Small angle values can be surprisingly easy to misread. A result written in arcminutes may look unfamiliar when a map, telescope setting, or technical drawing expects degrees. The conversion is simple once the relationship is clear.

Exact conversion factor: 1 arcminute (arcmin) = 1/60 degree (deg) = 0.016666… deg. Therefore, to convert arcminutes to degrees, divide the arcminute value by 60.

What Is an Arcminute?

An arcminute is a unit used to measure angles. It is a smaller division of a degree, not a unit of time. The name comes from the way an angle is subdivided.

One degree contains 60 arcminutes:

1 deg = 60 arcmin

In this conversion, the source unit is the arcminute, written as arcmin. The target unit is the degree, written as deg.

What Is a Degree?

A degree is a standard unit for measuring angles. A complete turn contains 360 degrees, so a straight angle measures 180 degrees and a right angle measures 90 degrees.

Because one degree is divided into 60 arcminutes, an arcminute represents a much smaller angular amount:

1 arcmin = 0.016666… deg

The repeating decimal is exact when written as the fraction 1/60 deg. Decimal results may be rounded for easier reading.

Arcminute to Degree Conversion Formula

To convert an angle from arcminutes to degrees, divide the value in arcminutes by 60:

Degrees = Arcminutes ÷ 60

Using unit symbols, the formula is:

deg = arcmin ÷ 60

This works because 60 arcmin make exactly 1 deg.

How to Convert Arcminutes to Degrees

1. Start with the angle measured in arcminutes.
2. Divide that number by 60.
3. Write the result in degrees.
4. Round the decimal only when the required precision allows it.

Worked Example: Convert 30 Arcmin to Degrees

Start with 30 arcmin and apply the formula:

30 arcmin ÷ 60 = 0.5 deg

Therefore, 30 arcmin equals 0.5 deg. This is also one-half of a degree.

Worked Example: Convert 90 Arcmin to Degrees

Divide the angle by 60:

90 arcmin ÷ 60 = 1.5 deg

Therefore, 90 arcmin equals 1.5 deg.

Worked Example: Convert 7 Arcmin to Degrees

Some values do not produce a terminating decimal:

7 arcmin ÷ 60 = 0.116666… deg

So, 7 arcmin equals exactly 7/60 deg, or approximately 0.1167 deg when rounded to four decimal places.

Arcminute to Degree Conversion Table

Each row applies the same rule: divide arcminutes by 60. Decimal degree values are rounded to four decimal places where needed.

Practical Uses of Arcminutes and Degrees

Arcminutes are useful when an angle is too small to express conveniently in whole degrees. They provide more detail without requiring a long decimal value.

• Astronomy: Apparent sizes and positions in the sky are often described using degrees and arcminutes.
• Navigation: Direction and position measurements may use degrees with smaller angular divisions.
• Cartography: Map coordinates and angular measurements can require arcminute-level precision.
• Optics: The apparent separation of objects and viewing angles may be measured in small angle units.
• Engineering and surveying: Precise alignment and directional measurements may use arcminutes when degrees are too broad.

For example, an angular measurement of 2 degrees and 30 arcminutes can be expressed entirely in degrees as 2.5 degrees. The 30 arcminutes contribute an additional 0.5 degree.

Converting Mixed Degrees and Arcminutes

An angle may sometimes be written using both degrees and arcminutes. Convert the arcminute portion first, then add it to the degree portion.

For an angle of 4 deg 15 arcmin:

15 arcmin ÷ 60 = 0.25 deg

4 deg + 0.25 deg = 4.25 deg

Thus, 4 deg 15 arcmin equals 4.25 deg.

Common Arcminute to Degree Conversion Errors

Multiplying Instead of Dividing

When converting arcminutes to degrees, divide by 60. Multiplying by 60 converts degrees into arcminutes, which is the reverse direction.

Forgetting That the Decimal Repeats

The value of 1 arcmin is exactly 1/60 deg. Its decimal form, 0.016666…, repeats. A rounded value such as 0.0167 deg is an approximation, not a change to the exact relationship.

Confusing Arcminutes with Degrees

An arcminute is smaller than a degree. A value such as 45 arcmin is not 45 degrees. It equals 0.75 deg.

Quick Accuracy Check

A useful mental check is to compare the arcminute value with 60. Values below 60 arcmin must convert to less than 1 deg. A value of exactly 60 arcmin must equal 1 deg, while values above 60 arcmin must produce more than 1 deg.

For instance, 20 arcmin is one-third of 60 arcmin, so it must equal one-third of a degree: 0.3333… deg.

Key Takeaway

The relationship is exact and straightforward: 1 arcmin = 1/60 deg. To convert any arcminute value to degrees, divide by 60, and keep the fractional form when maximum precision matters.

Save the formula deg = arcmin ÷ 60 for quick reference whenever a small angular measurement needs to be expressed in degrees.