Angle in Degrees and Minutes Calculator

An angle in degrees and minutes is a way to express angular measurements with greater precision than just degrees alone. This calculator helps you convert between these units and understand how they work in practical applications.

What is an angle in degrees and minutes?

The degree (symbol: °) is a unit of angular measurement equal to 1/360 of a full circle. A minute of arc (symbol: ′) is 1/60 of a degree. This means there are 60 minutes in one degree. This system allows for more precise angle measurements than degrees alone, which is particularly useful in fields like astronomy, navigation, and surveying.

For example, 30° 30′ means 30 degrees plus 30 minutes of arc, which is equivalent to 30.5 degrees.

Angles in degrees and minutes are commonly used in:

Navigation and cartography
Astronomical observations
Land surveying
Engineering measurements
Photography (for precise camera angles)

How to convert between degrees and minutes

Degrees to Degrees and Minutes

To convert a decimal degree to degrees and minutes:

Take the decimal part of the degree (after the decimal point)
Multiply by 60 to get the minutes
Keep the whole number part as degrees

Degrees = floor(decimal degrees)

Minutes = (decimal degrees - Degrees) × 60

Degrees and Minutes to Degrees

To convert degrees and minutes to decimal degrees:

Divide the minutes by 60
Add this value to the degrees

Decimal degrees = Degrees + (Minutes ÷ 60)

Examples of angle conversions

Example 1: Converting 45.75 degrees to degrees and minutes

Using the formula:

Degrees = floor(45.75) = 45°

Minutes = (45.75 - 45) × 60 = 0.75 × 60 = 45′

So, 45.75° is equal to 45° 45′.

Example 2: Converting 30° 20′ to decimal degrees

Using the formula:

Decimal degrees = 30 + (20 ÷ 60) = 30 + 0.333... = 30.333...

So, 30° 20′ is approximately 30.333°.

FAQ

Why use degrees and minutes instead of just decimal degrees?: Degrees and minutes provide a more intuitive way to express angles, especially for measurements that don't require the precision of decimal degrees. They're commonly used in fields like navigation and astronomy where traditional angle measurement systems are still in use.
How many minutes are in a degree?: There are exactly 60 minutes in one degree. This is based on the original Babylonian sexagesimal system.
Can I convert degrees and minutes to seconds?: Yes, you can further break down minutes into seconds. There are 60 seconds in one minute, so 1° = 60′ = 3600″.
What's the difference between degrees and degrees of arc?: Degrees and degrees of arc are essentially the same measurement. The term "of arc" is sometimes used to distinguish angular degrees from temperature degrees.