Quadrant to Gradian Converter
Angle · unit-converter
Convert Quadrant 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 Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
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 quadrants to gradians
1 quadrant equals 99.99999999999999 gradian in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 0.015707963267948967 rad) grad = 99.99999999999999 grad
Each quadrant carries 1.5707963267948966 rad and each gradian 0.015707963267948967 rad, so one quadrant equals 1.5707963267948966 ÷ 0.015707963267948967 grad.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(quadrant) × (1.5707963267948966 / 0.015707963267948967)
Equivalently, divide by how many quadrant fit into one grad (rad per grad divided by rad per quadrant):
θ(grad) = θ(quadrant) ÷ 0.01
Examples
Example #1: Convert 1 quadrant to gradian
1 quadrant = 1 quadrant × (1.5707963267948966/0.015707963267948967) grad = 100 grad
1 quadrant = 1 quadrant ÷ 0.01 = 100 grad
1 quadrant × (1.5707963267948966/0.015707963267948967) = 100.000000 grad
Example #2: Convert 10 quadrant to gradian
10 quadrant = 10 quadrant × (1.5707963267948966/0.015707963267948967) grad = 1000 grad
10 quadrant = 10 quadrant ÷ 0.01 = 1000 grad
10 quadrant × (1.5707963267948966/0.015707963267948967) = 1,000.000000 grad
Summary
To convert Quadrant to Gradian, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_quadrant × (1.5707963267948966 / 0.015707963267948967). Numerically, 1 quadrant equals 99.99999999999999 grad.
Relationship context
Both Quadrant and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Gradian (grad) |
|---|---|
| 0.1 | 10 |
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
| 4 | 400 |
| 5 | 500 |
| 6 | 600 |
| 7 | 700 |
| 8 | 800 |
| 9 | 900 |
| Quadrant (quadrant) | Gradian (grad) |
|---|---|
| 10 | 1,000 |
| 20 | 2,000 |
| 30 | 3,000 |
| 40 | 4,000 |
| 50 | 5,000 |
| 60 | 6,000 |
| 70 | 7,000 |
| 80 | 8,000 |
| 90 | 9,000 |
| 100 | 10,000 |