Turns to Arcseconds (turn to ″)
1 turn equals 1,296,000 arcseconds exactly.
How to convert turns to arcseconds
To convert turns to arcseconds, multiply the number of turns by 1,296,000. This factor is exact. To go the other way, multiply arcseconds by 7.716049383×10⁻⁷ (rounded).
arcseconds = turns × 1,296,000
Example: 10 turns = 12,960,000 arcseconds.
About these units
Turn (turn)
One full revolution, 360 degrees or 2π radians.
A turn is the simplest angle to define: the whole way around, back to the starting direction. It also goes by cycle and revolution, and it equals 2π radians, 360 degrees, or 400 gradians. In the International System of Quantities, rotation is a plain count of revolutions, the angle divided by 2π radians, and it can be negative or exceed one.
Measuring in turns is older than it might seem. Percentage protractors marked in hundredths of a turn have existed since 1922, and in 1962 the astronomer Fred Hoyle proposed the terms centiturn, milliturn, and microturn. A 1974 German standard, DIN 1315, suggested the symbol pla, from the Latin for full angle. Some HP calculators, such as the HP Prime of 2013, accept tr as an angle unit. In CSS, 1turn equals 360deg, so a rule can rotate an element by 1.75turn. Binary angular measurement in computing also treats a full turn as the value 1, which lets integer overflow wrap an angle around for free.
The turn is the reference unit for angle on this site.
Sources: Wikipedia: Turn (angle); MDN Web Docs: CSS <angle>; NIST Guide to the SI, Appendix B.8 (angle conversion factors)
Arcsecond (″)
One sixtieth of an arcminute (1/3,600 degree). Used for tiny angles in astronomy.
An arcsecond is 1/3,600 of a degree, or 1/1,296,000 of a turn. In radians it is π/648,000, about 4.85 millionths, so it covers roughly 4.8 millimeters at a distance of 1 kilometer. The SI Brochure treats it as an alternative name for the second of plane angle, with the symbol as or ″, and counts it among the widely used non-SI units.
Astronomy is where it matters most. The parsec is the distance at which a star shows a parallax of one arcsecond, about 3.26 light-years, so a star's distance in parsecs is the reciprocal of its parallax in arcseconds. The unit also appears in planetary angular diameters, binary star separations, and star motions. For comparison, the Sun's disk is roughly 1,900 arcseconds across. Smaller angles use the prefixes milli- and micro-.
1 arcsecond = 7.716049383×10⁻⁷ turns (approximately).
Sources: BIPM SI Brochure, 9th edition (2019); ESA Gaia: Cosmic distances; NIST Guide to the SI, Appendix B.8 (angle conversion factors)
Related conversions
- Arcseconds to turns (reverse)
- Turns to degrees
- Turns to radians
- Turns to gradians
- Turns to arcminutes
- Degrees to arcseconds
- Radians to arcseconds
- Gradians to arcseconds
- Arcminutes to arcseconds
See all angle units.