Protractors are often used to measure angle

Convert Degrees to Radians

Convert from degrees to radians with this simple formula:
radians = degrees × 0.017453
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1 Degree = 0.017453 Radians

Learn How to Convert Degrees to Radians Using our Conversion Formula

Converting a degree angle measurement to a radian measurement involves multiplying your angle by the conversion ratio to find the result. A degree is equal to 0.017453 radians, so to convert simply multiply by 0.017453.

For example, 5° = (5 × 0.017453) = 0.087266rad.

Degrees and radians are both units used to measure angle. Learn more about angle and find more angle measurement conversion calculators. A degree is an angle measurement and can be abbreviated as °, for example 1°. A radian is an angle measurement and can be abbreviated as rad, for example 1rad.

There are 360 degrees in a revolution, or circle. 360 has 24 divisors, and is easily divided by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120 and 180. This makes it a fairly easy number to work with. There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day. Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor.

A radian is the measurement of the angle from the start to the end of an arc equal to the radius of the circle. 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle. The radian is the standard SI unit of measurement for an angle.

degrees and radians are units used to measure angle
Convert Radians to Degrees

More Angle Conversions

Convert to Grad Angle
1° is equal to 1.111111 grad
Convert to Revolutions Angle
1° is equal to 0.002778 revolutions
Convert to Circles Angle
1° is equal to 0.002778 circles
Convert to Mils Angle
1° is equal to 17.777778 mils

Degree Measurements and Equivalent Radian Conversions

Common degree values converted to the equivalent radian value
Degrees Radians Degrees Radians Degrees Radians
1 0.017453 21 0.366519 41 0.715585
2 0.034907 22 0.383972 42 0.733038
3 0.05236 23 0.401426 43 0.750492
4 0.069813 24 0.418879 44 0.767945
5 0.087266 25 0.436332 45 0.785398
6 0.10472 26 0.453786 46 0.802851
7 0.122173 27 0.471239 47 0.820305
8 0.139626 28 0.488692 48 0.837758
9 0.15708 29 0.506145 49 0.855211
10 0.174533 30 0.523599 50 0.872665
11 0.191986 31 0.541052 51 0.890118
12 0.20944 32 0.558505 52 0.907571
13 0.226893 33 0.575959 53 0.925025
14 0.244346 34 0.593412 54 0.942478
15 0.261799 35 0.610865 55 0.959931
16 0.279253 36 0.628319 56 0.977384
17 0.296706 37 0.645772 57 0.994838
18 0.314159 38 0.663225 58 1.0123
19 0.331613 39 0.680678 59 1.0297
20 0.349066 40 0.698132 60 1.0472