Degree to Microradian Converter
Angle · unit-converter
Convert Degree to Microradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
How to convert degrees to microradians
1 degree equals 17453.292519943298 microradian in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 0.000001 rad) urad = 17453.292519943298 urad
Each degree carries 0.017453292519943295 rad and each microradian 0.000001 rad, so one deg equals 0.017453292519943295 ÷ 0.000001 urad.
Let θ(deg) be the angle in Degree (deg), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(deg) × (0.017453292519943295 / 0.000001)
Equivalently, divide by how many deg fit into one urad (rad per urad divided by rad per deg):
θ(urad) = θ(deg) ÷ 0.00005729577951308232
Examples
Example #1: Convert 1 deg to microradian
1 deg = 1 deg × (0.017453292519943295/0.000001) urad = 17453.2925199 urad
1 deg = 1 deg ÷ 0.00005729577951308232 = 17453.2925199 urad
1 deg × (0.017453292519943295/0.000001) = 17,453.292520 urad
Example #2: Convert 10 deg to microradian
10 deg = 10 deg × (0.017453292519943295/0.000001) urad = 174532.925199 urad
10 deg = 10 deg ÷ 0.00005729577951308232 = 174532.925199 urad
10 deg × (0.017453292519943295/0.000001) = 174,532.925199 urad
Summary
To convert Degree to Microradian, multiply the value in deg by (0.017453292519943295 rad per deg) / (0.000001 rad per urad). Equivalently: value_urad = value_deg × (0.017453292519943295 / 0.000001). Numerically, 1 deg equals 17453.292519943298 urad.
Relationship context
Both Degree and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Microradian (urad) |
|---|---|
| 0.1 | 1,745.32925199 |
| 1 | 17,453.2925199 |
| 2 | 34,906.5850399 |
| 3 | 52,359.8775598 |
| 4 | 69,813.1700798 |
| 5 | 87,266.4625997 |
| 6 | 104,719.75512 |
| 7 | 122,173.04764 |
| 8 | 139,626.34016 |
| 9 | 157,079.632679 |
| Degree (deg) | Microradian (urad) |
|---|---|
| 10 | 174,532.925199 |
| 20 | 349,065.850399 |
| 30 | 523,598.775598 |
| 40 | 698,131.700798 |
| 50 | 872,664.625997 |
| 60 | 1,047,197.5512 |
| 70 | 1,221,730.4764 |
| 80 | 1,396,263.4016 |
| 90 | 1,570,796.3267900001 |
| 100 | 1,745,329.25199 |