Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, and turns.
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About this calculator
Angles come in degrees for everyday use, radians for mathematics and physics, gradians for surveying, and arcminutes and arcseconds for navigation and astronomy. This converter handles all of them, plus turns and milliradians.
One full circle is 360 degrees, 2π radians, 400 gradians or 1 turn. The table lists your angle in every unit at once.
How to use it
- Type the Value.
- Choose the From and To units.
- Read the result and the table.
Factors
180° = π rad, so 1 rad = 57.29578°. 1 grad = 0.9°, 1′ = 1/60°, 1″ = 1/3600° and 1 turn = 360°.
Worked example
Examples
| 90° | 1.5708 rad, 100 grad |
| 45° | 0.7854 rad |
| π radians | 180° |
| 1° | 60′ = 3,600″ |
Tips and common mistakes
- Calculators and programming languages work in radians. Check the mode before using trig functions.
- π/2 is a right angle, π a straight line and 2π a full turn.
- Latitude and longitude use degrees, minutes and seconds.
- A gradian makes a right angle exactly 100.
- Multiply degrees by π/180 to get radians.
Frequently asked questions
How many degrees in a radian?
57.29578.
How many radians in a degree?
0.01745329.
How many arcseconds in a degree?
3,600.
What is a gradian?
One hundredth of a right angle, 0.9 degrees.
Why do mathematicians use radians?
They make calculus formulas simpler.
How many degrees in a turn?
360.