Angle Converter
Convert degrees, radians, gradians, turns, arcminutes, and arcseconds with an explicit radians path. Built for trig inputs, CAD rotations, optics specs, and surveying-style references.
How It Works
Formula
Variables, symbols and units
- Input angle value
- The same angle expressed in radians(rad)
- Converted target-unit angle
- Radians per source unit(rad)
- Radians per target unit(rad)
Calculation method explained
The calculator uses radians as the canonical base unit. It converts the source angle into radians first, divides by the target-unit factor, and then repeats the same angle in degrees and radians so you can sanity-check the value before using it elsewhere.
Exact relationships used by the calculator:
- 180 deg = pi rad
- 200 grad = pi rad
- 1 turn = 2 pi rad
- 60 arcmin = 1 deg
- 3600 arcsec = 1 deg
Supported units stay intentionally narrow: degree, radian, gradian, turn, arcminute, and arcsecond only. No mil variants, bearing formats, or trig-function logic are mixed in.
Frequently Asked Questions
How does this angle converter work?
Every supported unit is routed through radians. The calculator converts your source value into radians first, then divides by the target-unit factor. The result panel shows that same source -> radians -> target trail explicitly.
Why does the result area also show degrees and radians?
Degrees and radians are the quickest cross-check for most math and engineering work. Keeping them visible lets you verify the converted angle without changing the selectors again.
Where do gradians, turns, arcminutes, and arcseconds usually show up?
Gradians appear in some surveying and technical references, turns show up in rotation specs, and arcminutes or arcseconds appear in finer angular notes where a full degree would be too coarse.
Does this page evaluate trig functions, solve triangles, or interpret bearings?
No. This page converts exact angle units only. Use a scientific calculator for trig evaluation, a triangle calculator for geometry relationships, and an arc-length calculator when the angle is only one part of a larger geometry calculation.
Are these relationships exact or estimated?
They are exact unit definitions: 180 deg = pi rad, 200 grad = pi rad, 1 turn = 2 pi rad, 60 arcmin = 1 deg, and 3600 arcsec = 1 deg.