Arcminute — Definition, Formula & Examples

An arcminute is a unit of angular measurement equal to one-sixtieth of a degree. It is written with a single prime symbol (′), so 30 arcminutes is written as 30′.

One arcminute is defined as $\frac{1}{60}$ of one degree of arc. Equivalently, one full rotation of 360° contains exactly 21,600 arcminutes. Each arcminute is further subdivided into 60 arcseconds (″), giving a hierarchical system analogous to hours, minutes, and seconds of time.

Key Formula

1^\circ = 60' = 3600''

Where:

$°$ = Degree, the base unit of angular measure (1/360 of a full rotation)
$'$ = Arcminute, equal to 1/60 of a degree
$''$ = Arcsecond, equal to 1/60 of an arcminute

How It Works

Degrees, arcminutes, and arcseconds work like a base-60 system for angles, similar to how time uses hours, minutes, and seconds. To convert a decimal degree value into degrees-minutes-seconds (DMS) notation, take the whole-number part as degrees, multiply the decimal remainder by 60 to get arcminutes, then multiply any remaining decimal by 60 again to get arcseconds. To go the other direction, divide arcminutes by 60 and arcseconds by 3600, then add everything together.

Worked Example

Problem: Convert 35.275° to degrees, arcminutes, and arcseconds (DMS notation).

Step 1: Separate the whole degrees from the decimal part.

35.275° = 35° + 0.275°

Step 2: Multiply the decimal part by 60 to get arcminutes.

0.275 \times 60 = 16.5'

Step 3: Take the decimal part of the arcminutes and multiply by 60 to get arcseconds.

0.5 \times 60 = 30''

Answer: 35.275° = 35° 16′ 30″

Why It Matters

Arcminutes are essential in navigation, astronomy, and surveying, where fractions of a degree matter. GPS coordinates and star catalogs routinely use DMS notation. Understanding arcminutes also helps in trigonometry and physics courses when working with precise angular measurements.

Common Mistakes

Mistake: Confusing arcminutes (angular measure) with minutes of time.

Correction: Although both use a base-60 subdivision, arcminutes measure angles while time-minutes measure duration. The symbols also differ: arcminutes use a prime (′) while time context is usually clear from labeling.