Arcminutes (′) to Radians (rad) Conversion
Arcminutes
The arcminute (′, Unicode U+2032) is a unit of angle equal to exactly 1/60 of a degree, or π/10,800 radians. It is used in astronomy to describe the apparent size of celestial objects — the full Moon subtends approximately 30 arcminutes (half a degree) as seen from Earth. In navigation, position coordinates are routinely expressed in degrees and arcminutes: 51°30′N is the latitude of London. In optics, the resolving power of the human eye is approximately 1 arcminute, which is why standard vision charts are designed accordingly.
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.
| Arcminutes (′) | Radians (rad) |
|---|---|
| 0.1 ′ | 0.0000291 rad |
| 1 ′ | 0.000291 rad |
| 2 ′ | 0.000582 rad |
| 3 ′ | 0.000873 rad |
| 5 ′ | 0.00145 rad |
| 10 ′ | 0.00291 rad |
| 20 ′ | 0.00582 rad |
| 30 ′ | 0.00873 rad |
| 50 ′ | 0.0145 rad |
| 100 ′ | 0.0291 rad |
| 1000 ′ | 0.2909 rad |
Frequently Asked Questions (FAQ)
How many radians are in 1 arcminutes?
1 arcminutes (′) is exactly 0.000291 radians (rad).
How do I convert arcminutes to radians?
Multiply the value in arcminutes by 0.000291 to get the result in radians. Or use the converter above — type any number and see the result instantly.