Microradian to Gradian Converter
Angle · unit-converter
Convert Microradian to Gradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
About Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
How to convert microradians to gradians
1 microradian equals 0.00006366197723675813 gradian in this tool (via radian):
1 urad = (0.000001 rad ÷ 0.015707963267948967 rad) grad = 0.00006366197723675813 grad
Each microradian carries 0.000001 rad and each gradian 0.015707963267948967 rad, so one urad equals 0.000001 ÷ 0.015707963267948967 grad.
Let θ(urad) be the angle in Microradian (urad), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(urad) × (0.000001 / 0.015707963267948967)
Equivalently, divide by how many urad fit into one grad (rad per grad divided by rad per urad):
θ(grad) = θ(urad) ÷ 15707.963267948968
Examples
Example #1: Convert 1 urad to gradian
1 urad = 1 urad × (0.000001/0.015707963267948967) grad = 0.000063662 grad
1 urad = 1 urad ÷ 15707.963267948968 = 0.000063662 grad
1 urad × (0.000001/0.015707963267948967) = 0.000064 grad
Example #2: Convert 10 urad to gradian
10 urad = 10 urad × (0.000001/0.015707963267948967) grad = 0.0006366198 grad
10 urad = 10 urad ÷ 15707.963267948968 = 0.0006366198 grad
10 urad × (0.000001/0.015707963267948967) = 0.000637 grad
Summary
To convert Microradian to Gradian, multiply the value in urad by (0.000001 rad per urad) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_urad × (0.000001 / 0.015707963267948967). Numerically, 1 urad equals 0.00006366197723675813 grad.
Relationship context
Both Microradian and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per urad) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Microradian (urad) | Gradian (grad) |
|---|---|
| 0.1 | 0.0000063662 |
| 1 | 0.000063662 |
| 2 | 0.000127324 |
| 3 | 0.0001909859 |
| 4 | 0.0002546479 |
| 5 | 0.0003183099 |
| 6 | 0.0003819719 |
| 7 | 0.0004456338 |
| 8 | 0.0005092958 |
| 9 | 0.0005729578 |
| Microradian (urad) | Gradian (grad) |
|---|---|
| 10 | 0.0006366198 |
| 20 | 0.0012732395 |
| 30 | 0.0019098593 |
| 40 | 0.0025464791 |
| 50 | 0.0031830989 |
| 60 | 0.0038197186 |
| 70 | 0.0044563384 |
| 80 | 0.0050929582 |
| 90 | 0.005729578 |
| 100 | 0.0063661977 |