Radian to Second of Arc Conversion Chart
| Radian (rad) | Second of arc (arcsec) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.000005 rad | 1.0313 arcsec | One Arcsecond Baseline Astronomical Parallax Angle | 0.000005 × 206265 = 1.0313 arcsec |
| 0.00001 rad | 2.0626 arcsec | Sub-Arcsecond Atmospheric Astronomical Seeing Limit | 0.00001 × 206265 = 2.0626 arcsec |
| 0.00005 rad | 10.3132 arcsec | Ten Arcseconds Telescope Mount Tracking Resolution | 0.00005 × 206265 = 10.3132 arcsec |
| 0.0001 rad | 20.6265 arcsec | One Tenth Milliradian Micro-Electro-Mechanical Gyro Deflection | 0.0001 × 206265 = 20.6265 arcsec |
| 0.0005 rad | 103.1324 arcsec | One Hundred Arcseconds Double Star Separation Threshold | 0.0005 × 206265 = 103.1324 arcsec |
| 0.001 rad | 206.2648 arcsec | One Milliradian Tactical Rifle Scope Reticle Subtension | 0.001 × 206265 = 206.2648 arcsec |
| 0.005 rad | 1031.324 arcsec | One Thousand Arcseconds Small Planet Orbital Discrepancy | 0.005 × 206265 = 1031.324 arcsec |
| 0.0087 rad | 1794.5038 arcsec | Apparent Diameter of Moon in Arcseconds from Earth | 0.0087 × 206265 = 1794.5038 arcsec |
| 0.0175 rad | 3609.6341 arcsec | One Degree Sexagesimal Standard Grid in Arcseconds | 0.0175 × 206265 = 3609.6341 arcsec |
| 0.05 rad | 10313.2403 arcsec | Fifty Milliradians Wide-Field Collimator Angular Span | 0.05 × 206265 = 10313.2403 arcsec |
| 0.1 rad | 20626.4806 arcsec | One Tenth Radian Engineering Sector Coverage Arc | 0.1 × 206265 = 20626.4806 arcsec |
| 0.5 rad | 103132.4031 arcsec | Half Radian Structural Curvature Angle in Arcseconds | 0.5 × 206265 = 103132.4031 arcsec |
| 1 rad | 206264.8062 arcsec | One Natural Radian Arc-to-Radius Equality in Arcseconds | 1 × 206265 = 206264.8062 arcsec |
| 1.5708 rad | 324000.7578 arcsec | Pi Over Two Radians Perpendicular Right Angle Sector | 1.5708 × 206265 = 324000.7578 arcsec |
| 3.1416 rad | 648002.124 arcsec | Exact Pi Radians Straight Semicircle Arcseconds Horizon | 3.1416 × 206265 = 648002.124 arcsec |
Radian to Second of arc Formula & Unit Definitions
The conversion from radians to seconds of arc is governed by the exact formula: Arcseconds = Radians × (648,000 / π) ≈ Radians × 206,264.8062. Conversely, to convert arcseconds into radians, multiply by π / 648,000 ≈ 0.00000484814.
Quick Estimation: Remember the classic astronomical constant: 1 radian ≈ 206,265 arcseconds. Similarly, 1 milliradian (0.001 rad) equals approximately 206.265 arcseconds. For quick estimates, multiply radians by 206,265.
Radian Unit (rad)
SI Dimensionless Angle- Creator & Origin: Formalized in British mathematical physics for natural calculus and mechanics.
- Standard Definition: Subtends an arc equal in length to circle radius (1 rad ≈ 57.2958°).
- Everyday Focus: Differential equations, harmonic oscillation, angular acceleration, and flight kinematics.
Second of Arc (arcsec / ″)
Fine Sexagesimal Division (1/3,600°)- Creator & Origin: Ptolemy's Almagest and Bessel's 19th-century astronomical measurements.
- Standard Definition: Defined as exactly 1/3,600 of an angular degree or π/648,000 radians.
- Everyday Focus: Stellar parallax, Hubble Space Telescope stability, VLBI radio interferometry, and laser gyros.
Frequently Asked Questions
Q.How many arcseconds are in one radian?
One radian equals approximately 206,264.8062 seconds of arc (exactly 648,000/π arcsec).
Q.What is the reverse conversion from arcseconds to radians?
To convert back, use the Second of Arc to Radian Converter where 1 arcsec equals approximately 0.00000484814 rad.
Q.Why is 206,265 important in astronomy?
206,265 is both the number of arcseconds in a radian and the number of astronomical units in one parsec.
Q.How many arcseconds is 1 milliradian (mrad)?
1 milliradian equals approximately 206.265 arcseconds.
Q.What formula converts radians to seconds of arc?
Multiply radians by 648,000 and divide by π: Arcseconds = Radians × (648,000 / π).