ConverterHub

Arcseconds to Radians Converter

Enter a value in arcseconds to convert it to radians, degrees.

Result

1.0000e+0 rad
57.2958 °

How it is calculated

The angle in arcseconds is multiplied by the exact conversion factor: radians = arcsec × 4.84813681109536×10-6 (that is π ÷ 648,000), and divided by 3600 for degrees: degrees = arcsec ÷ 3600. The radian value is printed in scientific notation with four decimals (for example 4.8481e-6 rad) because arcsecond angles are tiny, and the degree value is rounded to four decimals. Negative angles keep their sign, zero returns zero, and an empty or non-numeric field gives no result.

Worked example

Take an angle of 206265 arcseconds, roughly the size of one radian. Radians: 206265 × 4.84813681×10-6 ≈ 0.99999…, which the tool prints as 1.0000e+0 rad. Degrees: 206265 ÷ 3600 = 57.29583…, shown as 57.2958 °. This agrees with the well-known value of about 57.3 degrees per radian.

Try this example →

Common mistakes

  • Confusing arcseconds with arcminutes. One arcminute is 60 arcseconds, so typing minutes into this field makes the radian result 60 times too small.
  • Misreading scientific notation: 4.8481e-6 means 0.0000048481, not 4.8481.
  • Relying on the degree output for very tiny angles. With four decimals, 0.75 arcsecond shows as 0.0002 °, so the radian figure (3.6361e-6 rad) is the more precise one there.
  • Mixing up arcseconds of angle with seconds of time in right ascension. One second of time equals 15 arcseconds, so the two cannot be swapped.
  • Using the small-angle approximation (angle in radians ≈ sin or tan) for angles that are not small.

About this calculator

An arcsecond is 1/3600 of a degree, the finest unit commonly used to describe tiny angles; converting to the radian — the SI angle unit where a full circle is 2π — gives 1 arcsecond = π/648,000 radians ≈ 4.8481×10⁻⁶ rad.

Astronomers use arcseconds to express stellar parallax, telescope angular resolution, and proper motion (since these angles are naturally tiny), but the underlying physics and optics equations — like the diffraction limit or small-angle approximations — are written in radians, so converting between the two is a routine step in astronomical and optical calculations.

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