Degrees to Radians Converter
Convert degrees, or degrees, minutes and seconds, to radians as a decimal and as an exact multiple of pi, or convert radians back to degrees.
To convert degrees to radians, multiply by pi and divide by 180. 45 degrees is π/4 radians, about 0.7853981634, and 90 degrees is π/2, about 1.5707963268. To go back, multiply radians by 180 and divide by pi: 1 radian is about 57.2957795131 degrees.
Decimal results are rounded to the number of places you choose, using pi to 50 decimal places; the multiple of pi is exact wherever one is shown. Check the angle unit your calculator or software expects, since mixing degree and radian modes is a common source of wrong answers.
A minus sign on the degrees applies to the whole angle.
Radians
0.7853981634 rad
- As a multiple of pi
- π/4 rad
- Degrees
- 45°
- Degrees, minutes, seconds
- 45° 0′ 0.00″
- Radians
- 0.7853981634 rad
The multiple of pi is exact; decimals are rounded.
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About the Degrees to Radians Converter
A full turn is 360 degrees or 2π radians, so one degree is π/180 of a radian, the definition in the units guide credited below. Multiplying by π/180 gives the answer in two useful forms. As a multiple of pi, it is exact: 45 degrees is π/4 and 90 degrees is π/2, the forms textbooks use. As a decimal, it is rounded: 180 degrees is 3.1415926536 to ten places, and 1 degree is 0.0174532925. The converter keeps the degrees as an exact fraction, so a value like 12.5 degrees reduces to an exact multiple of pi as well. Survey, map and astronomy readings often come as degrees, minutes and seconds, with 60 minutes to a degree and 60 seconds to a minute. Enter the three parts and the converter adds them first: 12 degrees 30 minutes 15 seconds is 12.5041666667 degrees, or 0.2182388786 radians. Going the other way, type radians as a decimal or as a multiple of pi. pi/6 returns exactly 30 degrees and 0.5235987756 radians, while 1 radian returns 57.2957795131 degrees, which is 57° 17′ 44.81″. A decimal radian value can never equal a nonzero rational multiple of pi, because pi is irrational, so no pi form is shown for it.
Frequently asked questions
How do you convert degrees to radians?+
Multiply the degrees by pi and divide by 180. For 45 degrees that is 45 x π / 180 = π/4, which is about 0.7853981634 radians.
How do I write the answer in terms of pi?+
Divide the degrees by 180 and reduce the fraction, then put pi on top. 90/180 reduces to 1/2, so 90 degrees is π/2 radians, and 30/180 reduces to 1/6, so 30 degrees is π/6.
How do you convert radians to degrees?+
Multiply by 180 and divide by pi. pi/6 radians is 180/6 = 30 degrees exactly, and 1 radian is 180/π, about 57.2957795131 degrees.
How do I convert degrees, minutes and seconds to radians?+
First make decimal degrees: degrees + minutes/60 + seconds/3600. 12° 30′ 15″ is 12.5041666667 degrees. Then multiply by π/180 to get 0.2182388786 radians. The converter does both steps for you.
Degree, minute and second of plane angle in radians: NIST Special Publication 811, Guide for the Use of the International System of Units, chapter 5, Table 6.
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