Gradian to Degree Converter
Angle · unit-converter
Convert Gradian to Degree 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
How to convert gradians to degrees
1 gradian equals 0.9 degree in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 0.017453292519943295 rad) deg = 0.9 deg
Each gradian carries 0.015707963267948967 rad and each degree 0.017453292519943295 rad, so one grad equals 0.015707963267948967 ÷ 0.017453292519943295 deg.
Let θ(grad) be the angle in Gradian (grad), and θ(deg) in Degree (deg). Then:
θ(deg) = θ(grad) × (0.015707963267948967 / 0.017453292519943295)
Equivalently, divide by how many grad fit into one deg (rad per deg divided by rad per grad):
θ(deg) = θ(grad) ÷ 1.111111111111111
Examples
Example #1: Convert 1 grad to degree
1 grad = 1 grad × (0.015707963267948967/0.017453292519943295) deg = 0.9 deg
1 grad = 1 grad ÷ 1.111111111111111 = 0.9 deg
1 grad × (0.015707963267948967/0.017453292519943295) = 0.900000 deg
Example #2: Convert 10 grad to degree
10 grad = 10 grad × (0.015707963267948967/0.017453292519943295) deg = 9 deg
10 grad = 10 grad ÷ 1.111111111111111 = 9 deg
10 grad × (0.015707963267948967/0.017453292519943295) = 9.000000 deg
Summary
To convert Gradian to Degree, multiply the value in grad by (0.015707963267948967 rad per grad) / (0.017453292519943295 rad per deg). Equivalently: value_deg = value_grad × (0.015707963267948967 / 0.017453292519943295). Numerically, 1 grad equals 0.9 deg.
Relationship context
Both Gradian and Degree are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per deg) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Degree (deg) |
|---|---|
| 0.1 | 0.09 |
| 1 | 0.9 |
| 2 | 1.8 |
| 3 | 2.7 |
| 4 | 3.6 |
| 5 | 4.5 |
| 6 | 5.4 |
| 7 | 6.3 |
| 8 | 7.2 |
| 9 | 8.1 |
| Gradian (grad) | Degree (deg) |
|---|---|
| 10 | 9 |
| 20 | 18 |
| 30 | 27 |
| 40 | 36 |
| 50 | 45 |
| 60 | 54 |
| 70 | 63 |
| 80 | 72 |
| 90 | 81 |
| 100 | 90 |