Circle to Radian Converter
Enter the value that you want to convert circle (cir) to radian (rad) or radian to circle.Also written as CIR to RAD conversion.
1 circle = 6.2831853 radian
Formula: radian = circle value × 6.2831853
CIR to RAD — circle to radian
10 circle = 62.83185 radian
Popular Degree Converters:
Circle vs Radian
What is Circle?
The circle as an angular unit represents one complete revolution of 360°.
Used primarily in rotational mechanics and angular displacement, counting in "circles" simplifies problems involving multiple rotations. Wind turbine specifications, satellite orbits, and gear train calculations often express total angular displacement in full circles rather than degrees.
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.
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.
circle to radian metric conversion table
| 0.01 cir | = | 0.06283 rad |
| 0.1 cir | = | 0.62832 rad |
| 1 cir | = | 6.28319 rad |
| 2 cir | = | 12.56637 rad |
| 3 cir | = | 18.84956 rad |
| 4 cir | = | 25.13274 rad |
| 5 cir | = | 31.41593 rad |
| 6 cir | = | 37.69911 rad |
| 7 cir | = | 43.98230 rad |
| 8 cir | = | 50.26548 rad |
| 9 cir | = | 56.54867 rad |
| 10 cir | = | 62.83185 rad |
| 11 cir | = | 69.11504 rad |
| 12 cir | = | 75.39822 rad |
| 13 cir | = | 81.68141 rad |
| 14 cir | = | 87.96459 rad |
| 15 cir | = | 94.24778 rad |
| 16 cir | = | 100.53096 rad |
| 17 cir | = | 106.81415 rad |
| 18 cir | = | 113.09734 rad |
| 19 cir | = | 119.38052 rad |
| 20 cir | = | 125.66371 rad |
| 30 cir | = | 188.49556 rad |
| 40 cir | = | 251.32741 rad |
| 50 cir | = | 314.15927 rad |
| 60 cir | = | 376.99112 rad |
| 70 cir | = | 439.82297 rad |
| 80 cir | = | 502.65482 rad |
| 90 cir | = | 565.48668 rad |
| 100 cir | = | 628.31853 rad |
| 200 cir | = | 1256.63706 rad |
| 300 cir | = | 1884.95559 rad |
| 400 cir | = | 2513.27412 rad |
| 500 cir | = | 3141.59265 rad |
| 600 cir | = | 3769.91118 rad |
| 700 cir | = | 4398.22972 rad |
| 800 cir | = | 5026.54825 rad |
| 900 cir | = | 5654.86678 rad |
| 1000 cir | = | 6283.18531 rad |
How to Convert CIR to RAD (Circle to Radian)?
We can convert circle to radian by using an example.
Example:
Convert 20 Circle to Radian?
We know 1 Circle = 6.2831853 radian; 1 Radian = 0.1591549 circle.
20 circle = ___rad
20 × 6.2831853 = 125.66371 rad (we know 1 circle = 6.2831853 radian)
Answer:
20 circle = 125.66371 radian
Converting Circles to Radians
One circle equals 2π radians (≈ 6.2832). To convert:
- Write down the number of circles.
- Multiply by 2π (≈ 6.2832).
- The result is the angle in radians.
Solved Examples
Question 1: Convert 3 circles to radians.
Solution:
Radians = 3 × 2π
= 6π
≈ 18.85 rad
Answer: 3 circles = 6π ≈ 18.85 radians
Question 2: A flywheel rotates 0.5 circles. Express in radians.
Solution:
Radians = 0.5 × 2π
= π
≈ 3.1416 rad
Answer: 0.5 circles = π radians
Question 3: Angular displacement of 2.25 circles in radians?
Solution:
Radians = 2.25 × 2π
= 4.5π
≈ 14.14 rad
Answer: 2.25 circles = 4.5π ≈ 14.14 radians
Practice Questions
Try solving these on your own to test your understanding:
- Convert 10 circles to radians. (Answer: 20π ≈ 62.83 rad)
- A motor makes 0.25 circles. Radians? (Answer: π/2 ≈ 1.571 rad)
- Express 1.5 circles in radians. (Answer: 3π ≈ 9.425 rad)
Frequency and Angular Velocity
Frequency (f) in Hz means circles per second. Angular velocity (ω) in rad/s = f × 2π. A 60 Hz power supply completes 60 circles per second = 120π ≈ 377 rad/s. This relationship ω = 2πf is fundamental in electrical engineering, wave physics, and signal processing.
Key Takeaways
- Multiply circles by 2π (≈ 6.2832) to get radians.
- ω = 2πf converts frequency (circles/s) to angular velocity (rad/s).
- 1 circle = 2π rad = 360° = 400 gon.
Circle to Radian Conversion Formula
radian = circle × 6.2831853
1 circle = 6.2831853 radian
1 radian = 0.1591549 circle
Reverse: circle = radian × 0.1591549
Frequently Asked Questions
How many radian are in 1 circle?
There are 6.2831853 radian in 1 circle. To convert circle to radian, multiply the value by 6.2831853.
How do I convert circle to radian?
Multiply your circle value by 6.2831853 to get the equivalent in radian. For example, 5 circle = 5 × 6.2831853 = 31.41593 radian.
How do I convert radian to circle?
Multiply your radian value by 0.1591549 to get the equivalent in circle. Alternatively, divide by 6.2831853.
What is 10 circle in radian?
10 circle is equal to 62.83185 radian.
What is 100 circle in radian?
100 circle is equal to 628.31853 radian.