Degrees Conversion

The degree is a unit used to measure angle. Use one of the conversion calculators below to convert to another unit of measure, or read on to learn more about degrees.

Degree Conversion Calculators

Choose a unit of angle to convert to.

Convert degrees to radians

1 degree is equal to 0.017453 radians

Convert degrees to milliradians

1 degree is equal to 17.453293 milliradians

Convert degrees to minutes of arc

1 degree is equal to 60 minutes of arc

Convert degrees to seconds of arc

1 degree is equal to 3,600 seconds of arc

Convert degrees to gradians

1 degree is equal to 1.111111 gradians

Convert degrees to revolutions

1 degree is equal to 0.002778 revolutions

Convert degrees to circles

1 degree is equal to 0.002778 circles

Convert degrees to mils (NATO)

1 degree is equal to 17.777778 mils (NATO)

Convert degrees, minutes, and seconds to degrees decimal

1° 00' 00" can be expressed as 1°

Convert degrees decimal to degrees, minutes, and seconds

1° can be expressed as 1° 00' 00"

Degree Definition and Usage

A degree is a measure of angle equal to 1/360th of a revolution, or circle. The number 360 has 24 divisors, making it a fairly easy number to work with. There are also 360 days in the Persian calendar year, and many theorize that early astronomers used 1 degree per day.

The degree is an SI accepted unit for angle for use with the metric system. A degree is sometimes also referred to as a degree of arc, arc degree, or arcdegree. Degrees can be abbreviated as °, and are also sometimes abbreviated as deg. For example, 1 degree can be written as 1° or 1 deg.

Degrees can also be expressed using minutes and seconds as an alternative to using the decimal form. Minutes and seconds are expressed using the prime (′) and double-prime (″) characters, although a single-quote and double-quote are often used for convenience.

One minute is equal to 1/60th of a degree and one second is equal to 1/60th of a minute.

Protractors are commonly used to measure angles in degrees. They are semi-circle or full-circle devices with degree markings allowing a user to measure an angle in degrees. Learn more about how to use a protractor or download a printable protractor.

Background and Origin

Although the true origin of the degree is not certain, it likely originated in Babylonian astronomy. Babylonian, and later Greek, astronomers observed that stars advance about 1/360th of their circular path in the sky every night. They also divided the ecliptic, or circle representing the path of the sun, into 360 parts.

Another common theory is that degrees originated out of the Persian calendar, which is made up of 360 days in the year. 360 is also very close to the 365 actual days in a year and 354 average number of days in the luni-solar year.

Regardless of the origin, the number 360 is an easy number to use mathematically, which makes it appealing to use. The appeal comes from the fact that the number 360 has 24 divisors.

Uses

Degrees are a very widely used unit of angular measure, and are used in managed fields. Though the degree is not an SI unit, it is accepted for use as a measure of angle.