radian [rad] to arcsecond [arcsec] Converter
Quick Reference
1 radian (rad) = 206264.8062 arcsecond (arcsec)
1 arcsecond (arcsec) = 4.8481e-6 radian (rad)
How to Convert radian to arcsecond
1 rad = 206264.8062 arcsec
1 arcsec = 4.8481e-6 rad
To convert radian to arcsecond, multiply the value by 206264.8062. To convert arcsecond back to radian, divide by 206264.8062.
Example: convert 10 rad to arcsec:
10 rad = 10 x 206264.8062 = 2062648.062 arcsec
radian
Definition: A radian is the standard unit of angular measure, used in many areas of mathematics. One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
History/origin: The concept of radian measure was developed in the mid-18th century. Roger Cotes was one of the first to recognize the naturalness of using the radius as the unit of angle measurement. The term 'radian' first appeared in print on 1873, in examination questions set by James Thomson at Queen's College, Belfast.
Current use: Radians are widely used in mathematics, physics, and engineering, particularly in calculus, trigonometry, and signal processing. They simplify many formulas and are the standard unit for angular measurement in scientific and mathematical contexts.
arcsecond
Definition: An arcsecond (symbol: '') is a unit of angular measure equal to 1/60 of an arcminute or 1/3600 of a degree. It is used to express very small angles, particularly in astronomy and surveying.
History/origin: Like the arcminute, the arcsecond originates from the Babylonian sexagesimal system.
Current use: Arcseconds are used in astronomy for high-precision measurements of stellar positions, parallaxes, and proper motions. They are also used in surveying and geodesy for precise angle determination.
radian to arcsecond Conversion Table
| radian [rad] | arcsecond [arcsec] |
|---|---|
| 1 rad | 206264.8062 arcsec |
| 2 rad | 412529.6125 arcsec |
| 5 rad | 1031324.031 arcsec |
| 10 rad | 2062648.062 arcsec |
| 20 rad | 4125296.125 arcsec |
| 50 rad | 10313240.31 arcsec |
| 100 rad | 20626480.62 arcsec |
| 200 rad | 41252961.25 arcsec |
| 500 rad | 103132403.1 arcsec |
| 1000 rad | 206264806.2 arcsec |
Common radian to arcsecond conversions
- 1 rad = 206,264.806247 arcsec
- 2 rad = 412,529.612494 arcsec
- 3 rad = 618,794.418741 arcsec
- 4 rad = 825,059.224988 arcsec
- 5 rad = 1,031,324.031235 arcsec
- 6 rad = 1,237,588.837483 arcsec
- 7 rad = 1,443,853.64373 arcsec
- 8 rad = 1,650,118.449977 arcsec
- 9 rad = 1,856,383.256224 arcsec
- 10 rad = 2,062,648.062471 arcsec
- 12 rad = 2,475,177.674965 arcsec
- 15 rad = 3,093,972.093706 arcsec
- 20 rad = 4,125,296.124942 arcsec
- 25 rad = 5,156,620.156177 arcsec
- 30 rad = 6,187,944.187413 arcsec
- 40 rad = 8,250,592.249884 arcsec
- 50 rad = 10,313,240.312355 arcsec
- 60 rad = 12,375,888.374826 arcsec
- 75 rad = 15,469,860.468532 arcsec
- 100 rad = 20,626,480.62471 arcsec
- 150 rad = 30,939,720.937064 arcsec
- 200 rad = 41,252,961.249419 arcsec
- 250 rad = 51,566,201.561774 arcsec
- 300 rad = 61,879,441.874129 arcsec
- 500 rad = 103,132,403.123548 arcsec
- 750 rad = 154,698,604.685322 arcsec
- 1,000 rad = 206,264,806.247096 arcsec