How this instrument works
Angle measure in degrees descends from Babylonian base-60 arithmetic by way of Greek astronomy. Ptolemy, writing in Alexandria around 150 CE, split each degree into partes minutae primae — first small parts — then split those again into partes minutae secundae. Latin translators kept both names, which is why we say minute and second today, and why one degree still holds exactly sixty arcminutes.
That sixty is a counting rule, not a measurement, so this conversion carries no uncertainty whatever. A full turn spans 360 degrees, a degree spans 60 arcminutes, an arcminute spans 60 arcseconds; multiply through and one revolution comes to 1,296,000 arcseconds. Neither degree nor arcminute belongs to SI proper — radians hold that job — but BIPM lists both among units accepted for use alongside SI, where 1° = π/180 rad and 1′ = π/10800 rad, about 0.00029089 rad.
Sixty parts sounds fussy until you meet trades where an arcminute is a natural working size. One arcminute of latitude along a meridian became a nautical mile, fixed at 1852 m by a hydrographic conference at Monaco in 1929. Marksmen quote group sizes in minutes of angle because one subtends 1.047 inches at 100 yards, near enough an inch. Ophthalmologists peg 20/20 vision to detail one arcminute wide. Tycho Brahe, observing before telescopes existed, pushed naked-eye positions to roughly one or two arcminutes — precision that later let Kepler find elliptical orbits.
- Type your angle into Degrees (deg); 1.5 is loaded as a starting value.
- Use decimal degrees, not degrees-and-minutes notation: 1°30′ goes in as 1.5, never as 1.30.
- Read Arcminutes (arcmin) below it, recomputed as you type and shown to six decimals.
- Working backwards from arcminutes? Divide your figure by 60 and enter that in Degrees (deg).
- Negative entries are refused, so subtract angles first and convert their positive difference.
Worked example — 1.5° of latitude on a chart
A navigator plans one leg due north, 40°00′N to 41°30′N. Entering 1.5 in Degrees (deg) returns 90.000000 in Arcminutes (arcmin). Because an arcminute of latitude was standardised as one nautical mile, that leg runs 90 nautical miles, or 166.68 km — exactly six hours at 15 knots.
Those same 90 arcminutes read very differently elsewhere. Through a telescope they span about three lunar diameters, since our Moon covers roughly 31′ edge to edge. Hand them to a rifle shooter and 90 minutes of angle throws point of impact some 94 inches sideways at 100 yards, which is why scope turrets click in quarter-minutes rather than whole ones.
Questions
Is 1.5 degrees the same as 1 degree and 50 arcminutes?
No — 1.5 decimal degrees is 1°30′, or 90 arcminutes. Decimal notation cuts a degree into hundredths while sexagesimal notation cuts it into sixtieths, so 0.5° maps to 30′ rather than 50′. Read backwards, 1°50′ works out at 1.8333° once you divide 50 by 60. This sheet expects decimal degrees, which is what GPS receivers, spreadsheets and most trigonometry functions emit. If your figure came off a paper chart as degrees and minutes, convert it before typing.
Is that factor of 60 exact, or is it rounded?
Exact, and exact by definition rather than by experiment. Sixty arcminutes per degree is a convention about how we slice a circle, inherited from scribes who counted in base 60. No physical constant is involved, no measurement could ever refine it, and no uncertainty attaches to it. Any error in a result here comes from your own input figure or from display rounding at six decimals — never from that 60.
How does an arcminute differ from a minute of time?
They quantify different things and merely share a name. An arcminute, written with a prime (′), is one-sixtieth of a degree of angle. A minute of time is one-sixtieth of an hour. Astronomers meet both at once: right ascension is quoted in hours, where 1 h equals 15° of arc, so a single minute of right ascension covers 15 arcminutes along the celestial equator — and less than that nearer either pole. Longitude carries an identical trap, since Earth turns 15° per hour.
How big is one arcminute in everyday terms?
About as fine as unaided human sight. Standard 20/20 acuity is defined by resolving detail one arcminute across — roughly a 1.7 mm stroke on a Snellen letter read at 6 m. Our Moon spans some 31 arcminutes, so a single minute is about a thirtieth of its width. At sea, one arcminute of latitude is one nautical mile. On a target, one minute covers 1.047 inches at 100 yards, which shooters habitually round to an inch.
How do I go from arcminutes back to degrees?
Divide by 60. Ninety arcminutes ÷ 60 gives 1.5°, and typing that into Degrees (deg) checks your round trip. One step finer, multiply arcminutes by 60 for arcseconds, so 90′ is 5400″. Rebuilding degrees-minutes-seconds from a decimal figure works in stages: take whole degrees first, multiply what remains by 60 for arcminutes, then repeat on that leftover for arcseconds.
Are degrees and arcminutes SI units?
Neither is an SI unit, though both are accepted for use with SI. BIPM's brochure lists degree, arcminute and arcsecond among non-SI units retained because navigation, astronomy and surveying rely on them so heavily. Plane angle's coherent SI unit is the radian: 1° = π/180 rad and 1′ = π/10800 rad, or about 0.00029089 rad. Trigonometric functions in most programming languages expect radians, a frequent source of silent errors.