Trigonometry Calculator Radians to Degrees

Convert radians to degrees with our precise trigonometry calculator. Learn the conversion formula, see examples, and understand when to use radians vs degrees.

Conversion Formula

The relationship between radians and degrees is defined by the formula:

Degrees = Radians × (180/π)

This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, one radian equals 180/π degrees.

Conversely, to convert degrees to radians, you use:

Radians = Degrees × (π/180)

When to Use Radians vs Degrees

Both radians and degrees are used in trigonometry, but each has its advantages depending on the context:

Degrees are more intuitive for everyday measurements and are commonly used in navigation, geography, and construction.
Radians are the natural unit of angular measurement in calculus and higher mathematics. They simplify many trigonometric formulas and identities.

In physics and engineering, radians are often preferred because they make calculations involving rotation and circular motion more straightforward.

Conversion Examples

Let's look at some practical examples of converting radians to degrees:

Radians	Degrees	Example
π/2	90°	Right angle
π	180°	Straight angle
3π/2	270°	Three-quarters of a circle
2π	360°	Full circle

For non-standard angles, you can use our calculator to get precise conversions.

Common Angle Conversions

Here are some common angle conversions between radians and degrees:

Radians	Degrees
0.5	28.6479°
1.0	57.2958°
1.5	85.9437°
2.0	114.5916°
2.5	143.2394°
3.0	171.8873°

These values are rounded to 4 decimal places for practical use.

Frequently Asked Questions

How do I convert radians to degrees?

To convert radians to degrees, multiply the radian value by 180/π. For example, π/2 radians × 180/π = 90 degrees.

When should I use radians instead of degrees?

Radians are preferred in calculus and higher mathematics because they simplify many trigonometric formulas and identities. Degrees are more intuitive for everyday measurements.

What is the difference between a radian and a degree?

A radian is the angle created when the radius of a circle is wrapped around its circumference. A degree is 1/360th of a full circle. There are approximately 57.2958 degrees in one radian.

Can I convert degrees to radians with this calculator?

Yes, our calculator can convert both radians to degrees and degrees to radians. Simply select the appropriate conversion direction in the calculator controls.