Angle Converter

Convert between degrees, radians, gradians, arcminutes, arcseconds, turns, and milliradians instantly.

Value

From

Common Angle Conversions

From	To	Result
π rad (3.14159…)	Degrees	180°
1 rad	Degrees	57.2958°
90°	Radians	π/2 ≈ 1.5708 rad
360°	Radians	2π ≈ 6.2832 rad
1 Turn	Degrees	360°
100 grad	Degrees	90°
1°	Arcminutes	60'
1'	Arcseconds	60"

Frequently Asked Questions

Multiply degrees by π/180 (≈ 0.017453). For example: 90° × π/180 = π/2 ≈ 1.5708 rad. To convert radians to degrees, multiply by 180/π (≈ 57.2958). A full circle = 360° = 2π radians.

A gradian (also called gon or grade) divides a right angle into 100 equal parts. So a full circle = 400 gradians, a right angle = 100 grad, and 180° = 200 grad. Gradians are used in surveying, civil engineering, and some European countries. 1 grad = 0.9° = π/200 radians.

An arcminute (') is 1/60 of a degree. An arcsecond (") is 1/60 of an arcminute = 1/3600 of a degree. They are used in astronomy (measuring star positions), GPS coordinates (latitude/longitude), and optics. 1° = 60' = 3,600". The angular resolution of the human eye is about 1 arcminute.

A milliradian (mrad) is 1/1000 of a radian. 1 mrad ≈ 0.0572958°. At 1 km distance, 1 mrad subtends approximately 1 meter. This property makes milliradians extremely useful in military targeting, firearms scopes, and precision optics where angular measurements correlate directly with distances.

How It Works

Enter Angle

Enter any angle value. All conversions use the degree as the internal base unit for angle measurement.

Select Units

Choose from degrees, radians, gradians, arcminutes, arcseconds, turns, and milliradians. Swap with one click.

Instant Result

Results appear instantly with the exact conversion factor. The reference table shows common angle equivalents.

Common Use Cases

Programming & Math

Convert between degrees and radians when working with trigonometric functions in code — most math libraries use radians by default.

Surveying & Navigation

Convert angles between degrees and gradians for land surveying, civil engineering, and GPS coordinate calculations.

Astronomy

Convert between arcminutes, arcseconds, and degrees for measuring star positions, angular diameters of celestial objects, and telescope fields of view.

Optics & Targeting

Convert between milliradians and degrees for scope adjustments, ballistics calculations, and precision optical instrument calibration.

Engineering & CAD

Convert rotation angles between degrees and radians for mechanical design, robotics, CNC machining, and CAD software input fields.

Education

Verify angle conversions for trigonometry, geometry, and precalculus homework. Understand the radian-degree relationship intuitively.

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