Revolution to Quadrant Converter
Angle · unit-converter
Convert Revolution 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
About Quadrant
A quadrant is one quarter-turn: 90° or π/2 radians. It is useful in geometric and directional notation.
How to convert revolutions to quadrants
1 revolution equals 4 quadrant in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 1.5707963267948966 rad) quadrant = 4 quadrant
Each revolution carries 6.283185307179586 rad and each quadrant 1.5707963267948966 rad, so one turn equals 6.283185307179586 ÷ 1.5707963267948966 quadrant.
Let θ(turn) be the angle in Revolution (turn), and θ(quadrant) in Quadrant (quadrant). Then:
θ(quadrant) = θ(turn) × (6.283185307179586 / 1.5707963267948966)
Equivalently, divide by how many turn fit into one quadrant (rad per quadrant divided by rad per turn):
θ(quadrant) = θ(turn) ÷ 0.25
Examples
Example #1: Convert 1 turn to quadrant
1 turn = 1 turn × (6.283185307179586/1.5707963267948966) quadrant = 4 quadrant
1 turn = 1 turn ÷ 0.25 = 4 quadrant
1 turn × (6.283185307179586/1.5707963267948966) = 4.000000 quadrant
Example #2: Convert 10 turn to quadrant
10 turn = 10 turn × (6.283185307179586/1.5707963267948966) quadrant = 40 quadrant
10 turn = 10 turn ÷ 0.25 = 40 quadrant
10 turn × (6.283185307179586/1.5707963267948966) = 40.000000 quadrant
Summary
To convert Revolution to Quadrant, multiply the value in turn by (6.283185307179586 rad per turn) / (1.5707963267948966 rad per quadrant). Equivalently: value_quadrant = value_turn × (6.283185307179586 / 1.5707963267948966). Numerically, 1 turn equals 4 quadrant.
Relationship context
Both Revolution and Quadrant are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per quadrant) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Quadrant (quadrant) |
|---|---|
| 0.1 | 0.4 |
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |
| 8 | 32 |
| 9 | 36 |
| Revolution (turn) | Quadrant (quadrant) |
|---|---|
| 10 | 40 |
| 20 | 80 |
| 30 | 120 |
| 40 | 160 |
| 50 | 200 |
| 60 | 240 |
| 70 | 280 |
| 80 | 320 |
| 90 | 360 |
| 100 | 400 |