Convert Radians to Degrees

To convert radians to degrees, use the radians-to-degrees formula:

• Degrees = Radians × 180 ÷ π

This works because π radians = 180 degrees.
Steps: take your radian value, multiply by 180, then divide by π.

Common reference values:

• π/6 rad = 30°
• π/4 rad = 45°
• π/3 rad = 60°
• π/2 rad = 90°
• π rad = 180°
• 2π rad = 360°

What’s the difference between radians and degrees?

Radians and degrees are two ways to measure angles. Degrees split a full turn into 360 equal parts. Radians measure angles by using the radius of a circle. One full turn equals (2\pi) radians.

How do you convert radians to degrees?

Use this formula: [ \text{degrees}=\text{radians}\times\frac{180}{\pi} ] Multiply the radian value by 180, then divide by (\pi).

Why does the radian to degree formula use (180/\pi)?

A half-turn is 180 degrees. That same half-turn is (\pi) radians. Since (180^\circ=\pi) radians, the conversion factor becomes (180/\pi).

What is 1 radian in degrees?

1 radian equals: [ 1\times\frac{180}{\pi}\approx57.2958^\circ ] So 1 radian is about (57.3^\circ).

What are common radian values in degrees?

Here are some quick conversions many people use:

• (\pi/6) rad = (30^\circ)
• (\pi/4) rad = (45^\circ)
• (\pi/3) rad = (60^\circ)
• (\pi/2) rad = (90^\circ)
• (\pi) rad = (180^\circ)
• (2\pi) rad = (360^\circ)

How do you convert radians to degrees without a calculator?

Use known (\pi) fractions when you can. If the value is a multiple of (\pi), convert by matching it to common angles (like (\pi/2 = 90^\circ)). For other values, you can estimate by using ( \pi \approx 3.14 ) and then apply: [ \text{degrees}\approx\text{radians}\times57.3 ]

How do you convert negative radians to degrees?

Convert the same way: [ \text{degrees}=\text{radians}\times\frac{180}{\pi} ] A negative angle in radians becomes a negative angle in degrees. Example: [ -\pi/3 \text{ rad} = -60^\circ ]

How do you convert radians to degrees in terms of (\pi)?

If the angle is written with (\pi), multiply the fraction by 180. Example: [ \frac{3\pi}{4}\text{ rad}=\frac{3}{4}\times180^\circ=135^\circ ] The (\pi) cancels out when you multiply by (180/\pi).

Are radians and degrees both used in trigonometry?

Yes. Degrees are common in basic geometry and many real-world angle measures. Radians are common in trigonometry, calculus, and physics because many formulas work best in radians.

Do I need to use radians or degrees for sine, cosine, and tangent?

It depends on the setting and the formula. Many math formulas (especially in calculus) assume radians. Some tools and classes use degrees by default. Check your mode or settings before you calculate.

What is the quickest way to estimate radians to degrees?

Multiply by (57.3) for a fast estimate: [ \text{degrees}\approx\text{radians}\times57.3 ] This works well for quick checks and rough answers.

What does (2\pi) radians equal in degrees?

(2\pi) radians equals one full turn: [ 2\pi\times\frac{180}{\pi}=360^\circ ] So (2\pi) radians is (360^\circ).