Angle converter
This angle converter tool helps you convert between 38 different units:
Common angle units explained
Learn more about these commonly used angle units:
All possible angle conversions
Below, we provide an overview of all the angle conversions available on this website to help you navigate and utilize our resources efficiently.
What is an Angle?
An angle is a measure of the rotation between two intersecting lines or planes, typically expressed in degrees or radians. It is a fundamental concept in geometry, physics, and engineering, used to describe directions, orientations, and rotations.
Common Units of Angular measurement
Angles are measured using different units depending on the application and measurement system. Below are the most commonly used units:
| Unit | Symbol | Measurement System |
|---|---|---|
| Degree | ° | Common/Conventional |
| Radian | rad | SI (Metric System) |
| Gradian | gon | Metric System |
| Minute of Arc | ' | Astronomical/Navigation |
| Second of Arc | " | Astronomical/Navigation |
How are angles measured?
Angles are measured using tools such as protractors, theodolites, and digital angle finders. In mathematical calculations, angles are often expressed in radians, where 1 radian equals approximately 57.3 degrees.
Applications of angular measurement
- Architecture and engineering for structural design
- Navigation and astronomy for positioning and orientation
- Physics and mechanics to analyze motion and forces
- Computer graphics for 3D modeling and animation
FAQs
What is the difference between degrees and radians?
Degrees divide a full rotation into 360 parts, while radians measure angles in terms of the radius of a circle, with a full rotation equal to 2π radians.
What is the difference between radians and gradians?
Radians and gradians are two different angular measurement units. A full circle is 2π radians (≈ 6.2832 rad) or 400 gradians (gon). One radian is approximately 57.3 degrees, while one gradian is 0.9 degrees. Radians are widely used in mathematics and physics, whereas gradians are mainly used in surveying and engineering.
Why are there 360 degrees in a circle?
The 360-degree system originates from ancient Babylonian mathematics, which used a base-60 numbering system, making 360 a convenient number for calculations involving fractions and symmetry.
What is a negative angle?
A negative angle represents a rotation in the clockwise direction, whereas a positive angle represents a counterclockwise rotation.