Convert Arcminutes to Radians
Convert Arcminutes (′) to Radians (rad) instantly and accurately.
Conversion Formula
rad = ′ × 0.0002908882087
About Arcminutes
An arcminute (′) is 1/60 of a degree - π/10,800 rad ≈ 2.909 × 10⁻⁴ rad. One arcminute of latitude equals exactly one nautical mile (1,852 m), which is the origin of the nautical mile unit. The Moon and Sun both subtend ~30 arcminutes in apparent diameter - the coincidence exploited in total solar eclipses. Human 20/20 visual acuity resolves letters 5 arcminutes tall at 6 m. Binocular and telescope apparent fields of view are quoted in arcminutes. 1′ = π/10,800 rad ≈ 0.01667° ≈ 290.9 µrad.
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″.
Quick Reference Table
| Arcminutes (′) | Radians (rad) |
|---|---|
| 1 ′ | 0.000290888 rad |
| 2 ′ | 0.000581776 rad |
| 5 ′ | 0.00145444 rad |
| 10 ′ | 0.00290888 rad |
| 25 ′ | 0.00727221 rad |
| 50 ′ | 0.0145444 rad |
| 100 ′ | 0.0290888 rad |