Degree (°) Angle Conversion Calculator

Degree Conversion Calculator

Enter a value in degrees below to convert to another unit of angle.

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What is a Degree?

A degree is a unit used to measure angle.

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 arcminutes and arcseconds as an alternative to using the decimal form. Arcminutes and arcseconds are expressed using the prime (′) and double-prime (″) characters, respectively, although a single-quote and double-quote are often used for convenience.

One arcminute is equal to 1/60th of a degree, and one arcsecond is equal to 1/60th of an arcminute.

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.

How Much is a Degree?

A degree is a measure of angle equal to 1/360th of a revolution, or circle.^[1] 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.

How to Convert Degrees

To convert degrees to another unit of angle, you need to multiply the value by a conversion factor. A conversion factor is a numerical value used to change the units of a measurement without changing the value.^[2]

You can find the conversion factors for degrees in the conversion table below.

Then, multiply the angle measurement by the conversion factor to find the equivalent value in the desired unit of measurement.

degrees × conversion factor = result

You can also use a calculator, such as one of the converters below, for the conversion.

Degree 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)
1°	0.017453 rad	17.453293 mrad	60'	3,600"	1.111111^g	0.002778 r	0.002778 cir	17.777778 mil
2°	0.034907 rad	34.906585 mrad	120'	7,200"	2.222222^g	0.005556 r	0.005556 cir	35.555556 mil
3°	0.05236 rad	52.359878 mrad	180'	10,800"	3.333333^g	0.008333 r	0.008333 cir	53.333333 mil
4°	0.069813 rad	69.81317 mrad	240'	14,400"	4.444444^g	0.011111 r	0.011111 cir	71.111111 mil
5°	0.087266 rad	87.266463 mrad	300'	18,000"	5.555556^g	0.013889 r	0.013889 cir	88.888889 mil
6°	0.10472 rad	104.719755 mrad	360'	21,600"	6.666667^g	0.016667 r	0.016667 cir	106.666667 mil
7°	0.122173 rad	122.173048 mrad	420'	25,200"	7.777778^g	0.019444 r	0.019444 cir	124.444444 mil
8°	0.139626 rad	139.62634 mrad	480'	28,800"	8.888889^g	0.022222 r	0.022222 cir	142.222222 mil
9°	0.15708 rad	157.079633 mrad	540'	32,400"	10^g	0.025 r	0.025 cir	160 mil
10°	0.174533 rad	174.532925 mrad	600'	36,000"	11.111111^g	0.027778 r	0.027778 cir	177.777778 mil
11°	0.191986 rad	191.986218 mrad	660'	39,600"	12.222222^g	0.030556 r	0.030556 cir	195.555556 mil
12°	0.20944 rad	209.43951 mrad	720'	43,200"	13.333333^g	0.033333 r	0.033333 cir	213.333333 mil
13°	0.226893 rad	226.892803 mrad	780'	46,800"	14.444444^g	0.036111 r	0.036111 cir	231.111111 mil
14°	0.244346 rad	244.346095 mrad	840'	50,400"	15.555556^g	0.038889 r	0.038889 cir	248.888889 mil
15°	0.261799 rad	261.799388 mrad	900'	54,000"	16.666667^g	0.041667 r	0.041667 cir	266.666667 mil
16°	0.279253 rad	279.25268 mrad	960'	57,600"	17.777778^g	0.044444 r	0.044444 cir	284.444444 mil
17°	0.296706 rad	296.705973 mrad	1,020'	61,200"	18.888889^g	0.047222 r	0.047222 cir	302.222222 mil
18°	0.314159 rad	314.159265 mrad	1,080'	64,800"	20^g	0.05 r	0.05 cir	320 mil
19°	0.331613 rad	331.612558 mrad	1,140'	68,400"	21.111111^g	0.052778 r	0.052778 cir	337.777778 mil
20°	0.349066 rad	349.06585 mrad	1,200'	72,000"	22.222222^g	0.055556 r	0.055556 cir	355.555556 mil