How do you convert radians to degrees?

To convert radians to degrees, multiply the radian value by 180/π (approximately 57. 2958). For example: 1) π rad = 180°, 2) π/2 rad = 90°, 3) π/4 rad = 45°. Our calculator handles this automatically.

What is 1 radian equal to in degrees?

1 radian equals approximately 57.2958 degrees (180/π degrees). This is a standard conversion used worldwide in mathematics and engineering. Common conversions include π radians = 180° and π/2 radians = 90°.

Why would I need to convert radians to degrees?

Converting radians to degrees is useful when: 1) Working with trigonometry problems, 2) Converting between mathematical notations, 3) Programming graphics or animations, 4) Working with engineering calculations.

What are the common angle measurements in radians and degrees?

Common angle measurements include: 1) Full circle: 2π rad = 360°, 2) Half circle: π rad = 180°, 3) Quarter circle: π/2 rad = 90°, 4) Eighth circle: π/4 rad = 45°.

Radians to Degrees Conversion Calculator

Radian (rad) to Degree (°) Converter

Symbol: rad (radians), ° (degrees)

What they are:

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A degree is 1/360 of a complete rotation. Both are units used to measure angles and rotations.

Conversion Facts:

1 radian = 57.2958 degrees
1 degree = 0.0174533 radians
π radians = 180 degrees
2π radians = 360 degrees

From:

Radian (rad)

To:

Degree (°)

Conversion Result

1 rad=

1.000 °

Use the converter above to calculate different values and units

What are Angle Measurements?

Angle measurements quantify the amount of rotation between two intersecting lines or planes. Radians and degrees are two standard units used for measuring angles, with radians being the preferred unit in mathematics and scientific calculations.

The relationship between radians and degrees is based on the properties of a circle: a complete circle spans 2π radians or 360 degrees. This relationship gives us the conversion factor: 1 radian equals 180/π degrees (approximately 57.2958°). This conversion is fundamental in trigonometry, calculus, physics, and engineering.

Common Radians to Degrees Conversions

Radians (rad)	Degrees (°)	Common Reference
π/6	30°	Angle in a 30-60-90 triangle
π/4	45°	Diagonal angle in a square
π/3	60°	Angle in an equilateral triangle
π/2	90°	Right angle
π	180°	Straight angle
3π/2	270°	Three-quarter circle
2π	360°	Full circle
1	57.2958°	One radian (standard unit)

Practical Use Cases

Mathematics: Solving calculus problems, trigonometric equations, and series expansions where radians are the natural unit
Physics: Calculating angular velocity, frequency, and wave properties in oscillations and waves
Engineering: Designing circular components, gears, and mechanical systems that involve rotational motion
Computer Graphics: Programming animations, rotations, and perspective transformations in 2D and 3D environments
Navigation: Converting between different coordinate systems and mapping applications
Astronomy: Measuring celestial angles, orbital mechanics, and telescope positioning

Educational Resource

This educational video explains the relationship between radians and degrees and demonstrates how to convert between these units with practical examples and applications.

Conversion Tools

Download Conversion Chart (PDF)

Get our comprehensive radians to degrees conversion chart for quick reference when you're offline.

Radians to Degrees Conversion FAQs

Find answers to common questions about converting between radians and degrees.