Angle Calculator
Convert between degrees and radians and calculate complementary and supplementary angles with our easy-to-use angle calculator. This tool helps students, teachers, and professionals quickly convert angle measurements and understand angle relationships.
Common Angle Conversions
- 30° = π/6 ≈ 0.5236 rad
- 45° = π/4 ≈ 0.7854 rad
- 60° = π/3 ≈ 1.0472 rad
- 90° = π/2 ≈ 1.5708 rad
- 180° = π ≈ 3.1416 rad
Conversion Result: 0.7854 radians
Angle Relationships
Complementary Angle: 45° (0.7854 rad)
Supplementary Angle: 135° (2.3562 rad)
About Angle Measurement
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles are used in mathematics, physics, engineering, and many other fields to describe the orientation of lines, planes, and other geometric elements.
Angle Measurement Units
There are two main units used to measure angles:
- Degrees (°): A degree is a measurement of plane angle, representing 1/360 of a full rotation. Degrees are the most common unit for measuring angles in everyday applications.
- Radians (rad): A radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Radians are the standard unit of angular measure in mathematics.
Conversion Formula
The formulas to convert between these units are:
- From degrees to radians: radians = degrees × (π/180)
- From radians to degrees: degrees = radians × (180/π)
Angle Relationships
Angles have special relationships that are important in geometry:
Complementary Angles
Two angles are complementary when they add up to 90 degrees (π/2 radians). For example, 30° and 60° are complementary angles.
Supplementary Angles
Two angles are supplementary when they add up to 180 degrees (π radians). For example, 45° and 135° are supplementary angles.
Reference Angles
A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. It's always between 0° and 90° (0 and π/2 radians).