Radian to Second Converter
Enter the value that you want to convert radian (rad) to second (") or second to radian.Also written as RAD to " conversion.
1 radian = 206264.6412351 second
Formula: second = radian value × 206264.6412351
RAD to " — radian to second
10 radian = 2062646.41235 second
Popular Degree Converters:
How Radian Relates to Second
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 Second?
Second (") is a unit of degree measurement. 1 second is equal to 0.0000048 radian.
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 second metric conversion table
| 0.01 rad | = | 2062.64641 " |
| 0.1 rad | = | 20626.46412 " |
| 1 rad | = | 206264.64124 " |
| 2 rad | = | 412529.28247 " |
| 3 rad | = | 618793.92371 " |
| 4 rad | = | 825058.56494 " |
| 5 rad | = | 1031323.20618 " |
| 6 rad | = | 1237587.84741 " |
| 7 rad | = | 1443852.48865 " |
| 8 rad | = | 1650117.12988 " |
| 9 rad | = | 1856381.77112 " |
| 10 rad | = | 2062646.41235 " |
| 11 rad | = | 2268911.05359 " |
| 12 rad | = | 2475175.69482 " |
| 13 rad | = | 2681440.33606 " |
| 14 rad | = | 2887704.97729 " |
| 15 rad | = | 3093969.61853 " |
| 16 rad | = | 3300234.25976 " |
| 17 rad | = | 3506498.90100 " |
| 18 rad | = | 3712763.54223 " |
| 19 rad | = | 3919028.18347 " |
| 20 rad | = | 4125292.82470 " |
| 30 rad | = | 6187939.23705 " |
| 40 rad | = | 8250585.64940 " |
| 50 rad | = | 10313232.06175 " |
| 60 rad | = | 12375878.47411 " |
| 70 rad | = | 14438524.88646 " |
| 80 rad | = | 16501171.29881 " |
| 90 rad | = | 18563817.71116 " |
| 100 rad | = | 20626464.12351 " |
| 200 rad | = | 41252928.24702 " |
| 300 rad | = | 61879392.37053 " |
| 400 rad | = | 82505856.49403 " |
| 500 rad | = | 103132320.61754 " |
| 600 rad | = | 123758784.74105 " |
| 700 rad | = | 144385248.86456 " |
| 800 rad | = | 165011712.98807 " |
| 900 rad | = | 185638177.11158 " |
| 1000 rad | = | 206264641.23509 " |
How to Convert RAD to " (Radian to Second)?
We can convert radian to second by using an example.
Example:
Convert 20 Radian to Second?
We know 1 Radian = 206264.6412351 second; 1 Second = 0.0000048 radian.
20 radian = ___"
20 × 206264.6412351 = 4125292.82470 " (we know 1 radian = 206264.6412351 second)
Answer:
20 radian = 4125292.82470 second
How to Convert Radians to Arcseconds
The conversion factor from radians to arcseconds is (180 × 3600)/π = 648000/π ≈ 206265:
- Write down the angle in radians.
- Multiply by 206264.8 (= 648000/π).
- The result is the angle in arcseconds.
Solved Examples
Question 1: Convert 0.000001 radians (1 microradian) to arcseconds.
Solution:
Arcseconds = Radians × 206264.8
= 0.000001 × 206264.8
= 0.2063
Answer: 1 microradian ≈ 0.206 arcseconds
Question 2: The Hubble Space Telescope resolves 0.0000002 radians. How many arcseconds?
Solution:
Arcseconds = 2 × 10⁻⁷ × 206264.8
= 0.0413
Answer: Hubble resolves ≈ 0.04 arcseconds
Question 3: A laser beam diverges at 0.003 radians. Express in arcseconds.
Solution:
Arcseconds = 0.003 × 206264.8
= 618.8
Answer: 0.003 rad ≈ 619 arcseconds ≈ 10.3 arcminutes
Practice Questions
Try solving these on your own to test your understanding:
- Convert 0.00001 radians to arcseconds. (Answer: ≈ 2.063″)
- Earth's axial tilt changes by 0.0000002 rad/year. Express in arcseconds/year. (Answer: ≈ 0.041″/year)
- Convert π/180 radians to arcseconds. (Answer: 3600″ = 1°)
- A star's proper motion is 10 microradians/year. How many arcseconds/year? (Answer: ≈ 2.06″/yr)
The "206265" Constant in Astronomy
The value 206264.8 (arcseconds per radian) is fundamental in observational astronomy. The parsec is defined such that a star at 1 parsec distance shows exactly 1 arcsecond of parallax. The small-angle approximation sin(θ) ≈ θ (in radians) combined with the 206265 conversion gives direct physical sizes: angular size (arcseconds) = physical size / distance × 206265. This formula underpins all distance-independent size measurements in astronomy.
Sub-Arcsecond Precision in Modern Technology
Modern technology routinely achieves sub-arcsecond precision. Adaptive optics on telescopes correct atmospheric distortion to 0.01-0.05 arcseconds. Inertial navigation systems (aircraft, submarines) measure angular rates to micro-arcsecond precision. The GAIA space telescope measures stellar positions to 7 micro-arcseconds (7 millionths of an arcsecond) — equivalent to reading a newspaper on the Moon from Earth.
Key Takeaways
- Multiply radians by 206264.8 to get arcseconds.
- 206265 arcseconds = 1 radian (key astronomical constant).
- 1 arcsecond at 1 parsec distance = the definition of parallax.
- Modern telescopes resolve 0.01-0.05 arcseconds with adaptive optics.
- Small angle formula: size = angle(rad) × distance, or angle(″) = size/distance × 206265.
Radian to Second Conversion Formula
second = radian × 206264.6412351
1 radian = 206264.6412351 second
1 second = 0.0000048 radian
Reverse: radian = second × 0.0000048
Frequently Asked Questions
How many second are in 1 radian?
There are 206264.6412351 second in 1 radian. To convert radian to second, multiply the value by 206264.6412351.
How do I convert radian to second?
Multiply your radian value by 206264.6412351 to get the equivalent in second. For example, 5 radian = 5 × 206264.6412351 = 1031323.20618 second.
How do I convert second to radian?
Multiply your second value by 0.0000048 to get the equivalent in radian. Alternatively, divide by 206264.6412351.
What is 10 radian in second?
10 radian is equal to 2062646.41235 second.
What is 100 radian in second?
100 radian is equal to 20626464.12351 second.