Radians (rad) to Arcseconds (″) Conversion

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.

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.

Convert Radians (rad) to other units of Angle