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
Reduce modulo 360°, then measure the angle to the nearest horizontal axis.
The calculator validates geometric domains and reports degenerate vectors, impossible measurements, or unsupported ranges explicitly.
Worked example
Worked example
The reference angle for 210° is 30°.
Reduce modulo 360°, then measure the angle to the nearest horizontal axis.
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.