Common Angle Units
This converter supports commonly used units including:
- Degrees (°)
- Radians (rad)
- Gradians (grad)
- Arcminutes (′)
- Arcseconds (″)
- Revolutions (rev)
When to Convert Angle Units
Angle conversion is useful for geometry, trigonometry, navigation, surveying, engineering, machining, astronomy, and computer graphics. An online converter helps reduce manual calculation errors and makes it easier to compare values expressed in different units.
Angle Conversion FAQ
What is an angle?
An angle measures the amount of rotation between two rays that meet at a common point called the vertex. Angles are commonly measured in degrees, radians, or gradians.
What are the most common units used to measure angles?
The most common angle units are degrees (°), radians (rad), and gradians (gon or grad). Degrees are widely used in geometry and everyday measurement, while radians are commonly used in advanced mathematics, physics, and engineering.
How many degrees are in a complete turn?
One complete turn equals 360 degrees. A half turn equals 180 degrees, and a quarter turn equals 90 degrees.
What is a radian?
One radian is the angle formed at the center of a circle when the length of the intercepted arc equals the radius of the circle. One complete turn contains exactly 2π radians.
How are degrees and radians related?
180° = π radians. Therefore, one degree equals π/180 radians, and one radian equals 180/π degrees.
How do I convert degrees to radians?
Multiply the number of degrees by π/180. For example, 60° × π/180 = π/3 radians.
How do I convert radians to degrees?
Multiply the number of radians by 180/π. For example, π/4 radians × 180/π = 45°.
What are some common degree-to-radian conversions?
- 0° = 0 rad
- 30° = π/6 rad
- 45° = π/4 rad
- 60° = π/3 rad
- 90° = π/2 rad
- 180° = π rad
- 270° = 3π/2 rad
- 360° = 2π rad
What is a gradian?
A gradian divides a complete turn into 400 equal parts. A right angle equals 100 gradians, a straight angle equals 200 gradians, and a complete turn equals 400 gradians.
How do I convert degrees to gradians?
Multiply the number of degrees by 10/9. For example, 90° × 10/9 = 100 gradians.
How do I convert gradians to degrees?
Multiply the number of gradians by 9/10. For example, 50 gradians × 9/10 = 45°.
What is the difference between degrees and radians?
Degrees divide a complete turn into 360 parts, while radians measure angles using the relationship between a circle's radius and arc length. Both units describe the same amount of rotation.
Why are radians important in mathematics?
Radians connect angles directly to the geometry of a circle. Formulas involving arc length, angular velocity, calculus, and trigonometric functions are usually simplest when angles are measured in radians.
How do I calculate arc length from an angle?
When the angle is measured in radians, use the formula s = rθ, where s is the arc length, r is the radius, and θ is the angle in radians.
What is a positive or negative angle?
A positive angle usually represents counterclockwise rotation, while a negative angle represents clockwise rotation. For example, −90° represents a quarter turn clockwise.
Can two different angle measurements represent the same direction?
Yes. Coterminal angles differ by one or more complete turns. For example, 30°, 390°, and −330° all end in the same direction.
What are degrees, arcminutes, and arcseconds?
One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds. Therefore, 1° = 60′ = 3,600″. These units are commonly used in astronomy, navigation, and geographic coordinates.
How can I check whether an angle conversion is reasonable?
Compare the result with familiar angles. A right angle should equal 90°, π/2 radians, or 100 gradians. A straight angle should equal 180°, π radians, or 200 gradians.
Why might a converted angle contain many decimal places?
Conversions involving π often produce irrational decimal values. For example, one radian is approximately 57.2958 degrees, so the displayed answer may be rounded.