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Angle
Arcseconds to Turns
Convert arcseconds (arcsec) to turns (tr). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 arcsec = 7.7160e-7 tr
Arcseconds to Turns Conversion Table
Common values, ready to copy:
| arcseconds | turns |
|---|---|
| 1 arcsec | 7.7160e-7 tr |
| 2 arcsec | 1.5432e-6 tr |
| 5 arcsec | 3.8580e-6 tr |
| 10 arcsec | 7.7160e-6 tr |
| 25 arcsec | 1.9290e-5 tr |
| 50 arcsec | 3.8580e-5 tr |
| 100 arcsec | 7.7160e-5 tr |
| 1,000 arcsec | 0.000772 tr |
Formula
turns = arcseconds × 7.71604938e-7
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Arcseconds and Turns
Arcseconds (arcsec): 1/60 of an arcminute, or 1/3600 of a degree; the unit for very small angles in astronomy. Common uses: Astronomical resolution (a telescope's resolving power in arcseconds), positional precision of stars, and very fine engineering angle specifications.
Turns (tr): A full revolution; the most natural way to describe rotation (one turn = 360° = 2π rad = 400 gon). Common uses: Engineering specifications for rotation (number of turns of a bolt, a screw thread, or a knob), and clear communication when degree confusion is a risk.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is turns = arcseconds × 7.71604938e-7, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between arcseconds and turns comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.