformation
Transform survey coordinates between two 2D coordinate systems using a Helmert similarity transformation, with forward and inverse calculations, control-point fitting and residual checks.
2D Helmert Transformation
Use translation, rotation and scale to transform Easting/Northing coordinates. Rotation is positive counter-clockwise in the mathematical EN coordinate plane.
Transformation Parameters
Coordinate to Transform
Enter transformation parameters and a coordinate.
Fit Transformation from Control Points
Enter matching coordinates in the source and target systems. Three or more control pairs are recommended; the calculator estimates translation, rotation and scale by least squares.
Control Point Pairs
PointSource ESource NTarget ETarget N
A
B
C
D
E
F
A–C are required. D–F are optional; leave an optional row completely blank.
Fitted Transformation
Enter matching control coordinates.
Transformation Formula Reference
Equations used by the calculator.
Forward equationE₂ = ΔE + s(E₁ cosθ − N₁ sinθ)
NorthingN₂ = ΔN + s(E₁ sinθ + N₁ cosθ)
InverseRemove translation, divide by scale, then rotate by −θ.
Fitted parametersControl pairs are solved using the 2D similarity/Helmert least-squares model.
Survey note: Coordinate transformations depend on the definition of the source and target systems, axis directions, units and rotation convention. Confirm the convention of your project before applying fitted parameters to production coordinates.