Angle Converter

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

Value
From
To
1 Radian = — Degrees
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 for instant results.

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
  • Scope and optics calculations using milliradians

Standards & References

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