Degree to Gradian Converter
Angle · unit-converter
Convert Degree 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 Degree
Degrees divide a circle into 360 parts. Common in everyday angles, maps, and many engineering drawings.
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 degrees to gradians
1 degree equals 1.111111111111111 gradian in this tool (via radian):
1 deg = (0.017453292519943295 rad ÷ 0.015707963267948967 rad) grad = 1.111111111111111 grad
Each degree carries 0.017453292519943295 rad and each gradian 0.015707963267948967 rad, so one deg equals 0.017453292519943295 ÷ 0.015707963267948967 grad.
Let θ(deg) be the angle in Degree (deg), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(deg) × (0.017453292519943295 / 0.015707963267948967)
Equivalently, divide by how many deg fit into one grad (rad per grad divided by rad per deg):
θ(grad) = θ(deg) ÷ 0.9
Examples
Example #1: Convert 1 deg to gradian
1 deg = 1 deg × (0.017453292519943295/0.015707963267948967) grad = 1.1111111111 grad
1 deg = 1 deg ÷ 0.9 = 1.1111111111 grad
1 deg × (0.017453292519943295/0.015707963267948967) = 1.111111 grad
Example #2: Convert 10 deg to gradian
10 deg = 10 deg × (0.017453292519943295/0.015707963267948967) grad = 11.1111111111 grad
10 deg = 10 deg ÷ 0.9 = 11.1111111111 grad
10 deg × (0.017453292519943295/0.015707963267948967) = 11.111111 grad
Summary
To convert Degree to Gradian, multiply the value in deg by (0.017453292519943295 rad per deg) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_deg × (0.017453292519943295 / 0.015707963267948967). Numerically, 1 deg equals 1.111111111111111 grad.
Relationship context
Both Degree and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per deg) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Degree (deg) | Gradian (grad) |
|---|---|
| 0.1 | 0.1111111111 |
| 1 | 1.1111111111 |
| 2 | 2.2222222222 |
| 3 | 3.3333333333 |
| 4 | 4.4444444444 |
| 5 | 5.5555555556 |
| 6 | 6.6666666667 |
| 7 | 7.7777777778 |
| 8 | 8.8888888889 |
| 9 | 10 |
| Degree (deg) | Gradian (grad) |
|---|---|
| 10 | 11.1111111111 |
| 20 | 22.2222222222 |
| 30 | 33.3333333333 |
| 40 | 44.4444444444 |
| 50 | 55.5555555556 |
| 60 | 66.6666666667 |
| 70 | 77.7777777778 |
| 80 | 88.8888888889 |
| 90 | 100 |
| 100 | 111.111111111 |