Convert arcsecond to radians

Arcsecond

An arcsecond is an angle unit equal to one sixtieth of an arcminute or one three-thousand-six-hundredth of a degree.

Arcseconds come from sexagesimal angle subdivision and remain central to astronomy and precision measurement.

Arcseconds are used in astronomy, optics, geodesy, surveying, angular resolution, telescope pointing, and precision alignment.

Radian

A radian is an angle unit based on the ratio of arc length to radius.

Radians became central in mathematics and physics because they simplify circular and trigonometric relationships.

Radians are used in trigonometry, calculus, physics, programming, robotics, engineering, and signal analysis.

How to Convert Arcsecond to Radian

Mathematically, radian (rad) = arcsecond (″) converted with the formula below.

1 ″ = 0.000005 rad

1 rad = 206,264.806247 ″

Formula: value × 0.0000048481368111

Example: 15 ″ = 0.000073 rad

1. Start with the angle value in arcseconds.
2. Use the relationship that 648,000 arcseconds equals pi radians.
3. Multiply the arcsecond value by pi.
4. Divide by 648,000 to get radians.

Precision note: Use radians = arcseconds x pi / 648,000. Keep pi precision and avoid rounding away small values in technical work.

How many ″ in rad and rad in ″

1 ″ = 0.000005 rad

1 rad = 206,264.806247 ″

Common Use Cases for ″ to rad

• Preparing telescope, optics, or angular-resolution values for formulas.
• Converting survey or geodesy tolerances into radians.
• Checking physics or engineering calculations that use very small angles.
• Translating arcsecond measurements for simulation or online tool models.

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