Angle Converter

Free Angle Converter — Convert Degrees, Radians, Gradians & More Instantly

Convert angles between any units instantly with OmniConverter's free online angle converter. Supports degrees (deg), radians (rad), grad (gradian), minutes of arc (arcmin), seconds of arc (arcsec), gon, sign, mil, revolution (r), circle, turn, quadrant, right angle, and sextant. Whether you're a mathematician, surveyor, astronomer, navigator, engineer, or student studying geometry and trigonometry, our converter delivers precise angle conversions in real time.

How It Works

Convert in three simple steps.

1

Enter the Angle Value

2

Select Source and Target Angle Units

3

View Your Converted Angle

Popular Conversions

Common Benchmarks

Reference

1 °°

1 °

Reference

1 °rad

0.0174532925 rad

Reference

1 °grad

1.1111111111 grad

Reference

1 °'

59.99999988 '

Reference

1 °"

3599.999712 "

Reference

1 °gon

1.1111111111 gon

Reference

1 °sign

0.0333333333 sign

Reference

1 °mil

17.7777777778 mil

Real-World Use Cases

Angle conversion is used in mathematics and geometry (solving trigonometric problems, converting between degrees and radians), surveying and civil engineering (bearing measurements, slope calculations, property boundary angles), astronomy and navigation (measuring celestial positions in arcminutes and arcseconds, GPS coordinates, sextant readings), military and defense (artillery targeting using mils, radar azimuth), architecture and construction (roof pitches, stair angles, structural load angles), physics and engineering (rotational motion, optics, wave phase angles), shooting sports and hunting (adjusting rifle scopes in mil-radians and MOA), and geographic information systems (map projection angles and bearings).

Frequently asked questions

Quick answers to common conversion questions

What is a degree?+

A degree (°) is a unit of angle where one full rotation equals 360 degrees. It is the most commonly used unit for measuring angles in everyday contexts.

What is a radian?+

A radian (rad) is the SI unit of angle, defined as the angle formed when the arc length equals the radius. One full rotation equals 2π radians (≈6.283 rad).

How do I convert degrees to radians?+

Multiply degrees by π/180 (≈0.0174533) to get radians. For example, 180° = π radians.

How do I convert radians to degrees?+

Multiply radians by 180/π (≈57.2958) to get degrees. For example, π/2 radians = 90°.

What is a gradian?+

A gradian (grad) divides a full circle into 400 units, so each right angle equals 100 gradians. It is used primarily in surveying and civil engineering.

What is the difference between a minute and a second of arc?+

A minute of arc (') is 1/60 of a degree. A second of arc (") is 1/60 of a minute or 1/3600 of a degree. They are used in astronomy and navigation.

What is a mil used for?+

A mil is a military angle unit used for artillery aiming and targeting. NATO uses 6400 mils per circle, where one mil ≈ 0.05625°.

How many degrees are in a revolution?+

One revolution (or full turn) equals exactly 360 degrees. A quadrant is 90° (one-fourth of a revolution), and a sextant is 60° (one-sixth of a revolution).

What is a right angle?+

A right angle is an angle of exactly 90 degrees, formed by two perpendicular lines. It is one of the fundamental concepts in geometry.

Can I convert between all angle units?+

Yes, all angle units are directly convertible using fixed mathematical relationships based on the full circle (360°).

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