🔄 Angle Unit Converter
Convert angles between degrees, radians, gradians, and turns instantly. Perfect for mathematics, engineering, and physics calculations.
Understanding Angle Units
Angles are fundamental measurements in mathematics, physics, and engineering, representing the amount of rotation between two lines or rays. Different fields and applications use various units to measure angles, each with its own advantages and conventions. Understanding how to convert between these units is essential for working across different mathematical and scientific domains.
The most common angle units are degrees (used in everyday life and basic geometry), radians (preferred in calculus and physics), gradians (used in surveying and some European countries), and turns (used in computer graphics and rotational mechanics). Each unit system has historical and practical reasons for its adoption in specific fields.
Our angle converter provides instant, accurate conversions between all major angle units, including arc minutes and arc seconds for precise astronomical and navigational calculations. Whether you're a student learning trigonometry, an engineer designing mechanical systems, or a programmer working with graphics transformations, this tool ensures accurate angle conversions for your specific needs.
Convert Your Angle
Common Angle Conversions
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 | 33.33 | 1/12 |
| 45° | π/4 | 50 | 1/8 |
| 60° | π/3 | 66.67 | 1/6 |
| 90° | π/2 | 100 | 1/4 |
| 180° | π | 200 | 1/2 |
| 270° | 3π/2 | 300 | 3/4 |
| 360° | 2π | 400 | 1 |
Angle Unit Explanations
📐 Degrees
The most familiar angle unit, dividing a circle into 360 equal parts. Used in everyday life, navigation, and basic geometry. The choice of 360 comes from ancient Babylonian mathematics.
🎯 Radians
The natural unit of angular measure in mathematics. One radian equals the angle subtended by an arc equal to the radius. There are 2π radians in a circle. Essential for calculus and physics.
📊 Gradians
Also called grads or gons, divide a circle into 400 equal parts. Popular in surveying and some European countries. A right angle equals exactly 100 gradians, making mental calculations easier.
🔄 Turns
Also called revolutions or cycles. One turn equals a complete rotation (360°). Useful in describing rotational motion, frequency, and periodic phenomena in physics and engineering.
Frequently Asked Questions
Why are there different units for measuring angles?
Different angle units evolved for different purposes and in different cultures. Degrees (360 in a circle) originated with ancient Babylonian astronomers who used a base-60 number system. Radians emerged from pure mathematics as the natural unit for calculus and analysis. Gradians were created as a decimal-based system during the French Revolution's push for metric units. Turns are intuitive for describing rotational motion. Each unit has advantages in specific contexts, which is why multiple systems persist today.
When should I use radians instead of degrees?
Use radians for calculus, advanced mathematics, and physics calculations. Many mathematical formulas become simpler in radians - for example, the derivative of sin(x) is cos(x) only when x is in radians. Physics equations involving angular velocity, angular acceleration, and rotational dynamics typically use radians. Use degrees for navigation, basic geometry, everyday angle measurements, and when communicating with general audiences who are more familiar with degrees.
What are arc minutes and arc seconds used for?
Arc minutes (') and arc seconds (") are subdivisions of degrees used for extremely precise angular measurements. One degree equals 60 arc minutes, and one arc minute equals 60 arc seconds. These units are crucial in astronomy for measuring celestial positions and parallax, in surveying for precise land measurements, in navigation for GPS coordinates, and in optometry for measuring visual acuity. For example, the Moon's angular diameter as seen from Earth is about 31 arc minutes.