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Arcminute to Degree Converter

Enter a value and direction to convert between arcminutes and degrees.

Result

1.6667 deg
60 arcminutes = 1 degree
100.0000 arcmin

How it is calculated

One degree is divided into 60 arcminutes, so the conversion is a single multiplication or division. From arcminutes to degrees: degrees = arcminutes ÷ 60. From degrees to arcminutes: arcminutes = degrees × 60. You enter one value and choose the direction; the tool shows the converted number to four decimals, a line stating the rate, and your input repeated with its unit. Negative values and decimals are accepted, and the sign is kept. The result is a decimal number of degrees, not degrees-minutes-seconds. If the direction is anything other than degrees to arcminutes, the tool converts arcminutes to degrees. Arcseconds are not handled, so convert them to arcminutes first (divide by 60).

Worked example

Convert 100 arcminutes to degrees. Degrees = 100 ÷ 60 = 1.6667 deg. In the other notation, the whole part is 1 degree, and the remaining 0.6667 × 60 = 40 arcminutes, so 100′ is 1° 40′. In the opposite direction, 2.75 degrees × 60 = 165 arcminutes. The Moon's apparent width of about 30 arcminutes works out to 30 ÷ 60 = 0.5 degrees.

Try this example →

Common mistakes

  • Reading 1.6667 degrees as 1 degree 66.67 minutes; the part after the decimal point is a fraction of a degree, so 0.6667 degrees is 40 arcminutes, not 66.
  • Choosing the wrong direction and not noticing: the unit printed after the number (deg or arcmin) shows which way the conversion ran.
  • Mixing up arcminutes and arcseconds: 1 arcminute is 60 arcseconds, so a value in arcseconds must be divided by 60 first, or by 3600 for degrees.
  • Confusing arcminutes with minutes of time: 60 arcminutes in a degree is an angle, while right ascension or time zones use hours, minutes and seconds of time.
  • Dropping the sign of a negative angle: the tool keeps it, so −30 arcminutes gives −0.5 degrees, which is a different direction from +0.5.

Sources

About this calculator

An arcminute is a unit of angular measurement equal to 1/60th of a degree, further subdivided into 60 arcseconds — the same base-60 system the Babylonians used for both angles and time, which is why "minutes" and "seconds" show up in both contexts.

Arcminutes give astronomers and opticians a finer unit than the degree for describing small angles: the Moon's apparent diameter is about 30 arcminutes (half a degree), and a telescope's resolving power or a lens's field of view are commonly specified in arcminutes — units too small to conveniently express as a fraction of a degree.

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Comments (1)

  • Editorial team

    If the angle comes from optics or sighting, the arcminute has a handy physical meaning: one arcminute spans about 29 millimetres at 100 metres, or about 29 centimetres at a kilometre. So 90 arcminutes, which the tool turns into 1.5 degrees, covers roughly 26 metres at 1 kilometre. Small-angle arithmetic like this holds well only for small angles. Are you converting telescope field of view, rifle scope adjustments or map coordinates?

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