Radian to Degree Converter
Angle · unit-converter
Convert Radian to Degree with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
About Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
How to convert radians to degrees
1 radian equals 57.29577951308232 degree in this tool (via radian):
1 rad = (1 rad ÷ 0.017453292519943295 rad) deg = 57.29577951308232 deg
Each radian carries 1 rad and each degree 0.017453292519943295 rad, so one rad equals 1 ÷ 0.017453292519943295 deg.
Let θ(rad) be the angle in Radian (rad), and θ(deg) in Degree (deg). Then:
θ(deg) = θ(rad) × (1 / 0.017453292519943295)
Equivalently, divide by how many rad fit into one deg (rad per deg divided by rad per rad):
θ(deg) = θ(rad) ÷ 0.017453292519943295
Examples
Example #1: Convert 1 rad to degree
1 rad = 1 rad × (1/0.017453292519943295) deg = 57.2957795131 deg
1 rad = 1 rad ÷ 0.017453292519943295 = 57.2957795131 deg
1 rad × (1/0.017453292519943295) = 57.295780 deg
Example #2: Convert 10 rad to degree
10 rad = 10 rad × (1/0.017453292519943295) deg = 572.957795131 deg
10 rad = 10 rad ÷ 0.017453292519943295 = 572.957795131 deg
10 rad × (1/0.017453292519943295) = 572.957795 deg
Summary
To convert Radian to Degree, multiply the value in rad by (1 rad per rad) / (0.017453292519943295 rad per deg). Equivalently: value_deg = value_rad × (1 / 0.017453292519943295). Numerically, 1 rad equals 57.29577951308232 deg.
Relationship context
Both Radian and Degree are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per deg) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Degree (deg) |
|---|---|
| 0.1 | 5.7295779513 |
| 1 | 57.2957795131 |
| 2 | 114.591559026 |
| 3 | 171.887338539 |
| 4 | 229.183118052 |
| 5 | 286.478897565 |
| 6 | 343.774677078 |
| 7 | 401.070456592 |
| 8 | 458.366236105 |
| 9 | 515.662015618 |
| Radian (rad) | Degree (deg) |
|---|---|
| 10 | 572.957795131 |
| 20 | 1,145.91559026 |
| 30 | 1,718.87338539 |
| 40 | 2,291.83118052 |
| 50 | 2,864.78897565 |
| 60 | 3,437.74677078 |
| 70 | 4,010.70456592 |
| 80 | 4,583.66236105 |
| 90 | 5,156.62015618 |
| 100 | 5,729.57795131 |