Revolution to Microradian Converter
Angle · unit-converter
Convert Revolution 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
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 revolutions to microradians
1 revolution equals 6283185.307179587 microradian in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 0.000001 rad) urad = 6283185.307179587 urad
Each revolution carries 6.283185307179586 rad and each microradian 0.000001 rad, so one turn equals 6.283185307179586 ÷ 0.000001 urad.
Let θ(turn) be the angle in Revolution (turn), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(turn) × (6.283185307179586 / 0.000001)
Equivalently, divide by how many turn fit into one urad (rad per urad divided by rad per turn):
θ(urad) = θ(turn) ÷ 1.5915494309189532e-7
Examples
Example #1: Convert 1 turn to microradian
1 turn = 1 turn × (6.283185307179586/0.000001) urad = 6283185.3071799995 urad
1 turn = 1 turn ÷ 1.5915494309189532e-7 = 6283185.3071799995 urad
1 turn × (6.283185307179586/0.000001) = 6,283,185.307180 urad
Example #2: Convert 10 turn to microradian
10 turn = 10 turn × (6.283185307179586/0.000001) urad = 62831853.071800001 urad
10 turn = 10 turn ÷ 1.5915494309189532e-7 = 62831853.071800001 urad
10 turn × (6.283185307179586/0.000001) = 62,831,853.071796 urad
Summary
To convert Revolution to Microradian, multiply the value in turn by (6.283185307179586 rad per turn) / (0.000001 rad per urad). Equivalently: value_urad = value_turn × (6.283185307179586 / 0.000001). Numerically, 1 turn equals 6283185.307179587 urad.
Relationship context
Both Revolution and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Microradian (urad) |
|---|---|
| 0.1 | 628,318.530718 |
| 1 | 6,283,185.3071799995 |
| 2 | 12,566,370.6143999994 |
| 3 | 18,849,555.9215000011 |
| 4 | 25,132,741.2287000008 |
| 5 | 31,415,926.5359000005 |
| 6 | 37,699,111.8430999964 |
| 7 | 43,982,297.1503000036 |
| 8 | 50,265,482.4574000016 |
| 9 | 56,548,667.7646000013 |
| Revolution (turn) | Microradian (urad) |
|---|---|
| 10 | 62,831,853.071800001 |
| 20 | 125,663,706.1439999938 |
| 30 | 188,495,559.2150000036 |
| 40 | 251,327,412.2870000005 |
| 50 | 314,159,265.3590000272 |
| 60 | 376,991,118.4309999943 |
| 70 | 439,822,971.503000021 |
| 80 | 502,654,824.574000001 |
| 90 | 565,486,677.6460000277 |
| 100 | 628,318,530.7180000544 |