Convert Radians to Arcseconds

Convert Radians (rad) to Arcseconds (″) instantly and accurately.

Conversion Formula

″ = rad × 206264.8062

About Radians

The radian (rad) is the SI unit of plane angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle = 2π rad; a right angle = π/2 rad. The radian is dimensionless (arc length / radius), so it can be omitted in equations. All calculus and physics formulas are simplest in radians: d/dx(sin x) = cos x holds only in radians; Taylor series sin x = x − x³/6 + x⁵/120 hold only for x in radians; angular frequency ω = 2πf gives energy E = ħω. 1 rad = 180°/π ≈ 57.2958° ≈ 206,264.8″.

About Arcseconds

An arcsecond (″) is 1/3,600 of a degree - π/648,000 rad ≈ 4.848 × 10⁻⁶ rad. It is the fundamental resolution unit of classical astronomy and geodetic surveying. The Hubble Space Telescope delivers ~0.05″ resolution; atmospheric seeing at excellent sites gives 0.4-0.6″. Stellar parallax of Proxima Centauri is 0.7687″, defining its distance of 1.3009 parsecs. The parsec is defined as the distance at which 1 AU subtends exactly 1 arcsecond - giving 1 pc = 3.0857 × 10¹⁶ m. 1″ = π/648,000 rad ≈ 4.848 µrad.

Quick Reference Table

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