arcsecond [arcsec] to radian [rad] Converter
Quick Reference
1 arcsecond (arcsec) = 4.8481e-6 radian (rad)
1 radian (rad) = 206264.8062 arcsecond (arcsec)
How to Convert arcsecond to radian
1 arcsec = 4.8481e-6 rad
1 rad = 206264.8062 arcsec
To convert arcsecond to radian, divide the value by 206264.8062 (equivalently, multiply by 4.8481e-6). To convert radian back to arcsecond, multiply by 206264.8062.
Example: convert 10 arcsec to rad:
10 arcsec = 10 x 4.8481e-6 = 4.8481e-5 rad
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
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 to radian Conversion Table
| arcsecond [arcsec] | radian [rad] |
|---|---|
| 1 arcsec | 4.8481e-6 rad |
| 2 arcsec | 9.6963e-6 rad |
| 5 arcsec | 2.4241e-5 rad |
| 10 arcsec | 4.8481e-5 rad |
| 20 arcsec | 9.6963e-5 rad |
| 50 arcsec | 0.0002424068406 rad |
| 100 arcsec | 0.0004848136811 rad |
| 200 arcsec | 0.0009696273622 rad |
| 500 arcsec | 0.002424068406 rad |
| 1000 arcsec | 0.004848136811 rad |
Common arcsecond to radian conversions
- 1 arcsec = 0.000004848136811 rad
- 2 arcsec = 0.000009696273622 rad
- 3 arcsec = 0.00001454441043 rad
- 4 arcsec = 0.00001939254724 rad
- 5 arcsec = 0.00002424068406 rad
- 6 arcsec = 0.00002908882087 rad
- 7 arcsec = 0.00003393695768 rad
- 8 arcsec = 0.00003878509449 rad
- 9 arcsec = 0.0000436332313 rad
- 10 arcsec = 0.00004848136811 rad
- 12 arcsec = 0.00005817764173 rad
- 15 arcsec = 0.00007272205217 rad
- 20 arcsec = 0.00009696273622 rad
- 25 arcsec = 0.0001212034203 rad
- 30 arcsec = 0.0001454441043 rad
- 40 arcsec = 0.0001939254724 rad
- 50 arcsec = 0.0002424068406 rad
- 60 arcsec = 0.0002908882087 rad
- 75 arcsec = 0.0003636102608 rad
- 100 arcsec = 0.0004848136811 rad
- 150 arcsec = 0.0007272205217 rad
- 200 arcsec = 0.0009696273622 rad
- 250 arcsec = 0.001212034203 rad
- 300 arcsec = 0.001454441043 rad
- 500 arcsec = 0.002424068406 rad
- 750 arcsec = 0.003636102608 rad
- 1,000 arcsec = 0.004848136811 rad