Arcseconds (″) to Radians (rad) Conversion

Arcseconds

The arcsecond (″, Unicode U+2033) is a unit of angle equal to exactly 1/3,600 of a degree, or 1/60 of an arcminute (approximately 4.848 × 10⁻⁶ radians). It is the standard unit of angular resolution in astronomy: the Hubble Space Telescope achieves a resolution of approximately 0.05 arcseconds; the nearest star, Proxima Centauri, has a parallax of 0.769 arcseconds — the basis for measuring its distance. In geodesy, GPS coordinates are routinely recorded to sub-arcsecond precision, corresponding to positional accuracy of approximately 30 metres on Earth's surface.

Radians

The radian (rad) is the SI derived unit of plane angle, defined as the angle subtended at the centre of a circle by an arc whose length equals the radius. One full rotation equals exactly 2π radians (≈ 6.2832 rad), and one radian equals approximately 57.2958°. The radian is preferred in mathematics and physics because it makes the derivatives of trigonometric functions algebraically clean — d/dx(sin x) = cos x only when x is in radians. Rotational speed (rad/s) and angular frequency in oscillatory systems are always expressed in radians.

Convert Arcseconds (″) to other units of Angle