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Radian to Degree Converter

Enter the value that you want to convert radian (rad) to degree (°) or degree to radian.Also written as RAD to ° conversion.

1 radian = 57.2957795 degree

Formula: degree = radian value × 57.2957795

RAD to ° — radian to degree

rad
572.95780°

10 radian = 572.95780 degree

Popular Degree Converters:

radians to degreesdegrees to radians

Radians to Degrees for Visualization

When presenting angular results to users or debugging rotation issues, converting radians back to degrees makes values human-readable. An angle of 1.5708 radians is meaningless at a glance, but 90° is immediately understood. This conversion is essential when reading output from atan2() functions, interpreting gyroscope sensor data on mobile devices, or displaying compass headings calculated from GPS coordinates.

How Radian Relates to Degree

The Radian: History & Usage

The radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

Adopted as the SI unit of angular measure, the radian makes calculus and physics equations significantly simpler because it eliminates conversion constants. One full revolution equals 2π radians (≈ 6.2832 rad). Radians are essential in signal processing, robotics, computer graphics (3D rotations), oscillation analysis, and any domain where angular velocity or frequency calculations are performed.

What is Degree?

Dating back to ancient Babylonian astronomy, the degree divides a full rotation into 360 equal parts.

The Babylonians used a base-60 number system and observed that the sun moved approximately one degree per day across the sky over a year. The 360° circle became universal in navigation, surveying, architecture, and education. Degrees remain the standard angle unit in everyday life — from compass bearings and map coordinates to smartphone screen rotation and camera field-of-view specifications.

Why Angle Conversions Matter

Angle conversions bridge the gap between everyday measurement (degrees) and mathematical computation (radians). A mechanical engineer designing a robotic arm needs radians for inverse kinematics. A pilot reads compass headings in degrees. A surveyor might work in gradians. Game developers convert between degrees (artist-friendly) and radians (GPU shaders) hundreds of times per frame. Understanding these conversions is essential across STEM fields, navigation, and digital media production.

radian to degree metric conversion table

0.01 rad=0.57296 °
0.1 rad=5.72958 °
1 rad=57.29578 °
2 rad=114.59156 °
3 rad=171.88734 °
4 rad=229.18312 °
5 rad=286.47890 °
6 rad=343.77468 °
7 rad=401.07046 °
8 rad=458.36624 °
9 rad=515.66202 °
10 rad=572.95780 °
11 rad=630.25357 °
12 rad=687.54935 °
13 rad=744.84513 °
14 rad=802.14091 °
15 rad=859.43669 °
16 rad=916.73247 °
17 rad=974.02825 °
18 rad=1031.32403 °
19 rad=1088.61981 °
20 rad=1145.91559 °
30 rad=1718.87339 °
40 rad=2291.83118 °
50 rad=2864.78898 °
60 rad=3437.74677 °
70 rad=4010.70457 °
80 rad=4583.66236 °
90 rad=5156.62016 °
100 rad=5729.57795 °
200 rad=11459.15590 °
300 rad=17188.73385 °
400 rad=22918.31181 °
500 rad=28647.88976 °
600 rad=34377.46771 °
700 rad=40107.04566 °
800 rad=45836.62361 °
900 rad=51566.20156 °
1000 rad=57295.77951 °

How to Convert RAD to ° (Radian to Degree)?

We can convert radian to degree by using an example.

Example:

Convert 20 Radian to Degree?

We know 1 Radian = 57.2957795 degree; 1 Degree = 0.0174533 radian.

20 radian = ___°

20 × 57.2957795 = 1145.91559 ° (we know 1 radian = 57.2957795 degree)

Answer:

20 radian = 1145.91559 degree

How to Convert Radians to Degrees (Step-by-Step)

Since π radians equals 180°, converting radians to degrees requires multiplying by 180/π. Follow these steps:

  1. Write down the angle value in radians.
  2. Multiply the radian value by 180/π (approximately 57.2958).
  3. If the value is in terms of π (like 2π/3), cancel π first, then multiply by 180.
  4. The result is your angle in degrees.
💡 Tip: When the radian value contains π (like π/4 or 2π/3), the π cancels out and you just multiply the remaining fraction by 180. For example: π/4 × 180/π = 180/4 = 45°.

Common Radians to Degrees Conversions

These standard radian-to-degree values appear throughout trigonometry, calculus, and physics courses:

RadianDegree
π/6 rad30°
π/4 rad45°
π/3 rad60°
π/2 rad90°
2π/3 rad120°
π rad180°
3π/2 rad270°
2π rad360°
1 rad57.296°

Solved Examples

Question 1: Convert π/6 radians into degrees.

Solution:

Angle in degrees = Angle in radians × 180/π

= (π/6) × (180/π)

= 180/6 (the π cancels out)

Answer: π/6 radians = 30°

Question 2: Convert 2.5 radians to degrees.

Solution:

Angle in degrees = 2.5 × 180/π

= 2.5 × 57.2958

= 143.239°

Answer: 2.5 radians ≈ 143.24°

Question 3: Convert 3π/4 radians to degrees.

Solution:

Angle in degrees = (3π/4) × (180/π)

= (3 × 180) / 4 (π cancels)

= 540/4

Answer: 3π/4 radians = 135°

Question 4: Find the value of 1 radian in degrees, minutes and seconds.

Solution:

1 radian = 180/π ≈ 57.2958°

Decimal part: 0.2958° × 60 = 17.748′

Decimal part: 0.748′ × 60 = 44.88″

Answer: 1 radian ≈ 57° 17′ 45″

Question 5: Convert −π/3 radians to degrees.

Solution:

Angle in degrees = (−π/3) × (180/π)

= −180/3 (π cancels, negative sign preserved)

Answer: −π/3 radians = −60°

Practice Questions

Try solving these on your own to test your understanding:

  1. Convert 5π/6 radians to degrees. (Answer: 150°)
  2. How many degrees is 4 radians? (Answer: ≈ 229.18°)
  3. Convert 7π/4 radians to degrees. (Answer: 315°)
  4. Express 0.5 radians in degrees. (Answer: ≈ 28.65°)
  5. What is 11π/6 in degrees? (Answer: 330°)
  6. Convert −3π/2 radians to degrees. (Answer: −270°)

Understanding Radian Measure Intuitively

One radian is the angle created when you wrap the radius of a circle along its circumference. Since the circumference is 2πr, exactly 2π radians (≈ 6.283 radians) fit in a full circle. This makes 1 radian approximately 57.3° — larger than people typically expect. When you see an angle of 1.5 radians, think "just under a right angle" (it's about 86°).

Why Calculators Sometimes Give Wrong Answers

A common source of errors: scientific calculators have a DEG/RAD mode switch. If your calculator is set to degrees mode but you enter a radian value into sin() or cos(), you'll get incorrect results. Always verify your calculator mode matches your angle unit. On smartphone calculators, this setting is often hidden in the scientific mode options.

Radians in Degrees, Minutes, and Seconds (DMS)

To express a radian value in DMS format: First convert to decimal degrees (multiply by 180/π). Then take the decimal part and multiply by 60 to get minutes. Take the decimal part of minutes and multiply by 60 to get seconds. For example: 1 rad = 57.2958° = 57° + 0.2958×60′ = 57° 17.748′ = 57° 17′ + 0.748×60″ = 57° 17′ 44.9″.

Key Takeaways

  • Multiply radians by 180/π (≈ 57.2958) to get degrees.
  • When radians are expressed with π, cancel π first: (π/3) × (180/π) = 60°.
  • 1 radian ≈ 57.296° = 57° 17′ 45″.
  • Check your calculator is in the correct mode (DEG vs RAD) before computing.
  • A full circle = 2π rad = 360°, so π rad = 180° is the key relationship.
  • Negative radians convert the same way — the sign indicates clockwise rotation.

Radian to Degree Conversion Formula

degree = radian × 57.2957795

1 radian = 57.2957795 degree

1 degree = 0.0174533 radian

Reverse: radian = degree × 0.0174533

Frequently Asked Questions

How many degree are in 1 radian?

There are 57.2957795 degree in 1 radian. To convert radian to degree, multiply the value by 57.2957795.

How do I convert radian to degree?

Multiply your radian value by 57.2957795 to get the equivalent in degree. For example, 5 radian = 5 × 57.2957795 = 286.47890 degree.

How do I convert degree to radian?

Multiply your degree value by 0.0174533 to get the equivalent in radian. Alternatively, divide by 57.2957795.

What is 10 radian in degree?

10 radian is equal to 572.95780 degree.

What is 100 radian in degree?

100 radian is equal to 5729.57795 degree.