Math · Geometry
Degrees to radians converter.
Degrees, radians and degrees-minutes-seconds in one place, with exact fractions of pi.
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How do you convert degrees to radians?
A full turn is 360° or 2π radians, so 1° = π/180 rad. To convert degrees to radians multiply by π/180 (about 0.0174533); to convert radians to degrees multiply by 180/π (about 57.2958). A minute of arc is 1/60 of a degree and a second of arc is 1/60 of a minute, so degrees-minutes-seconds (DMS) is decimal degrees = D + M/60 + S/3600.
Worked examples. 90° is π/2, which is 1.570796 rad. 1 rad is 57.29578°, or 57° 17′ 44.81″. 40° 26′ 46″ is 40.446111° in decimal degrees, as used in latitude and longitude.
Frequently asked questions
How do I convert degrees to radians?
Multiply the degrees by π/180. For example 180° × π/180 = π rad, and 45° = π/4 rad.
How do I convert radians to degrees?
Multiply by 180/π. One radian is 57.29578°, and π/6 rad is 30°.
How do I convert DMS to decimal degrees?
Add the degrees, the minutes divided by 60 and the seconds divided by 3,600. 40° 26′ 46″ is 40.446111°. For a south or west coordinate tick the negative box.
Why use radians?
Radians make angle formulas simple: arc length is rθ and sector area is ½r²θ only when θ is in radians, and calculus formulas for sine and cosine assume radians.
Sources
Checked
- NIST SP 811, Chapter 5 (Units Outside the SI), Table 6
- Wolfram MathWorld: Radian
- Wolfram MathWorld: Degree
The relations 1 deg = (pi/180) rad, 1 minute = 1/60 degree and 1 second = 1/60 minute are from NIST SP 811 Chapter 5 Table 6. The fraction-of-pi display is exact arithmetic on the degree value you enter, shown only when the denominator is 1,000 or less. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Results are exact mathematics rounded for display, so they are only as good as the measurements you enter. Any length unit works as long as every value uses the same one; areas come out in that unit squared and volumes in that unit cubed. For homework, DIY layout and estimating, not a substitute for a surveyor, engineer or your teacher's required method.