Gradian to Quadrant Converter
Angle · unit-converter
Convert Gradian to Quadrant 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 Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert gradians to quadrants
1 gradian equals 0.01 quadrant in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 1.5707963267948966 rad) quadrant = 0.01 quadrant
Each gradian carries 0.015707963267948967 rad and each quadrant 1.5707963267948966 rad, so one grad equals 0.015707963267948967 ÷ 1.5707963267948966 quadrant.
Let θ(grad) be the angle in Gradian (grad), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(grad) × (0.015707963267948967 / 1.5707963267948966)
Equivalently, divide by how many grad fit into one quadrant (rad per quadrant divided by rad per grad):
θ(quadrant) = θ(grad) ÷ 99.99999999999999
Examples
Example #1: Convert 1 grad to quadrant
1 grad = 1 grad × (0.015707963267948967/1.5707963267948966) quadrant = 0.01 quadrant
1 grad = 1 grad ÷ 99.99999999999999 = 0.01 quadrant
1 grad × (0.015707963267948967/1.5707963267948966) = 0.010000 quadrant
Example #2: Convert 10 grad to quadrant
10 grad = 10 grad × (0.015707963267948967/1.5707963267948966) quadrant = 0.1 quadrant
10 grad = 10 grad ÷ 99.99999999999999 = 0.1 quadrant
10 grad × (0.015707963267948967/1.5707963267948966) = 0.100000 quadrant
Summary
To convert Gradian to Quadrant, multiply the value in grad by (0.015707963267948967 rad per grad) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_grad × (0.015707963267948967 / 1.5707963267948966). Numerically, 1 grad equals 0.01 quadrant.
Relationship context
Both Gradian and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.001 |
| 1 | 0.01 |
| 2 | 0.02 |
| 3 | 0.03 |
| 4 | 0.04 |
| 5 | 0.05 |
| 6 | 0.06 |
| 7 | 0.07 |
| 8 | 0.08 |
| 9 | 0.09 |
| Gradian (grad) | Quadrant (quadrant) |
|---|---|
| 10 | 0.1 |
| 20 | 0.2 |
| 30 | 0.3 |
| 40 | 0.4 |
| 50 | 0.5 |
| 60 | 0.6 |
| 70 | 0.7 |
| 80 | 0.8 |
| 90 | 0.9 |
| 100 | 1 |