Arcseconds to Radians Converter
Enter the angle in arcseconds below to convert it to radians.
Convert Arcseconds to Radians
Enter a value in arcseconds (″) to convert to radians (rad).
Second of Arc to Radian Conversion Table
Table showing various second of arc measurements converted to radians. Click any preset value or arrow to load it into the converter.
| Arcseconds (″) | Radians (rad) |
|---|---|
| 1 ″ | 0.000004848 rad |
| 10 ″ | 0.000048481 rad |
| 100 ″ | 0.000484814 rad |
| 1,000 ″ | 0.0048481 rad |
| 10,000 ″ | 0.0484814 rad |
| 100,000 ″ | 0.4848137 rad |
| 1,000,000 ″ | 4.8481368 rad |
| 5,000,000 ″ | 24.2406841 rad |
| 10,000,000 ″ | 48.4813681 rad |
| 25,400,000 ″ | 123.142675 rad |
How to Convert Arcseconds to Radians
To convert arcseconds to radians, multiply the angle by the following conversion ratio: 0.000004848 radians/second of arc.
Since one second of arc is equal to 0.000004848 radians, you can use this simple formula to convert:
The angle in radians is equal to the angle in arcseconds multiplied by 0.000004848.
For example, here's how to convert 5 arcseconds to radians using the formula above.
How Many Radians Are in a Second of Arc?
There are 0.000004848 radians in a second of arc, which is why we use this value in the formula above.
Our second of arc to radian calculator automatically converts your angle measurements with full decimal and scientific precision across US customary, imperial, and SI metric standards.
Arcseconds and radians are both units used to measure angle. Keep reading to learn more about each unit.
What Is a Second of Arc?
A second of arc is a unit of angle equal to 1/3,600 of a degree (0.000277778 °). 1/3600 of a degree. [1]
The second of arc is classified as a standard unit of angle. Arcseconds can be abbreviated as ″; for example, 1 second of arc can be written as 1 ″.
When working with arcseconds (″) in formulas or technical specifications, always verify whether your target system uses SI metric, US customary, or British imperial standards.
In practice, arcseconds (″) are widely used across fine-tolerance laboratory, analytical, and micro-scale angle measurements within international standard workflows, engineering documentation, and technical data sheets.
What Is a Radian?
A radian is a unit of angle equal to 57.2957795 degrees (°), the base unit for angle. SI angle unit (1 rad ≈ 57.29578°). [2]
The radian is classified as an International System of Units (SI) unit of angle. Radians can be abbreviated as rad; for example, 1 radian can be written as 1 rad.
When working with radians (rad) in formulas or technical specifications, always verify whether your target system uses SI metric, US customary, or British imperial standards.
In practice, radians (rad) are widely used across standard angle applications within International System of Units (SI) workflows, engineering documentation, and technical data sheets.
When converting angle between arcseconds (″) and radians (rad), keep full floating-point precision (1 ″ = 0.000004848 rad; 1 rad = 206,264.8062471 ″) during intermediate calculations and round only the final radian figure to match your instrument tolerance.
More Second of Arc & Radian Conversions
Need to calculate in the opposite direction? Use our radians to arcseconds calculator to switch your starting unit immediately. You can also explore related tools such as converting radians to arcseconds, converting degrees to radians, or converting radians to degrees.
Frequently Asked Questions
References
- [1]NIST CUU StandardNIST CUU (Non-SI Units Accepted for Use (deg, arcmin, arcsec))·Angle Metrology Standard — Arcseconds (″) to Radians (rad)
- [2]NIST SI SpecificationNIST SI (SI Coherent Unit: Radian (rad))·Unit Specifications: Second of Arc (″) & Radian (rad)
- [3]NIST SP 811 ReferenceNIST SP 811 (NIST SP 811 App. B.9 (Plane Angle))·Conversion Factors & Mathematical Basis (″ to rad)