One arcsecond is 1/3600 degree.
Arcseconds to Circles Converter — arcsec to circle
Convert Arcsecond (arcsec) to Circle (circle) using the exact conversion factor (1 arcsecond = 7.716049e-7 circle). See the formula, worked examples, and conversion table.
Arcseconds to Circles converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
One complete circle.
Result = input x 4.84813681e-6 / 6.283185307.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Arcseconds to Circles
Arcsecond and Circle are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One arcsecond is 1/3600 degree, and one complete circle.
Formula
circles = arcseconds × 7.716049e-7
This factor comes from each unit's defined relationship to the category's base unit: 1 arcsecond equals 0.0000048481368111 base units, and 1 circle equals 6.28318530718 base units, so dividing one by the other gives the direct arcsecond-to-circle factor of 7.716049e-7.
Simple example
1 arcsec × 7.716049e-7 = 7.716049e-7 circle
1 arcsecond = 7.716049e-7 circles.
Real-world example
90 arcsec × 7.716049e-7 = 0.0000694444 circle
90 arcseconds = 0.0000694444 circles.
Conversion table
| Arcsecond (arcsec) | Circle (circle) |
|---|---|
| 0 arcsec | 0 circle |
| 30 arcsec | 0.0000231481 circle |
| 45 arcsec | 0.0000347222 circle |
| 90 arcsec | 0.0000694444 circle |
| 180 arcsec | 0.0001388889 circle |
| 360 arcsec | 0.0002777778 circle |
Reverse conversion: Circle to Arcsecond
7.716049e-7 circle × 1296000 = 0.9999999504 arcsec
7.716049e-7 circles = 0.9999999504 arcseconds.
arcseconds = circles × 1296000
For a page dedicated to this direction, see Circle to Arcsecond.
Understanding the Arcsecond (arcsec)
One arcsecond is 1/3600 degree.
Understanding the Circle (circle)
One complete circle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many circles are in 1 arcsecond?
1 arcsecond equals 7.716049e-7 circles, using the exact defined conversion factor rather than an estimate.
How do I convert arcsecond to circle?
Multiply the arcsecond value by 7.716049e-7. The converter above does this instantly to whatever precision you set.
How do I convert circle back to arcsecond?
Use the reverse factor: 1 circle equals 1,296,000 arcseconds. You can also use the swap control in the converter above to flip the direction instantly.
What is a arcsecond?
Arcsecond (arcsec) is a unit of angle.
What is a circle?
Circle (circle) is a unit of angle.
Is the arcsecond to circle conversion exact?
Yes. Both arcsecond and circle are defined by fixed standards rather than physical artifacts, so the factor of 7.716049e-7 used above is exact to as many digits as you choose to display.