What it converts
Converts one signed plane-angle value across six explicitly labelled angular conventions.
ANGULAR MEASURE WORKSPACE
Plane Angle Converter
Convert signed plane angles among radians, degrees, gradians, turns, arcminutes, and arcseconds through one radian reference.
Reviewed reference factorsValues stay in this browser tabThis changes angular units only; it does not solve geometry, bearings, solid angles, or wrapped orientation.
Conversion result
Your checked conversion appears here
Load the reviewed example or enter a value to compare every available plane angle unit.
What this tool delivers
Plane Angle conversion contract
This workspace rescales one known two-dimensional angle and does not infer an angle from sides, coordinates, vectors, or a surveying observation.
What you provide
The numeric angle, its exact source unit, the destination unit, a sign convention, and suitable decimal precision.
What you receive
A selected result, the radian conversion path, a complete equivalent table, and CSV output.
Calculation method
Why every angle passes through radians
The source angle is multiplied by its exact or displayed radians-per-unit factor, then divided by the destination factor. A full turn is 2 pi radians, 360 degrees, or 400 gradians; arcminute and arcsecond factors follow from degree subdivision.
Review the BIPM SI treatment of plane angleQuick answers
Plane Angle Converter questions
Are radians dimensionless or a separate physical dimension?
A radian is the coherent SI unit for plane angle and can be expressed as metre per metre, so its dimensional expression reduces to one. The unit name still matters because it distinguishes an angular quantity from an ordinary ratio. This converter preserves the radian label and never silently treats a bare number as degrees.
Why can this converter accept a negative angle?
A negative sign can represent rotation opposite to the positive orientation chosen by a drawing, coordinate system, or application. Conversion preserves that sign but cannot determine what positive means. Verify whether the source uses clockwise, counterclockwise, mathematical, navigation, or screen coordinates before combining the result with other angular data.
Does converting an angle wrap it between zero and 360 degrees?
No. Unit conversion and angle normalization are different operations. A value of 450 degrees converts directly to its equivalent radians, gradians, turns, arcminutes, or arcseconds without removing full revolutions. Normalize separately only when the receiving system requires a principal interval, and document which interval and endpoint convention it expects.