Arcseconds to Turns
An instant arcseconds-to-turns converter, with the formula and a reference table below.
| Arcseconds | Turns |
|---|---|
| 1 ″ | 7.71605e-07 turn |
| 2 ″ | 1.54321e-06 turn |
| 3 ″ | 2.31481e-06 turn |
| 5 ″ | 3.85802e-06 turn |
| 10 ″ | 7.71605e-06 turn |
| 25 ″ | 1.92901e-05 turn |
| 50 ″ | 3.85802e-05 turn |
| 100 ″ | 7.71605e-05 turn |
How to use
- Enter a value in the Arcseconds field.
- The Turns figure appears immediately — no button to press.
- Typing in the Turns field converts back to Arcseconds the same way.
- Use the reference table for the values that come up most often.
Arcseconds to Turns formula
To convert arcseconds to turns, multiply by 7.71604938e-07.
turn = ″ × 7.71604938e-07
Why this factor: the arcsecond and the turn are both defined against the degree, so dividing one definition by the other gives 7.71604938e-07 directly. Both definitions are set out in full below.
To go the other way, divide by 7.71604938e-07 — or use the Turns to Arcseconds converter, which is the same calculation reversed.
Worked example
Take 30 ″ and multiply by the factor 7.71604938e-07: the result is 2.31481e-05 turn.
30 ″ × 7.71604938e-07 = 2.31481e-05 turn
The converter above does this for any value you type, in either direction.
What is an arcsecond?
An arcsecond is one 3,600th of a degree — the precision unit of astronomy.
Definition: Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).
Where it is used: Telescope resolution and seeing, stellar parallax (the basis of the parsec), and precision surveying.
What is a turn?
A turn is one complete revolution — a full circle.
Definition: Exactly 360 degrees, or 2π radians.
Where it is used: Rotational counting, gear and pulley ratios, and coil and winding specifications.
Arcseconds vs Turns
The arcsecond and the turn belong to the same family of units, so converting between them is usually a matter of shifting a decimal point or applying a small whole-number factor.
Frequently asked questions
How many turns are in an arcsecond?
One arcsecond equals 7.71604938e-07 turns.
What is the formula to convert arcseconds to turns?
Multiply the number of arcseconds by 7.71604938e-07. To reverse it, divide by 7.71604938e-07 instead.
How do I convert turns back to arcseconds?
Divide by 7.71604938e-07, which is the same as multiplying by 1296000.
How many turns are in 10 arcseconds?
10 ″ works out to 7.71605e-06 turn.
How is the arcsecond defined?
Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).