Degrees Conversion

Protractors are often used to measure angle

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)
Related Calculators
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.

Degrees Measurement Conversion Table

Common degree values and equivalent imperial and metric angle measurements
degrees radians milliradians minutes of arc seconds of arc gradians revolutions circles mils (NATO)
0.017453 rad 17.453293 mrad 60' 3,600" 1.111111g 0.002778 r 0.002778 cir 17.777778 mil
0.034907 rad 34.906585 mrad 120' 7,200" 2.222222g 0.005556 r 0.005556 cir 35.555556 mil
0.05236 rad 52.359878 mrad 180' 10,800" 3.333333g 0.008333 r 0.008333 cir 53.333333 mil
0.069813 rad 69.81317 mrad 240' 14,400" 4.444444g 0.011111 r 0.011111 cir 71.111111 mil
0.087266 rad 87.266463 mrad 300' 18,000" 5.555556g 0.013889 r 0.013889 cir 88.888889 mil
0.10472 rad 104.719755 mrad 360' 21,600" 6.666667g 0.016667 r 0.016667 cir 106.666667 mil
0.122173 rad 122.173048 mrad 420' 25,200" 7.777778g 0.019444 r 0.019444 cir 124.444444 mil
0.139626 rad 139.62634 mrad 480' 28,800" 8.888889g 0.022222 r 0.022222 cir 142.222222 mil
0.15708 rad 157.079633 mrad 540' 32,400" 10g 0.025 r 0.025 cir 160 mil
10° 0.174533 rad 174.532925 mrad 600' 36,000" 11.111111g 0.027778 r 0.027778 cir 177.777778 mil
11° 0.191986 rad 191.986218 mrad 660' 39,600" 12.222222g 0.030556 r 0.030556 cir 195.555556 mil
12° 0.20944 rad 209.43951 mrad 720' 43,200" 13.333333g 0.033333 r 0.033333 cir 213.333333 mil
13° 0.226893 rad 226.892803 mrad 780' 46,800" 14.444444g 0.036111 r 0.036111 cir 231.111111 mil
14° 0.244346 rad 244.346095 mrad 840' 50,400" 15.555556g 0.038889 r 0.038889 cir 248.888889 mil
15° 0.261799 rad 261.799388 mrad 900' 54,000" 16.666667g 0.041667 r 0.041667 cir 266.666667 mil
16° 0.279253 rad 279.25268 mrad 960' 57,600" 17.777778g 0.044444 r 0.044444 cir 284.444444 mil
17° 0.296706 rad 296.705973 mrad 1,020' 61,200" 18.888889g 0.047222 r 0.047222 cir 302.222222 mil
18° 0.314159 rad 314.159265 mrad 1,080' 64,800" 20g 0.05 r 0.05 cir 320 mil
19° 0.331613 rad 331.612558 mrad 1,140' 68,400" 21.111111g 0.052778 r 0.052778 cir 337.777778 mil
20° 0.349066 rad 349.06585 mrad 1,200' 72,000" 22.222222g 0.055556 r 0.055556 cir 355.555556 mil