Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns instantly.
Result
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All conversions
What is Angle Converter?
An angle converter lets you switch between different units used to measure rotation and angular displacement. Degrees are the most familiar unit for everyday use and navigation. Radians are the natural unit in mathematics and physics. Gradians (used in surveying), arcminutes, arcseconds (used in astronomy and optics), and turns are also supported.
How to use
- 1 Enter the angle value in the Value field.
- 2 Select the source unit from the From dropdown.
- 3 Select the target unit from the To dropdown.
- 4 The result and a full conversion table appear instantly.
- 5 Use the swap button to reverse the conversion direction.
Formula
Example calculation
To convert 90 degrees to radians: 90 * (pi / 180) = pi/2 = approximately 1.5708 radians. To convert 1 radian to degrees: 1 * (180 / pi) = approximately 57.296 degrees.
Frequently asked questions
Why are radians used instead of degrees in mathematics?
Radians make trigonometric calculus formulas simpler and more natural. The derivative of sin(x) is cos(x) only when x is in radians. In degrees the formula requires a conversion factor. Most programming languages and calculators use radians by default in trig functions.
What is a gradian?
A gradian (also called gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. It was designed to simplify surveying calculations. It is used in some European surveying and civil engineering contexts.
How many arcseconds are in a degree?
One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds, so one degree equals 3600 arcseconds. Arcseconds are used in astronomy to express very small angular separations between stars or planets.
What is a turn in angle measurement?
One turn equals one full rotation, which is 360 degrees or 2*pi radians. Turns (also called revolutions or cycles) are used in engineering and physics when describing rotational motion, gear ratios, or angular frequency.
What is a milliradian used for?
A milliradian (mrad) is one thousandth of a radian, approximately 0.0573 degrees. It is widely used in military and long-range shooting for scope adjustments, as 1 mrad subtends approximately 10 cm at 100 metres.