Quadrant to Revolution Converter
Angle · unit-converter
Convert Quadrant to Revolution 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
How to convert quadrants to revolutions
1 quadrant equals 0.25 revolution in this tool (via radian):
1 quadrant = (1.5707963267948966 rad ÷ 6.283185307179586 rad) turn = 0.25 turn
Each quadrant carries 1.5707963267948966 rad and each revolution 6.283185307179586 rad, so one quadrant equals 1.5707963267948966 ÷ 6.283185307179586 turn.
Let θ(quadrant) be the angle in Quadrant (quadrant), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(quadrant) × (1.5707963267948966 / 6.283185307179586)
Equivalently, divide by how many quadrant fit into one turn (rad per turn divided by rad per quadrant):
θ(turn) = θ(quadrant) ÷ 4
Examples
Example #1: Convert 1 quadrant to revolution
1 quadrant = 1 quadrant × (1.5707963267948966/6.283185307179586) turn = 0.25 turn
1 quadrant = 1 quadrant ÷ 4 = 0.25 turn
1 quadrant × (1.5707963267948966/6.283185307179586) = 0.250000 turn
Example #2: Convert 10 quadrant to revolution
10 quadrant = 10 quadrant × (1.5707963267948966/6.283185307179586) turn = 2.5 turn
10 quadrant = 10 quadrant ÷ 4 = 2.5 turn
10 quadrant × (1.5707963267948966/6.283185307179586) = 2.500000 turn
Summary
To convert Quadrant to Revolution, multiply the value in quadrant by (1.5707963267948966 rad per quadrant) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_quadrant × (1.5707963267948966 / 6.283185307179586). Numerically, 1 quadrant equals 0.25 turn.
Relationship context
Both Quadrant and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per quadrant) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Quadrant (quadrant) | Revolution (turn) |
|---|---|
| 0.1 | 0.025 |
| 1 | 0.25 |
| 2 | 0.5 |
| 3 | 0.75 |
| 4 | 1 |
| 5 | 1.25 |
| 6 | 1.5 |
| 7 | 1.75 |
| 8 | 2 |
| 9 | 2.25 |
| Quadrant (quadrant) | Revolution (turn) |
|---|---|
| 10 | 2.5 |
| 20 | 5 |
| 30 | 7.5 |
| 40 | 10 |
| 50 | 12.5 |
| 60 | 15 |
| 70 | 17.5 |
| 80 | 20 |
| 90 | 22.5 |
| 100 | 25 |