Work out coordinate transformation instantly with clear inputs, formula shown and shareable results.
A conformal or Helmert transformation applies a scale factor and a rotation, preserving shape and angles. Rotation mixes the easting and northing through sine and cosine terms, and the scale factor stretches both equally. A translation would be added afterwards; here the origin is common to both systems.
Two dimensional conformal transformation
E' = s(E cos θ + N sin θ); N' = s(-E sin θ + N cos θ)
E' = s(E cos θ + N sin θ); N' = s(-E sin θ + N cos θ). A conformal or Helmert transformation applies a scale factor and a rotation, preserving shape and angles.
Because it preserves angles and shape, so a transformed survey remains internally consistent. Affine transformations can fit control better but distort the geometry.
This calculator takes 4 inputs: Easting in the source system, Northing in the source system, Rotation, Scale factor. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.