Revolution to Arc Second Converter
Angle · unit-converter
Convert Revolution to Arc Second 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 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.
How to convert revolutions to arc seconds
1 revolution equals 1296000 arc second in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 0.00000484813681109536 rad) arcsec = 1296000 arcsec
Each revolution carries 6.283185307179586 rad and each arc second 0.00000484813681109536 rad, so one turn equals 6.283185307179586 ÷ 0.00000484813681109536 arcsec.
Let θ(turn) be the angle in Revolution (turn), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(turn) × (6.283185307179586 / 0.00000484813681109536)
Equivalently, divide by how many turn fit into one arcsec (rad per arcsec divided by rad per turn):
θ(arcsec) = θ(turn) ÷ 7.71604938271605e-7
Examples
Example #1: Convert 1 turn to arc second
1 turn = 1 turn × (6.283185307179586/0.00000484813681109536) arcsec = 1296000 arcsec
1 turn = 1 turn ÷ 7.71604938271605e-7 = 1296000 arcsec
1 turn × (6.283185307179586/0.00000484813681109536) = 1,296,000.000000 arcsec
Example #2: Convert 10 turn to arc second
10 turn = 10 turn × (6.283185307179586/0.00000484813681109536) arcsec = 12960000 arcsec
10 turn = 10 turn ÷ 7.71604938271605e-7 = 12960000 arcsec
10 turn × (6.283185307179586/0.00000484813681109536) = 12,960,000.000000 arcsec
Summary
To convert Revolution to Arc Second, multiply the value in turn by (6.283185307179586 rad per turn) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_turn × (6.283185307179586 / 0.00000484813681109536). Numerically, 1 turn equals 1296000 arcsec.
Relationship context
Both Revolution and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Arc Second (arcsec) |
|---|---|
| 0.1 | 129,600 |
| 1 | 1,296,000 |
| 2 | 2,592,000 |
| 3 | 3,888,000 |
| 4 | 5,184,000 |
| 5 | 6,480,000 |
| 6 | 7,776,000 |
| 7 | 9,072,000 |
| 8 | 10,368,000 |
| 9 | 11,664,000 |
| Revolution (turn) | Arc Second (arcsec) |
|---|---|
| 10 | 12,960,000 |
| 20 | 25,920,000 |
| 30 | 38,880,000 |
| 40 | 51,840,000 |
| 50 | 64,800,000 |
| 60 | 77,760,000 |
| 70 | 90,720,000 |
| 80 | 103,680,000 |
| 90 | 116,640,000 |
| 100 | 129,600,000 |