Second of Arc to Radian Conversion Chart
| Second of arc (arcsec) | Radian (rad) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 1.0313 arcsec | 0.000005 rad | One Arcsecond Baseline Astronomical Parallax Angle | 1.0313 × 0.00000485 = 0.000005 rad |
| 2.0626 arcsec | 0.00001 rad | Sub-Arcsecond Atmospheric Astronomical Seeing Limit | 2.0626 × 0.00000485 = 0.00001 rad |
| 10.3132 arcsec | 0.00005 rad | Ten Arcseconds Telescope Mount Tracking Resolution | 10.3132 × 0.00000485 = 0.00005 rad |
| 20.6265 arcsec | 0.0001 rad | One Tenth Milliradian Micro-Electro-Mechanical Gyro Deflection | 20.6265 × 0.00000485 = 0.0001 rad |
| 103.1324 arcsec | 0.0005 rad | One Hundred Arcseconds Double Star Separation Threshold | 103.1324 × 0.00000485 = 0.0005 rad |
| 206.2648 arcsec | 0.001 rad | One Milliradian Tactical Rifle Scope Reticle Subtension | 206.2648 × 0.00000485 = 0.001 rad |
| 1031.324 arcsec | 0.005 rad | One Thousand Arcseconds Small Planet Orbital Discrepancy | 1031.324 × 0.00000485 = 0.005 rad |
| 1794.5038 arcsec | 0.0087 rad | Apparent Diameter of Moon in Arcseconds from Earth | 1794.5038 × 0.00000485 = 0.0087 rad |
| 3609.6341 arcsec | 0.0175 rad | One Degree Sexagesimal Standard Grid in Arcseconds | 3609.6341 × 0.00000485 = 0.0175 rad |
| 10313.2403 arcsec | 0.05 rad | Fifty Milliradians Wide-Field Collimator Angular Span | 10313.2403 × 0.00000485 = 0.05 rad |
| 20626.4806 arcsec | 0.1 rad | One Tenth Radian Engineering Sector Coverage Arc | 20626.4806 × 0.00000485 = 0.1 rad |
| 103132.4031 arcsec | 0.5 rad | Half Radian Structural Curvature Angle in Arcseconds | 103132.4031 × 0.00000485 = 0.5 rad |
| 206264.8062 arcsec | 1 rad | One Natural Radian Arc-to-Radius Equality in Arcseconds | 206264.8062 × 0.00000485 = 1 rad |
| 324000.7578 arcsec | 1.5708 rad | Pi Over Two Radians Perpendicular Right Angle Sector | 324000.7578 × 0.00000485 = 1.5708 rad |
| 648002.124 arcsec | 3.1416 rad | Exact Pi Radians Straight Semicircle Arcseconds Horizon | 648002.124 × 0.00000485 = 3.1416 rad |
Second of arc to Radian Formula & Unit Definitions
The conversion from seconds of arc to radians is governed by the exact formula: Radians = Arcseconds × (π / 648,000) ≈ Arcseconds × 0.00000484814. Conversely, to convert radians into arcseconds, multiply by 648,000 / π ≈ 206,264.8062.
Quick Estimation: Multiply the arcsecond value by 4.848 to find the angle in microradians (μrad), then shift six decimal places left for radians (or divide arcseconds by 206,265). For example: 1 arcsec ≈ 4.848 μrad; 206.265 arcsec ≈ 1 mrad (0.001 rad); 3,600 arcsec ≈ 0.01745 rad.
Second of Arc (arcsec / ″)
Fine Sexagesimal Division (1/3,600°)- Creator & Origin: Ptolemaic sexagesimal geometry and Friedrich Bessel's stellar parallax observations.
- Standard Definition: Defined as exactly 1/3,600 of a degree (1 arcsec ≈ 0.00000484814 rad = 4.848 μrad).
- Everyday Focus: Atmospheric optical seeing, telescope resolving power, double star orbits, and lithography.
Radian Unit (rad)
SI Dimensionless Angle- Creator & Origin: Introduced by Roger Cotes and adopted as the international standard for angular calculus.
- Standard Definition: Subtends a circular arc equal to the radius (2π rad = 1 full circle).
- Everyday Focus: Computational physics, spacecraft orbital simulation, vector graphics, and robotics.
Frequently Asked Questions
Q.How many radians are in one second of arc?
One second of arc equals approximately 0.00000484814 radians (4.84814 microradians, exactly π/648,000 rad).
Q.What is the reverse conversion from radians to arcseconds?
To convert in reverse, use the Radian to Second of Arc Converter where 1 rad equals approximately 206,265 arcsec.
Q.How many radians is 3,600 arcseconds (1 degree)?
3,600 arcseconds equals approximately 0.017453 radians (π/180 rad).
Q.How many radians is 1 arcsecond?
1 arcsecond equals approximately 4.84814 × 10⁻⁶ radians.
Q.What formula converts seconds of arc to radians?
Multiply arcseconds by π and divide by 648,000: Radians = Arcseconds × (π / 648,000).