Degree to Minute of Arc Converter (° to ′)

How to Convert Degrees to Minutes of Arc

Converting degrees to minutes of arc is one of the most fundamental operations in precise angular measurement. While a degree is a large enough unit to describe compass bearings or geometric angles in everyday life, a single degree is far too coarse for astronomy, precision navigation, and geodesy — fields where angular differences smaller than a degree carry enormous real-world significance. One degree is divided into exactly 60 arc-minutes, making the conversion straightforward: multiply the degree value by 60. Use the converter above for instant results, or follow the formula and examples below.

Step-by-step example — Convert 3° to minutes of arc:

Step-by-step example — Convert 0.5° to minutes of arc:

Step-by-step example — Convert 2.75° to minutes of arc:

What is a Degree and a Minute of Arc?

Degree (°) is the standard unit of angular measurement used across geometry, navigation, geography, and everyday science. A full circle contains exactly 360 degrees — a convention rooted in ancient Babylonian astronomy, which used a base-60 number system and observed approximately 360 days in a year. One degree represents 1/360th of a complete rotation. Degrees are the universal language of angle: compass bearings, latitude and longitude coordinates, slope gradients in road design, and joint angles in biomechanics are all expressed in degrees. A right angle is 90°, a straight angle is 180°, and a full rotation is 360°.

Minute of Arc (′), also written as arcminute and symbolized by the prime character (′), is a subdivision of the degree equal to exactly 1/60th of one degree. The name "minute" comes from the Latin pars minuta prima, meaning "first small part" — a historical term from the sexagesimal (base-60) division of the circle. One arcminute is a remarkably small angle: at a distance of 1 kilometer, 1 arcminute corresponds to a lateral displacement of approximately 29 centimeters. Arcminutes are used extensively in astronomy to describe the apparent size of celestial objects (the full Moon subtends about 30′), in navigation as the basis for the nautical mile (1 nautical mile = 1 arcminute of latitude), in optometry to define visual acuity (20/20 vision resolves details at 1 arcminute), and in precision shooting to describe scope adjustments (MOA — minute of angle).

Degree to Minute of Arc Quick Reference Chart

Degrees (°)	Minutes of Arc (′)	Common Reference
0.017°	1′	1 nautical mile of latitude on Earth
0.25°	15′	Sun/Moon travels this in 1 minute of time
0.5°	30′	Apparent diameter of the full Moon
1°	60′	1 degree — basic angular unit
5°	300′	Angular width of an outstretched fist at arm's length
10°	600′	Angular separation — common star field span
45°	2,700′	Half a right angle (diagonal)
90°	5,400′	Right angle — quarter circle
180°	10,800′	Straight angle — half circle
360°	21,600′	Full circle — one complete rotation

Real World Uses of Degree to Minute of Arc Conversion

• Astronomy & Telescope Optics: Astronomers routinely describe the apparent angular size of celestial objects — star clusters, nebulae, planetary disks, and galaxies — in arcminutes and arc-seconds rather than degrees, because most objects in the night sky are smaller than a single degree. Converting a telescope's field of view from degrees to arcminutes helps observers determine exactly which objects will fit within the eyepiece view, calculate the angular separation between binary stars, and plan astrophotography sessions by matching the camera's angular field to target object sizes.
• Maritime & Aviation Navigation: The nautical mile is defined as exactly one arcminute of latitude along Earth's surface — approximately 1,852 meters. Navigators converting chart coordinates or plotting courses must work fluidly between degrees (used for large-scale position reporting and course headings) and arcminutes (used for precise position fixes and distance calculations). A vessel or aircraft navigating 30 nautical miles is covering exactly 30 arcminutes of latitude, requiring constant degree-to-arcminute conversion during voyage planning and real-time position tracking.
• Precision Rifle Shooting & Ballistics: The Minute of Angle (MOA) is the standard angular unit used in long-range shooting to describe scope adjustments, group sizes, and target subtension. Most rifle scopes adjust in ¼ MOA or ⅛ MOA increments per click. Shooters converting bullet drop charts (often expressed in degrees or milliradians) to scope-click adjustments in MOA must convert between degrees and arcminutes accurately. At 100 yards, 1 MOA equals approximately 1.047 inches — a relationship shooters depend on for consistent accuracy at extended ranges.
• Geodesy & GPS Coordinate Systems: Geographic coordinates (latitude and longitude) are traditionally expressed in degrees, minutes, and seconds (DMS format) — for example, 28°36′45″N. GPS software, surveying instruments, and GIS platforms regularly convert between decimal degrees (DD) and DMS format, which requires splitting the fractional part of a degree into arcminutes. Geodesists and GIS professionals converting coordinate datasets between DD and DMS must apply the ° to ′ conversion precisely to avoid positional errors that could cascade into significant spatial inaccuracies in mapping and boundary determination.

Frequently Asked Questions

How many minutes of arc are in a degree?

There are exactly 60 minutes of arc in one degree. So 1° = 60′. This is the defining relationship in the sexagesimal (base-60) angular subdivision system used since ancient Babylonian astronomy.

What is the formula to convert degrees to minutes of arc?

The formula is: ′ = ° × 60. Simply multiply any degree value by 60 to get the equivalent angle expressed in arcminutes.

What is 1 degree in minutes of arc?

1° = 60′ (sixty arcminutes). One degree is divided into 60 equal arcminutes, and each arcminute is further divided into 60 arc-seconds — giving the DMS (Degrees, Minutes, Seconds) coordinate system used in navigation and geography.

What is 0.5 degrees in minutes of arc?

0.5° = 30′. Half a degree equals 30 arcminutes — which is also the approximate apparent angular diameter of the full Moon as seen from Earth.

What is a minute of arc also called?

A minute of arc is also called an arcminute or MOA (minute of angle). It is symbolized by the prime mark (′). In navigation and GPS coordinates, it appears as the middle value in DMS notation (e.g., 45°30′15″ — where 30 is the arcminute value). In shooting sports, MOA is the dominant term.

How does arcminute relate to the nautical mile?

One arcminute of latitude on Earth's surface equals exactly one nautical mile (1,852 meters). This elegant relationship is why nautical miles — not kilometers or statute miles — became the standard distance unit in maritime and aviation navigation: distance and angular position are directly interchangeable using the degree-to-arcminute conversion.

What is the difference between arcminute and arc-second?

An arcminute (′) equals 1/60th of a degree, while an arc-second (″) equals 1/60th of an arcminute — or 1/3,600th of a degree. Arc-seconds are used for even finer angular measurements: stellar parallax, precise GPS coordinates, and the angular resolution of high-magnification telescopes. The conversion is: 1° = 60′ = 3,600″.

Why is the arcminute important in optometry?

Visual acuity is defined using arcminutes. Standard 20/20 vision means the eye can resolve two distinct points separated by exactly 1 arcminute of angle. An optician's eye chart is designed so that the critical features of the letters on the 20/20 line subtend 1 arcminute at the standard 20-foot viewing distance. Converting degrees to arcminutes is therefore central to designing vision tests, specifying optical instruments, and evaluating camera and sensor resolution in imaging systems.