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Coordinate Transformation Calculator

Work out coordinate transformation instantly with clear inputs, formula shown and shareable results.

About Coordinate Transformation Calculator

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.

Formula

Two dimensional conformal transformation

E' = s(E cos θ + N sin θ); N' = s(-E sin θ + N cos θ)

Worked example

With the default values below, Coordinate Transformation Calculator returns Transformed easting of 1,866.3986. Change any input above and every figure here is recalculated in your browser.

Inputs used

Easting in the source system
1,000 m
Northing in the source system
2,000 m
Rotationaccepts -360–360 °
30 °
Scale factoraccepts 0.5–2
1.0002

Results

Transformed easting
1,866.3986 m
Transformed northing
1,232.2972 m
Rotation in radians
0.523599 rad
Change in radial distance
0.4472 m

Step by step

  1. 1Values used
  2. 2Two dimensional conformal transformation
  3. 3Transformed easting= 1,866.3986 m
  4. 4Transformed northing= 1,232.2972 m
  5. 5Rotation in radians= 0.523599 rad
  6. 6Change in radial distance= 0.4472 m

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Coordinate Transformation figure worked out?

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.

Why is a conformal transformation preferred?

Because it preserves angles and shape, so a transformed survey remains internally consistent. Affine transformations can fit control better but distort the geometry.

What values do I need to enter?

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.

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