Degrees to radians
Unit conversionHow do you convert degrees to radians?
180° is π radians. Multiply degrees by π/180 to get radians.
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Result
3.142 rad
180 degrees is about 3.142 radians
- The other way round: 1 rad ≈ 57.3°.
In all units
- Degrees
- 180°
- Radians
- 3.142 rad
- Milliradians
- 3,142 mrad
- Gradians (gon)
- 200 gon
- Arcminutes
- 10,800′
- Arcseconds
- 648,000″
- Turns
- 0.5 tr
- Mils (NATO)
- 3,200 mil
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180° is π radians. Multiply degrees by π/180 to get radians.
How to use
- Type the angle you want to convert.
- Choose the units to convert from and to. Use the swap button to flip them.
How it works
Every unit is converted through radians, the SI unit of plane angle. A full turn is 2π radians, which is 360 degrees, 400 gradians (also called gons) or 6,400 NATO mils. A degree has 60 arcminutes and an arcminute has 60 arcseconds.
So degrees become radians by multiplying by π/180: 90° × π/180 = π/2 ≈ 1.5708 rad. Going back, 1 rad = 180/π ≈ 57.2958°. A milliradian is a thousandth of a radian, close to but not the same as a NATO mil (2π/6400 rad ≈ 0.982 mrad).
The definitions come from the BIPM SI Brochure and NIST Special Publication 811. Negative angles convert the same way; the converter does not wrap angles into one turn.
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Frequently asked questions
What is the formula for degrees to radians?
Radians = degrees × π/180. For example, 45° × π/180 = π/4 ≈ 0.7854 rad.
How many radians are in 360 degrees?
2π radians, about 6.2832.
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