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Angle Converter

Popular Angle unit conversions

Angle Converter — Convert Degrees, Radians, Gradians & More

Our free online Angle Converter lets you instantly convert between 14 units of angle — from everyday degrees and minutes to mathematical radians, surveying gradians, and navigational units. Whether you need to convert degrees to radians, radians to degrees, gradians to degrees, or minutes to degrees, this tool delivers instant and accurate results.

An angle is the measure of rotation between two rays from a common point. It is used in mathematics, physics, engineering, navigation, and astronomy. Common angle units include:

  • Degree (°): The most common unit. A full circle = 360°. Each degree = 60 arcminutes = 3,600 arcseconds.
  • Radian (rad): The SI unit. A full circle = 2π radians ≈ 6.2832 rad. Used in mathematics and physics.
  • Gradian / Gon (g): A full circle = 400 gradians. Each right angle = 100 grad. Used in surveying.
  • Arcminute ('): 1/60 of a degree. Used in navigation and astronomy.
  • Arcsecond (\"): 1/3600 of a degree. Used in precision astronomy and geodesy.
  • Military mil: 1/6400 of a full circle. Used in military range-finding and artillery.
  • Revolution, turn, circle: Each = 360°. Used in rotational measurements.

All conversions use mathematically exact definitions and high-precision arithmetic, suitable for mathematics, engineering, surveying, navigation, and astronomy.

Common Angle Conversion Reference

Here are the most frequently used angle conversions for quick reference:

  • 1 radian = 57.2958° (degrees) = 63.6620 gradians
  • 1 degree = 0.0174533 radians = 1.11111 gradians = 60 arcminutes = 3,600 arcseconds
  • 1 gradian (gon) = 0.9 degrees = 0.015708 radians
  • Full circle = 360° = 2π radians = 400 gradians = 1 revolution = 4 quadrants
  • Right angle = 90° = π/2 radians = 100 gradians = 1 quadrant
  • Straight angle = 180° = π radians = 200 gradians
  • 1 arcminute = 0.016667° = 0.000291 radians
  • 1 arcsecond = 0.000278° = 4.848 × 10⁻⁶ radians

Frequently Asked Questions — Angle Converter

Question: How do I use the Angle Converter?

Answer: Select the unit you are converting from in the left list and the unit to convert to in the right list, then type your value. The result appears instantly across all listed units.

Question: How do I convert degrees to radians?

Answer: Multiply the degrees by π/180 (approximately 0.0174533). For example, 90° × π/180 = π/2 ≈ 1.5708 radians. To convert radians to degrees, multiply by 180/π (approximately 57.2958).

Question: What is a radian?

Answer: A radian is the SI unit of angle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is 2π radians ≈ 6.2832 rad. Radians are the natural unit of angle in mathematics and physics because they simplify many formulas.

Question: What is a gradian?

Answer: A gradian (also gon or grade, symbol g) divides a right angle into 100 parts and a full circle into 400 parts. It was developed during the French Revolution as part of the metric system. 1 gradian = 0.9 degrees = π/200 radians. Gradians are used primarily in surveying.

Question: What is the difference between arcminutes and arcseconds?

Answer: An arcminute (denoted ') is 1/60 of a degree. An arcsecond (denoted ") is 1/60 of an arcminute, or 1/3600 of a degree. These are used in navigation, astronomy, and geodesy. For example, 1° = 60' = 3,600".

Question: How many degrees are in a full circle?

Answer: A full circle contains exactly 360 degrees, which equals 2π radians, 400 gradians, 1 revolution, 4 quadrants, or 6 sextants.

Question: What is a mil in angle measurement?

Answer: A military mil (or mrad-based mil) is 1/6400 of a full circle, equal to 0.05625 degrees. It is used in military applications for range-finding and artillery because at 1,000 meters range, 1 mil corresponds to approximately 1 meter of width.

Question: What is the difference between a radian and a degree?

Answer: Radians are the mathematically natural unit (derived from the ratio of arc length to radius) while degrees are a historical convention that divides a circle into 360 parts. 1 radian ≈ 57.296°. Radians are preferred in calculus and physics; degrees are used in everyday contexts.

Question: How accurate are the angle conversions in this tool?

Answer: All conversions use mathematically exact definitions and constants with up to 12 significant digits of precision, suitable for engineering, surveying, navigation, astronomy, and mathematical applications.