CalcLibrary

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.

Examples

Translate 45 deg into radians before entering the angle into a trig function or technical calculator.

Converted angle
0.7853981634 rad
Same angle in degrees
45 deg
Same angle in radians
0.7853981634 rad
Radians conversion trail
45 deg -> 0.7853981634 rad -> 0.7853981634 rad

The result is smaller because the target angle unit is larger. One target unit contains about 57.30 source units.

Angle units only — this page does not evaluate trig functions, solve geometry, or interpret compass bearings.

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Examples

How It Works

Formula

rrad=v×ffromr_{\text{rad}} = v \times f_{\text{from}}

t=rradftot = \dfrac{r_{\text{rad}}}{f_{\text{to}}}

Variables

vv

Input angle value

rradr_{\text{rad}}

The same angle expressed in radians(rad)

tt

Converted target-unit angle

ffromf_{\text{from}}

Radians per source unit(rad)

ftof_{\text{to}}

Radians per target unit(rad)

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

01How 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.
02Why 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.
03Where 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.
04Does 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.
05Are 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.

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