Arc Second to Revolution Converter
Angle · unit-converter
Convert Arc Second 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 Arc Second
An arc second is 1/60 of an arc minute or 1/3600 of a degree. Common in astronomy and very fine angular resolution.
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 arc seconds to revolutions
1 arc second equals 7.71604938271605e-7 revolution in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 6.283185307179586 rad) turn = 7.71604938271605e-7 turn
Each arc second carries 0.00000484813681109536 rad and each revolution 6.283185307179586 rad, so one arcsec equals 0.00000484813681109536 ÷ 6.283185307179586 turn.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(arcsec) × (0.00000484813681109536 / 6.283185307179586)
Equivalently, divide by how many arcsec fit into one turn (rad per turn divided by rad per arcsec):
θ(turn) = θ(arcsec) ÷ 1296000
Examples
Example #1: Convert 1 arcsec to revolution
1 arcsec = 1 arcsec × (0.00000484813681109536/6.283185307179586) turn = 0.0000007716 turn
1 arcsec = 1 arcsec ÷ 1296000 = 0.0000007716 turn
1 arcsec × (0.00000484813681109536/6.283185307179586) = 0.000001 turn
Example #2: Convert 10 arcsec to revolution
10 arcsec = 10 arcsec × (0.00000484813681109536/6.283185307179586) turn = 0.000007716 turn
10 arcsec = 10 arcsec ÷ 1296000 = 0.000007716 turn
10 arcsec × (0.00000484813681109536/6.283185307179586) = 0.000008 turn
Summary
To convert Arc Second to Revolution, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_arcsec × (0.00000484813681109536 / 6.283185307179586). Numerically, 1 arcsec equals 7.71604938271605e-7 turn.
Relationship context
Both Arc Second and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Revolution (turn) |
|---|---|
| 0.1 | 0.0000000772 |
| 1 | 0.0000007716 |
| 2 | 0.0000015432 |
| 3 | 0.0000023148 |
| 4 | 0.0000030864 |
| 5 | 0.000003858 |
| 6 | 0.0000046296 |
| 7 | 0.0000054012 |
| 8 | 0.0000061728 |
| 9 | 0.0000069444 |
| Arc Second (arcsec) | Revolution (turn) |
|---|---|
| 10 | 0.000007716 |
| 20 | 0.0000154321 |
| 30 | 0.0000231481 |
| 40 | 0.0000308642 |
| 50 | 0.0000385802 |
| 60 | 0.0000462963 |
| 70 | 0.0000540123 |
| 80 | 0.0000617284 |
| 90 | 0.0000694444 |
| 100 | 0.0000771605 |