Angle Converter

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

Common Angle Conversions
FromToResult
π rad (3.14159…)Degrees180°
1 radDegrees57.2958°
90°Radiansπ/2 ≈ 1.5708 rad
360°Radians2π ≈ 6.2832 rad
1 TurnDegrees360°
100 gradDegrees90°
1°Arcminutes60'
1'Arcseconds60"

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.

Multiply degrees by π/180 to get radians. Key values to memorize: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π. To convert radians to degrees, multiply by 180/π ≈ 57.2958. Radians are the natural unit for mathematics and physics.

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

A full circle equals: 360 degrees, 2π radians (≈6.2832), 400 gradians, 6,400 milliradians (NATO standard), and 21,600 arcminutes. The degree was historically chosen because 360 has many divisors (24 of them), making it easy to divide a circle into equal parts without fractions.

A right angle (90°) equals π/2 radians ≈ 1.5708 rad. This is one of the most important values in mathematics and trigonometry. sin(π/2) = 1, cos(π/2) = 0. In geometry, a right angle is the angle between two perpendicular lines, and it defines the standard orientation used in coordinate systems.

Navigation uses bearings measured in degrees clockwise from north (0° = north, 90° = east, 180° = south, 270° = west). GPS coordinates use degrees, minutes, and seconds (DMS) for latitude and longitude. Aircraft headings are given as three-digit degree bearings (e.g., "heading 270" means flying west).

Arcminutes (') and arcseconds (") are subdivisions of a degree: 1° = 60' = 3,600". They are used in astronomy (star positions, telescope angular resolution), GPS and mapping (latitude/longitude precision), and optometry (visual acuity — 20/20 vision resolves details at 1 arcminute). One arcsecond of latitude ≈ 31 meters on Earth's surface.

About This Angle Converter

This free angle converter instantly converts between degrees, radians, gradians, arcminutes, and arcseconds. Enter a value in any unit and all others update simultaneously.

When to use this converter

  • Converting radians to degrees for trigonometry and programming
  • Working with navigation or astronomy angular coordinates
  • Converting between DMS (degrees–minutes–seconds) and decimal degrees

Standards & References

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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