Gradian to Microradian Converter
Angle · unit-converter
Convert Gradian 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 Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
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 gradians to microradians
1 gradian equals 15707.963267948968 microradian in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 0.000001 rad) urad = 15707.963267948968 urad
Each gradian carries 0.015707963267948967 rad and each microradian 0.000001 rad, so one grad equals 0.015707963267948967 ÷ 0.000001 urad.
Let θ(grad) be the angle in Gradian (grad), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(grad) × (0.015707963267948967 / 0.000001)
Equivalently, divide by how many grad fit into one urad (rad per urad divided by rad per grad):
θ(urad) = θ(grad) ÷ 0.00006366197723675813
Examples
Example #1: Convert 1 grad to microradian
1 grad = 1 grad × (0.015707963267948967/0.000001) urad = 15707.9632679 urad
1 grad = 1 grad ÷ 0.00006366197723675813 = 15707.9632679 urad
1 grad × (0.015707963267948967/0.000001) = 15,707.963268 urad
Example #2: Convert 10 grad to microradian
10 grad = 10 grad × (0.015707963267948967/0.000001) urad = 157079.632679 urad
10 grad = 10 grad ÷ 0.00006366197723675813 = 157079.632679 urad
10 grad × (0.015707963267948967/0.000001) = 157,079.632679 urad
Summary
To convert Gradian to Microradian, multiply the value in grad by (0.015707963267948967 rad per grad) / (0.000001 rad per urad). Equivalently: value_urad = value_grad × (0.015707963267948967 / 0.000001). Numerically, 1 grad equals 15707.963267948968 urad.
Relationship context
Both Gradian and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Microradian (urad) |
|---|---|
| 0.1 | 1,570.79632679 |
| 1 | 15,707.9632679 |
| 2 | 31,415.9265359 |
| 3 | 47,123.8898038 |
| 4 | 62,831.8530718 |
| 5 | 78,539.8163397 |
| 6 | 94,247.7796077 |
| 7 | 109,955.742876 |
| 8 | 125,663.706144 |
| 9 | 141,371.669412 |
| Gradian (grad) | Microradian (urad) |
|---|---|
| 10 | 157,079.632679 |
| 20 | 314,159.265359 |
| 30 | 471,238.898038 |
| 40 | 628,318.530718 |
| 50 | 785,398.1633970001 |
| 60 | 942,477.796077 |
| 70 | 1,099,557.42876 |
| 80 | 1,256,637.0614400001 |
| 90 | 1,413,716.6941199999 |
| 100 | 1,570,796.3267900001 |