Arcseconds to Radians Converter
Enter a value to instantly convert between angle units.
1 Arcsecond = 0 Radian
Key Formulas
Degree → Radian
rad = ° × 0.0174533Radian → Degree
° = rad × 57.2958Degree → Gradian
grad = ° × 1.11111Gradian → Degree
° = grad × 0.9Formula
radians = arcseconds × 4.84813681e-6The constant 4.848 × 10⁻⁶ radians per arcsecond (the reciprocal of 206,265) appears throughout precision astronomy. Stellar parallax, gravitational deflection of light, proper motion, and telescope diffraction limits are all computed in radians internally but measured in arcseconds by instruments. The Gaia mission cataloging stellar positions to 7 microarcsecond precision must convert those measurements to radians for orbit determination software. Every precision optics formula that computes resolution as 1.22λ/D in radians needs this conversion for comparison with an instrument's arcsecond-specified resolution.
Source: ISO 80000-3:2019 (Quantities and units — Space and time)
Last reviewed: · see our methodology
Frequently Asked Questions
Real-World Examples
One radian — 206,265 arcseconds, the astronomical conversion constant defining the parsec (1 AU subtending 1 arcsecond at 1 parsec).
206265 ″ = 1 rad
One arcsecond — 4.848 microradians, the resolution limit of a 28 cm aperture telescope observing at 550 nm (λ/D = 2.4 × 10⁻⁶ rad for diffraction-limited imaging).
1 ″ = 0.000004848 rad
Proxima Centauri's parallax — 0.7687 arcseconds, giving a distance of 1/0.7687 = 1.301 parsecs. The radian form is used in astrodynamics calculations.
0.77 ″ = 0.000003733 rad
1,000 arcseconds of angular measurement — 0.00485 radians, the radian input to an orbital mechanics formula computing satellite ground track separation.
1000 ″ = 0.004848 rad