Angle converter
Unit conversionHow many radians is that angle?
Convert between degrees, radians, gradians, arcminutes, arcseconds, turns and mils.
What you enter stays on your device while you use this tool. Opening a shared link sends the settings in its address to HowToolbox to prepare the page.
Result
57.3°
1 radian is about 57.3 degrees
- The other way round: 1° ≈ 0.01745 rad.
In all units
- Degrees
- 57.3°
- Radians
- 1 rad
- Milliradians
- 1,000 mrad
- Gradians (gon)
- 63.66 gon
- Arcminutes
- 3,438′
- Arcseconds
- 206,300″
- Turns
- 0.1592 tr
- Mils (NATO)
- 1,019 mil
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Convert between degrees, radians, gradians, arcminutes, arcseconds, turns and mils.
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
How many degrees is one radian?
About 57.2958 degrees: 180 divided by π.
What is a gradian?
A gradian (or gon) is 1/400 of a full turn, so a right angle is exactly 100 gradians. Surveyors in some countries use it.
Is a mil the same as a milliradian?
No. The NATO mil divides a turn into 6,400 parts, about 0.982 mrad; a milliradian is exactly 0.001 rad, so a turn has about 6,283 of them.
How do I convert degrees, minutes and seconds to decimal degrees?
Add minutes divided by 60 and seconds divided by 3600 to the degrees. For example, 30° 15′ 30″ is 30.258333…°.
Can I convert negative angles or more than one turn?
Yes. The converter preserves the sign and the number of turns; it does not wrap the answer into 0–360°.
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