Convert Angle from arcminutes to degrees (arcmin to deg)

arcminute to degree Conversion Formula

Example

Let's convert 5 arcminute (arcmin) to degree (deg).

Using the formula:

Therefore, 5 arcminute (arcmin) is equal to 0.083333333333333333335 degree (deg).

How many arcminutes are in one degree? One degree (deg) contains 60 arcminutes (arcmin) — the inverse of the factor above. Multiplying by 0.016666666666666666667 takes you from arcminutes to degrees; multiplying by 60 brings you back.

Put in words: one arcminute equals 0.016666666666666666667 degrees, so the arcminute is the smaller unit of this pair. Converting between them never changes the amount of angle being measured — only the size of the unit you count it in.

What Is an 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.

How Many Arcminutes Are in a Degree?

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.

• 1 degree (°) = 60 arcminutes (′)

What Is the Symbol for an Arcminute?

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′.

What Are Arcminutes Used For?

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 in Human Vision

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.

Arcminutes in Shooting and Optics

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.

What is a Degree (deg or °)?

In geometry and everyday life, we measure angles using degrees.

A degree (represented by the universal symbol °) is the basic unit for measuring rotation. It helps us describe the amount of turn between two lines that meet at a point.

For instance, a perfect corner, like the edge of a book, is a 90° right angle, and one complete, full-circle rotation measures 360°.

Why Are There 360 Degrees in a Circle?

The standard of a circle containing 360 degrees (360°) originated with the ancient Babylonians.

They used a base-60 (sexagesimal) number system, and 360 was a perfect number for them because it is highly divisible. Its large number of factors made it incredibly easy to perform fractional calculations in fields like astronomy and geometry.

How to Measure Angles Smaller Than a Degree

For fields that require extreme precision, like astronomy, cartography (map-making), and GPS navigation, a single degree is broken down into even smaller units:

• One degree is subdivided into 60 arcminutes (symbolized as ').
• Each arcminute is further divided into 60 arcseconds (symbolized as ").

This system ensures that even the tiniest angles can be measured with high accuracy.

Why a Circle Has 360 Degrees

There is no physical reason a full turn must be 360 of anything. The number is an inheritance from Babylonian astronomy, and it survived for two reasons that still matter.

The first is the calendar. Babylonian astronomers worked with a year of roughly 360 days, so the Sun appeared to advance about one degree along the ecliptic each day — a convenient bookkeeping unit for tracking the sky.

The second is arithmetic, and it is the reason the convention outlived the astronomy. 360 has 24 divisors. It splits evenly into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths, twelfths, fifteenths, eighteenths, twentieths, twenty-fourths and more. Every common fraction of a turn lands on a whole number of degrees: a right angle is 90°, a third of a turn is 120°, an eighth is 45°. A base-10 alternative such as the gradian, with 400 to a circle, is better for decimal arithmetic but produces fractions for thirds and sixths — which is roughly why it never displaced the degree outside surveying.

Degrees and Radians in Practice

Degrees are for people; radians are for mathematics and for machines.

The distinction is not stylistic. In calculus the derivative of sin(x) is cos(x) only when x is in radians; in degrees an awkward factor of π/180 appears and never leaves. Because of this, essentially every programming language's trigonometric library — JavaScript, Python, C, Java — takes radians, not degrees.

That mismatch is a reliable source of bugs. A value that looks plausible but is wrong by a factor of about 57.3 usually means degrees were passed where radians were expected. The conversions worth memorising are:

• radians = degrees × π / 180
• degrees = radians × 180 / π
• One radian is about 57.2958°; one degree is about 0.0174533 radians.

Scientific calculators expose the same trap through their DEG / RAD / GRAD mode switch, where an unnoticed mode is the classic cause of an answer that is confidently and completely wrong.

arcminute to degree Conversion Table

Here are some quick reference conversions from arcminute (arcmin) to degree (deg):