Q&A for How to Convert Degrees to Radians

Simply: π=180 or π=180*1 degree and therefore, 1degree= π/180, thus, degree measure= radian measure * π/180.

First convert the angle to a decimal. There are 60 seconds in a minute, 60 minutes in a degree, and 3600 seconds (60 x 60) in a degree. 14 minutes 51 seconds equals 891 seconds, which is 891/3600 of a degree or .2475 degree. For simplicity, let's call that ¼ of a degree. Therefore, the angle in question is 63¼ degrees. As shown in the above article, 63¼° multiplied by (π/180) = 1.1 radians.

1085° = 6.0277 radians. 1080° is equivalent to three complete circles, 1085° is the same angle as 5° and 0.0277 radian.

Multiply the number of radians by 180°. For example, 2 radians equal 360°. 5 radians equal 900°.

In general, multiply degrees by 0.0175 to get radians (1,691.25 radians in this case). If you prefer to treat multiple full circles (as in this case) as less than a full circle, first divide the total degrees by 360 (the number of degrees in a full circle). 22,550 divided by 360 is 62 with a remainder of 230, which is the number of degrees beyond 62 full circles contained in 22,550°. Multiply 230 by 0.0175 to get the radians in one partial circle.

That just means the angle is being measured in a counter-clockwise direction, but the size of the angle (whether measured in degrees or radians) is the same as if it were positive.

Since 90° is ¼ of a circle, it's also ¼ of 2π radians, or (π/2) radians.

Because sometimes a fraction is easier to work with than a decimal is, and 22/7 is the fraction that most closely approximates the value of pi.

Multiply each π radian by 180°. 3 x 180° = 540°. That's 1½ full circles, which for practical purposes is equivalent to one half-circle.

48° × π/180 = 0.8378 rad.

(1°)(π radians / 180°) = 3.14 radians / 180 = 0.0174 radian.

Multiply 48 radians by (180 / pi). 180 / pi = 180 / 3.14159, which equals 57.3). (48)(57.3) = 2750.67 degrees.

450 x pi/180 = 45 x pi /18 = 5 x pi/2 = 5(3.14)/2. (3.14 is pi to 2 decimal places, it is irrational) = 7.85 radians.

You're referring to the angle Θ ("theta"), which in this case is 345°. (345°)(π/ 180°) = 1.92 radians.

The process remains the same, although the numbers may be more awkward. You still reduce the fraction to simplest terms. For example, while 120° converts to (2π/3) radians, 120.5° converts to (120.5π/180) = (241π/360) radians.

Multiply the number of degrees by 60 to get the number of minutes. Divide the number of minutes by 60 to get the number of degrees. Thus, there are 120 minutes in 2 degrees, and there are 5 degrees in 300 minutes.

See Calculate the Radius of a Circle .

To convert 205° to radians, multiply 205° by 2π/180°. The answer is approximately 7.15 radians.

Multiply 70 degrees by π/180 degrees. The degrees cancel, so you are left with 70/180 x π, or 7π/18.

See Convert Celsius (°C) to Fahrenheit (°F) .

A circle always has exactly 2pi radians. If you want the measure of its perimeter in milllimetres, then just note that 1 radian is half the diameter or 7mm, so 2pi radians is 2(3.14)(7mm) or thereabouts depending on what approximation you use for pi.

1 degree =π/180 radians, so if we suppose a number with π is'4π' then (4π)degree=(4π).π/180, by simplifying this equation we will get: π.π/45=22/7.22/7/45→(3.14).3.14/45=0.21950.