Minute of Arc to Degree Converter (′ to °)

How to Convert Minutes of Arc to Degrees

Converting minutes of arc to degrees is a fundamental skill in astronomy, navigation, surveying, and optics — anywhere that precise angular measurement matters. Since one degree is divided into exactly 60 minutes of arc, the conversion is simple: divide the number of arcminutes by 60. Use the converter above for instant results, or follow the formula and examples below.

Step-by-step example — Convert 30′ to degrees:

Step-by-step example — Convert 90′ to degrees:

Step-by-step example — Convert 150′ to degrees:

What is a Minute of Arc and a Degree?

Minute of Arc (′), also called an arcminute or MOA (minute of angle), is a unit of angular measurement equal to one-sixtieth (1/60) of one degree. The symbol is a single prime mark: ′. The sexagesimal (base-60) subdivision of the degree into 60 minutes has ancient roots tracing back to Babylonian astronomy, and it remains the standard system for expressing precise angles in astronomy, geodesy, and navigation to this day. One arcminute subtends approximately 1.852 kilometres on the Earth's surface at the equator — which is precisely why one nautical mile is defined as one arcminute of latitude. In practical terms, 1 arcminute is roughly the angular size of a coin viewed from 60 metres away, and it is the approximate limit of angular resolution of the naked human eye under ideal conditions. Firearm shooters know this unit as MOA — 1 MOA equals approximately 1 inch at 100 yards, a standard precision benchmark in long-range shooting.

Degree (°) is the most widely used unit of angular measurement, dividing a full circle into 360 equal parts. Each degree is further subdivided into 60 arcminutes (′) and each arcminute into 60 arcseconds (″), giving the DMS (Degrees–Minutes–Seconds) notation used universally in GPS coordinates, star charts, and geographic maps. The choice of 360 for a full circle dates to ancient Babylonian astronomy, where the year was approximated at 360 days — making one degree correspond roughly to the Sun's daily movement along the ecliptic. Today, the degree is the default unit in navigation instruments, educational geometry, engineering drawing standards, and most everyday angular measurement contexts worldwide.

Minute of Arc to Degree Quick Reference Chart

Arcminutes (′)	Degrees (°)	Common Reference
1 ′	0.01667°	Angular resolution limit of human eye
5 ′	0.08333°	Angular diameter of the Moon's crater Tycho
15 ′	0.25°	Quarter-degree — common map grid interval
30 ′	0.5°	Approximate angular diameter of the full Moon
60 ′	1°	One full degree — 111 km on Earth's surface
90 ′	1.5°	1 degree 30 minutes
120 ′	2°	Two full degrees
180 ′	3°	Three full degrees
360 ′	6°	Six full degrees
1800 ′	30°	One clock-hour of sky rotation
5400 ′	90°	Right angle — quarter circle
21600 ′	360°	Full circle

Real-World Uses of Minute of Arc to Degree Conversion

• Astronomy & Telescope Optics: Astronomers express the angular size and separation of celestial objects in degrees and arcminutes. The full Moon measures approximately 30′ (0.5°) in diameter; the Andromeda Galaxy spans about 190′ (3.17°) across the sky. When planning telescope observations, calculating field of view, or recording star positions in catalogues, astronomers routinely convert between arcminutes and decimal degrees to match the input format of planetarium software, mount controllers, and coordinate databases. For instance, a telescope with a 45′ field of view covers exactly 0.75° of sky.
• GPS & Geographic Coordinate Systems: GPS coordinates are commonly expressed in DMS format (e.g., 40°42′46″N, 74°0′22″W for New York City). When importing coordinates into mapping APIs, GIS software, or navigation systems that require decimal degrees, users must convert the arcminute component to its decimal fraction. For example, a latitude of 51°30′ N converts to 51 + (30 ÷ 60) = 51.5° decimal — a conversion performed millions of times daily in digital mapping pipelines worldwide.
• Land Surveying & Legal Boundary Descriptions: Property boundaries and survey bearings in the United States are traditionally recorded in DMS notation — for example, "North 45°30′ East." When surveyors input these bearings into CAD software, coordinate geometry (COGO) programs, or GIS databases that accept only decimal degrees, they convert arcminutes to decimal fractions of a degree. A bearing of N 45°30′ E becomes N 45.5° E — and errors in this conversion can shift a legal property boundary by metres.
• Long-Range Shooting & Ballistics: In precision rifle shooting, scope adjustments and holdover values are commonly expressed in MOA (minutes of angle). A standard rifle scope click adjusts by ¼ MOA (0.25′ = 0.004167°). Shooters and ballistic calculators convert MOA values to decimal degrees when using angle-based drop tables, when programming digital ballistic computers, or when comparing MOA adjustments with mil-radian (mrad) scope systems. Understanding that 1 MOA = 1/60° is essential for accurate long-range target engagement.
• Nautical Navigation & Chart Work: One arcminute of latitude equals exactly one nautical mile (1,852 metres) — making the arcminute the natural unit for measuring distances on nautical charts. Navigators convert arcminutes to degrees when entering waypoints into electronic chart systems (ECDIS), calculating great-circle routes, or programming autopilot heading changes. A voyage course change of 120 arcminutes is a 2° heading adjustment — a conversion that must be precise for safe passage planning.

Understanding DMS — Degrees, Minutes, Seconds Notation

Angular measurements in navigation, astronomy, and surveying are often written in DMS format: Degrees° Minutes′ Seconds″. For example, the latitude of the Eiffel Tower is 48°51′29″N. To convert this full DMS value to decimal degrees, the formula is:

For 48°51′29″: 48 + (51 ÷ 60) + (29 ÷ 3600) = 48 + 0.85 + 0.00806 = 48.858°. The arcminute-to-degree conversion (÷ 60) is the core step in this widely used coordinate transformation.

Arcminute vs Degree — Key Differences at a Glance

Property	Minute of Arc (′)	Degree (°)
Full circle value	21,600 ′	360°
Relationship	1′ = 1/60°	1° = 60′
Right angle	5,400 ′	90°
Earth surface distance	~1.852 km (1 nautical mile)	~111 km
Symbol	′ (prime / single quote)	° (degree sign)
Primary use	Astronomy, GPS, precision optics, ballistics	Geometry, navigation, general angle measurement
Subdivided into	60 arcseconds (″)	60 arcminutes (′)

Frequently Asked Questions

How many minutes of arc are in one degree?

There are exactly 60 minutes of arc in one degree. This is the defining relationship: 1° = 60′. The division of degrees into 60 parts follows the ancient Babylonian sexagesimal (base-60) number system.

What is the formula to convert arcminutes to degrees?

The formula is: ° = ′ ÷ 60. Divide any arcminute value by 60 to get the equivalent angle in degrees. For example, 45′ ÷ 60 = 0.75°.

What is 1 minute of arc in degrees?

1 arcminute = 0.01667° (or exactly 1/60 of a degree). This is a very small angle — roughly the angular resolution limit of the unaided human eye and the basis of the MOA (minute of angle) standard used in precision shooting.

What is 30 minutes of arc in degrees?

30′ = 0.5° — exactly half a degree. This is also approximately the angular diameter of the full Moon as seen from Earth, which subtends about 29′ to 34′ depending on its distance in orbit.

What does MOA stand for in shooting?

MOA stands for Minute of Angle — the same unit as minute of arc (arcminute). In long-range rifle shooting, 1 MOA equals approximately 1.047 inches at 100 yards (or roughly 2.91 cm at 100 metres). Scope adjustments are typically made in ¼ MOA increments, and ballistic drop tables are often expressed in MOA per 100-yard distance increment.

Is arcminute the same as minute of arc?

Yes — arcminute and minute of arc are two names for exactly the same unit, both abbreviated with the prime symbol ′. The terms are used interchangeably in astronomy, navigation, surveying, and optics. "MOA" (minute of angle) in shooting contexts also refers to the identical unit.

How do I convert GPS coordinates from DMS to decimal degrees?

To convert GPS DMS coordinates to decimal degrees, use: DD = D + (M ÷ 60) + (S ÷ 3600), where D = degrees, M = minutes, S = seconds. For example, 35°45′30″ becomes 35 + (45 ÷ 60) + (30 ÷ 3600) = 35 + 0.75 + 0.00833 = 35.758°. The arcminute-to-degree step (M ÷ 60) is the key conversion in this calculation.

What is 1 arcminute in distance on Earth?

One arcminute of latitude on Earth's surface equals approximately 1.852 kilometres — which is the exact definition of one nautical mile. This relationship is why nautical miles are the standard unit in marine and air navigation: a navigator can directly read distances from latitude scales on charts, since each arcminute tick mark represents exactly one nautical mile.

Why is the degree divided into 60 minutes instead of 100?

The 60-minute subdivision comes from the ancient Babylonian sexagesimal (base-60) number system, which was used for astronomy and timekeeping over 3,000 years ago. The Babylonians chose base-60 partly because 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), making fractions clean and easy to work with without decimals. This system was adopted by Greek astronomers including Hipparchus and Ptolemy, passed into Arabic astronomy, and eventually became the global standard — which is why both angle measurement and timekeeping (60 minutes in an hour, 60 seconds in a minute) still use base-60 today.