Angle Measure Converter
Convert angles between degrees, radians, gradians and turns — plus arcminutes and arcseconds — with exact factors.
How it works
radians = value × factor(from) · result = radians ÷ factor(to) (180° = π rad · 1 turn = 2π rad · 400 gon = 1 turn)
Angles convert through the radian, the natural SI unit where a full circle is 2π. A degree is π/180 radians, a gradian (used in surveying) makes a right angle 100 gon so a full turn is 400 gon, and a turn is one full revolution. Arcminutes and arcseconds subdivide the degree into 60ths and 3600ths for fine astronomical and navigational work.
Worked example
Convert 180° to radians: 180 × (π/180) = π ≈ 3.14159 rad, half a full circle. The same angle is 200 gon or 0.5 turns.
Sources: Radian — Wikipedia
Frequently asked questions
How do I convert degrees to radians?
Multiply the degrees by π/180 (about 0.01745). So 90° = 90 × π/180 = π/2 ≈ 1.5708 rad. To go back, multiply radians by 180/π.
What is a gradian?
A gradian (or gon) divides a right angle into 100 parts, so a full circle is 400 gon. It is used in surveying and some European engineering because it fits the decimal system neatly.
What are arcminutes and arcseconds?
They subdivide a degree: one degree is 60 arcminutes, and one arcminute is 60 arcseconds. They are used for very small angles in astronomy, optics and navigation.
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This calculator is for educational purposes. Double-check important results before acting on them.