PhysicsCalcs
Units & Conversions

Angle Converter

Convert degrees to radians, radians to degrees, arcminutes, arcseconds, gradians, NATO mils, DMS, and more.

Interactive converter

Angle Converter

Convert degrees, radians, gradians, arcminutes, arcseconds, turns, compass points, milliradians, and NATO mils.

Angles may be negative or greater than one full circle. Military mils and milliradians are not identical.

From
To

Result

Enter a value and click Convert to see the conversion.

Quick Guide

  • Angles may be negative or exceed 360°.
  • Use the DMS panel for coordinate-style angles.
  • Check mil type — NATO mil ≠ milliradian.

Table of Contents

Key Takeaways

  • Radian is the SI coherent derived unit for plane angle.
  • 1 full circle = 360° = 2π rad = 400 gon.
  • 1° = 60 arcminutes = 3,600 arcseconds.
  • NATO mil (6400/circle), Soviet mil (6000), and Swedish mil (6300) differ from true milliradian.

What Is an Angle Converter?

It converts plane angles between degrees, radians, gradians, arc units, circle fractions, mils, and compass points using radians internally. Results show both radians and degrees.

For wave physics, see the Frequency to Wavelength Calculator. For distance measurements, use the Length Converter.

How to Use the Angle Converter

  1. 1Enter an angle (negative values and angles beyond 360° are allowed).
  2. 2Select from and to units, or use All units mode.
  3. 3Click Convert — the page scrolls to results showing rad and deg equivalents.
  4. 4Expand the DMS panel for decimal degrees ↔ degrees-minutes-seconds.
  5. 5Pick the correct mil system (NATO, Soviet, or Swedish) for navigation.

Angle and the Radian

θ=s/rθ = s / r

θ in radians, s = arc length, r = radius. A full circle = 2π rad.

Degrees and Radians

rad=deg×π/180rad = deg × π/180

180° = π rad; 90° = π/2 rad.

Degrees ↔ Radians Reference

DegreesRadiansNotes
30°π/6Common trig angle
45°π/4Right isosceles
90°π/2Right angle
180°πStraight angle
360°2πFull circle

Gradians, Gons, and Turns

1 circle = 400 gon. 1 turn = 360° = 2π rad.

Arcminutes and Arcseconds

1° = 60′ = 3600″. Used in astronomy, optics, and geodesy — not time units.

Military Mils and Milliradians

True mrad = 0.001 rad. NATO mil: 6400 per circle. Soviet mil: 6000 per circle. Swedish mil: 6300 per circle. They are close but not identical — select the correct system.

Decimal Degrees and DMS

decimal°=deg+min/60+sec/3600decimal° = deg + min/60 + sec/3600

Use the built-in DMS tool for coordinate conversion. Negative angles: apply sign to the whole angle, not just degrees.

Examples

180°

180° = π rad.

1°

1° = 60′ = 3600″.

100 gon

100 gon = 90°.

Common Mistakes

Confusing arcseconds with time seconds. Assuming mil always means milliradian. Forgetting calculators may need radians for trig functions.

Limitations

Mil conversions depend on system selected. DMS rounding can affect seconds carry. Not for certified surveying or artillery without verification.

FAQ

How do you convert degrees to radians?›

Multiply degrees by π/180. Example: 180° = π rad.

How many radians in a full circle?›

2π radians = 360°.

What is a gradian or gon?›

1 full circle = 400 gon; 1 right angle = 100 gon.

Are arcseconds the same as time seconds?›

No. Arcseconds measure angle; they are 1/3600 of a degree.

Is a military mil the same as a milliradian?›

No. NATO mil divides a circle into 6400; true mrad = 0.001 rad.

How do you convert radians to degrees?›

Multiply radians by 180/π. Example: π rad = 180°.

What is DMS?›

Degrees, minutes, seconds — a format for angles in coordinates and surveying.

Sources

  1. BIPM: SI Brochure
  2. NIST SP 811
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish