Degree to Radian Converter
Angle · unit-converter
Convert Degree to Radian 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
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.
How to convert degrees to radians
1 degree equals 0.017453292519943295 radian in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 1 rad) rad = 0.017453292519943295 rad
Each degree carries 0.017453292519943295 rad and each radian 1 rad, so one deg equals 0.017453292519943295 ÷ 1 rad.
Let θ(deg) be the angle in Degree (deg), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(deg) × (0.017453292519943295 / 1)
Equivalently, divide by how many deg fit into one rad (rad per rad divided by rad per deg):
θ(rad) = θ(deg) ÷ 57.29577951308232
Examples
Example #1: Convert 1 deg to radian
1 deg = 1 deg × (0.017453292519943295/1) rad = 0.0174532925 rad
1 deg = 1 deg ÷ 57.29577951308232 = 0.0174532925 rad
1 deg × (0.017453292519943295/1) = 0.017453 rad
Example #2: Convert 10 deg to radian
10 deg = 10 deg × (0.017453292519943295/1) rad = 0.1745329252 rad
10 deg = 10 deg ÷ 57.29577951308232 = 0.1745329252 rad
10 deg × (0.017453292519943295/1) = 0.174533 rad
Summary
To convert Degree to Radian, multiply the value in deg by (0.017453292519943295 rad per deg) / (1 rad per rad). Equivalently: value_rad = value_deg × (0.017453292519943295 / 1). Numerically, 1 deg equals 0.017453292519943295 rad.
Relationship context
Both Degree and Radian are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Radian (rad) |
|---|---|
| 0.1 | 0.0017453293 |
| 1 | 0.0174532925 |
| 2 | 0.034906585 |
| 3 | 0.0523598776 |
| 4 | 0.0698131701 |
| 5 | 0.0872664626 |
| 6 | 0.1047197551 |
| 7 | 0.1221730476 |
| 8 | 0.1396263402 |
| 9 | 0.1570796327 |
| Degree (deg) | Radian (rad) |
|---|---|
| 10 | 0.1745329252 |
| 20 | 0.3490658504 |
| 30 | 0.5235987756 |
| 40 | 0.6981317008 |
| 50 | 0.872664626 |
| 60 | 1.0471975512 |
| 70 | 1.2217304764 |
| 80 | 1.3962634016 |
| 90 | 1.5707963268 |
| 100 | 1.745329252 |