Angle converter
Convert angles between degrees, radians, gradians and full turns. Example: 180 degrees is 3.141593 rad; 90 degrees is 100 grad; 1 turn is 360 degrees.
What to know
The angle page converts four units: degree, radian, gradian and turn. Values pass through degrees using 1 rad = 180/pi degrees (about 57.29578), 1 grad = 0.9 degrees and 1 turn = 360 degrees.
Worked examples: 180 degrees is exactly pi, shown as 3.141593 rad; 90 degrees is 100 grad; a full turn is 360 degrees, 400 grad and 6.283185 rad. Going the other way, 0.5 rad is 28.64789 degrees.
Radians matter for trigonometric functions in programming, since most languages expect sine and cosine arguments in radians. Gradians appear in surveying and some calculators, and turns are common in CSS rotations and animation.
There are no arcminutes or arcseconds, so a coordinate such as 12 degrees 30 minutes must be written as 12.5 degrees first. The default pair is degrees to radians.
Common benchmarks are worth memorising: 30 degrees is pi/6 or 0.523599 rad, 45 degrees is 0.785398 rad, 60 degrees is 1.047198 rad and 90 degrees is 1.570796 rad. Compass work and slope calculations also use degrees, while CSS rotations accept deg, rad, grad and turn directly. Each value is an exact multiple of pi, rounded only at the sixth decimal.
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How to use Angle converter
- Type 180 in the Value field.
- Select deg in From and rad in To.
- Read the Result line, which shows 3.141593 rad.
- Switch To to grad to see 200 grad for the half circle.
Quick answers
How many degrees is one radian?
About 57.29578 degrees, from 180 divided by pi. Select rad to deg and enter 1.
What is 0.25 turn in degrees?
90 degrees. Multiply the turn count by 360.
Can I enter degrees, minutes and seconds?
No. Convert minutes by dividing by 60, so 12 degrees 30 minutes becomes 12.5, and type that decimal value.