Arcseconds to Radians Converter

To convert a measurement in arcseconds to radians, multiply the value by 0.000004848137. The conversion factor comes from the relationship between both units and the radian.

For example, to convert 5 ″ to radians: 5 × 0.000004848137 = 0.000024240684 rad.

An arcsecond is a unit of angle equal to 1/60 of an arcminute, 1/3,600 of a degree, or 1/1,296,000 of a full turn. It is written with a double-prime symbol (″). The arcsecond continues the Babylonian sexagesimal subdivision one step further and became essential in astronomy, where stellar parallaxes are measured in fractions of an arcsecond (the parsec is defined from it).

Common uses of arcseconds include: Stellar parallax and astrometry; Telescope resolution and seeing conditions; High-precision surveying and geodesy; Satellite and spacecraft pointing accuracy.

A radian is the SI unit of plane angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. A full turn equals 2π radians. The concept dates to the 18th century, but the term 'radian' was coined by James Thomson in 1873. It is the natural unit of angle in mathematics and physics because it makes calculus formulas for trigonometric functions clean and dimensionless.

Common uses of radians include: Calculus, physics, and engineering calculations; Angular velocity and rotational motion (rad/s); Computer graphics and game math libraries; Signal processing and wave phase (2π per cycle).

Here are some common values converted:

1 ″ = 0.000004848137 rad 5 ″ = 0.000024240684 rad 10 ″ = 0.000048481368 rad 50 ″ = 0.000242406841 rad 100 ″ = 0.000484813681 rad