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Multiple conversions
To convert from arcminute (arcmin) to radian (rad), use the following formula:
radian (rad)
= 160 × π180× arcminute (arcmin)
= 110800 × π× arcminute (arcmin)
= 0.00029088820866572157407× arcminute (arcmin)
To convert from arcminute (arcmin) to degree (deg), use the following formula:
degree (deg)
= 160× arcminute (arcmin)
= 0.016666666666666666667× arcminute (arcmin)
To convert from arcminute (arcmin) to gradian (grad), use the following formula:
gradian (grad)
= 160 × 109× arcminute (arcmin)
= 10 × 1540× arcminute (arcmin)
= 0.018518518518518518519× arcminute (arcmin)
To convert from arcminute (arcmin) to arcsecond (arcsec), use the following formula:
arcsecond (arcsec)
= 160 × 60 × 60× arcminute (arcmin)
= 60× arcminute (arcmin)
An arcminute (plural: arcminutes) is a precise unit of angular measurement, equal to 1/60th of a degree.
It provides a way to measure very small angles with high accuracy and is frequently used in scientific and technical fields. The common abbreviation for arcminute is arcmin.
There are precisely 60 arcminutes within a single degree.
This relationship is a core part of the "degrees, minutes, seconds" (DMS) system of measurement, which breaks down angles into smaller parts for greater precision.
The universally recognized symbol for an arcminute is the prime symbol (′).
This symbol is placed directly after the number to denote the measurement. For example, an angle of 45 and a half degrees can be expressed as 45° 30′.
Arcminutes are essential in fields that demand precise angular resolution. Key applications include:
Astronomy: Astronomers use arcminutes to measure the apparent size of celestial objects as seen from Earth and the distance between them in the sky.
Navigation: In celestial navigation and cartography, one arcminute of latitude along any meridian on the Earth's surface is approximately equal to one nautical mile.
Surveying: Surveyors use arcminutes to measure land boundaries and features over long distances accurately.
The arcminute is the unit in which normal eyesight is defined.
"20/20 vision" means that at 20 feet you can resolve detail subtending one arcminute of visual angle. On a Snellen eye chart, each stroke of a letter on the 20/20 line — and each gap in it — is exactly one arcminute wide as seen from the testing distance; the whole letter spans five. That is not an arbitrary benchmark: it is close to the physical resolution limit set by the spacing of cone cells in the fovea.
The same unit explains a familiar rule of thumb in the sky. The Sun and the full Moon each span about 30 arcminutes — half a degree — which is why a total solar eclipse works at all, and why the Moon photographs so much smaller than it appears.
In marksmanship the arcminute travels under the abbreviation MOA (minute of angle), and it is used because angular error scales linearly with distance.
One arcminute subtends almost exactly 1.047 inches at 100 yards, which shooters round to one inch. That approximation makes the arithmetic trivial: 1 MOA covers roughly 1 inch at 100 yards, 2 inches at 200 yards, 5 inches at 500 yards. A rifle described as "sub-MOA" groups its shots inside about an inch at 100 yards.
Rifle scopes inherit the unit directly — adjustment turrets typically move the point of impact by 1/4 MOA per click, or about a quarter inch at 100 yards. The metric alternative, the milliradian, divides a radian into thousandths instead, giving 10 cm at 100 m per mil; 1 mil is about 3.44 MOA.