Arcminutes and arcseconds — sub-degree angle units
Degrees are too coarse for the sky. Astronomy runs on arcminutes and arcseconds — sixtieths and thirty-six-hundredths of a degree.
Beyond the naked-eye scale, angular measurement gets subdivided in sixties — a Babylonian inheritance that survives because it keeps common fractions (1/2, 1/3, 1/4, 1/5, 1/6) as whole numbers.
The exact factors
1° = 60 arcminutes (′) = 3600 arcseconds (″) > 1′ = 60″ = 2.909 × 10⁻⁴ rad > 1″ = 4.848 × 10⁻⁶ rad ≈ 4.85 µrad
Where each is used
Arcminutes: naked-eye resolution (~1′), lunar and solar diameters (~30′), open-cluster diameters. Arcseconds: planetary disks, double-star separations, seeing conditions (2″ is a typical amateur site, 0.5″ is a mountain observatory). Milliarcseconds: interferometry, Gaia astrometry, VLBI radio source positions.
Worked example — pointing accuracy
A GoTo mount specced at ±30″ RMS pointing error looks fine until you image at 2000 mm focal length. Plate scale is 206 265 / 2000 = 103″/mm, so 30″ = 0.29 mm on the sensor — 30 pixels on a 10 µm sensor. Enough to miss a small planetary nebula on the first slew.
Recap
1° = 60′ = 3600″. Prime is minutes of arc, double-prime is seconds of arc — never confuse them with minutes and seconds of time.
Try the converters mentioned in this article
FAQ
Are arcminutes the same as minutes of right ascension?+
No. RA minutes are time units — 1 minute of RA = 15 arcminutes at the celestial equator, and less as you approach the poles.
What is the small-angle formula?+
For small angles, size (in same units as distance) ≈ distance × angle in radians. Or, size ≈ distance × angle_in_arcseconds / 206265.
This article was written by The Turbo Unit Converter engineering desk (Applied metrology & engineering units) and last reviewed on 2026-07-20 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.