Quick guide
How to use this calculator
- Choose the calculation mode when the page supports more than one direction.
- Enter the known measurements using the labels and angle units shown.
- Read the primary result first, then use the supporting rows to verify the convention or relationship.
Calculation method
Apply the selected angle relationship
NθE→θ; SθE→180°−θ; SθW→180°+θ; NθW→360°−θ.
The calculator validates geometric domains and reports degenerate vectors, impossible measurements, or unsupported ranges explicitly.
Worked example
Worked example
S 56° W corresponds to azimuth 236°.
NθE→θ; SθE→180°−θ; SθW→180°+θ; NθW→360°−θ.
Supported inputs
Precision and limits
Angle conventions
Positive Cartesian rotations are counterclockwise. North-referenced azimuths run clockwise. Unoriented line and plane calculators return the smaller acute or right angle; directed vector and dihedral tools can return up to 180°.
Numerical range
Inputs may be zero or have absolute magnitude from 1e-100 through 1e100. General angle magnitudes are limited to 1,000,000,000 degrees so periodic reduction remains meaningful in double-precision arithmetic.
Precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Results are numerical unless the page explicitly displays a fixed geometric identity.
Calculator-specific rule
Azimuth is measured clockwise from north. This pure angular conversion does not apply magnetic declination.