How to add and subtract degrees and minutes
Navigators write angles in degrees and decimal minutes, such as 34°27.5′. There are 60 minutes in a degree, so the arithmetic works like adding hours and minutes rather than ordinary decimals:
- Adding with a carry: 34°27.5′ + 12°45.8′: the minutes make 73.3′, which is 1° and 13.3′, so the result is 47°13.3′.
- Subtracting with a borrow: 47°05.2′ − 12°48.7′: 5.2′ is smaller than 48.7′, so borrow 1° (60′) to get 65.2′ − 48.7′ = 16.5′ and 46° − 12° = 34°. The result is 34°16.5′.
- Working around 360°: for GHA and LHA choose the 0–360° result. LHA = GHA 352°15.3′ + longitude 15°30.0′ E = 367°45.3′, which is 7°45.3′.
Typing angles as decimal degrees on a normal calculator (34.275 instead of 34°27.5′) is the most common mistake in celestial navigation exams; this calculator keeps everything in degrees and minutes, like the Nautical Almanac and the sight reduction tables.
Correcting a sextant altitude: from Hs to Ho
The altitude read on the sextant (Hs) is corrected in a fixed order before it can be used with the calculated altitude (Hc) to find the intercept:
- Index error: if the error is off the arc add it, if it is on the arc subtract it (“if it's on, take it off”).
- Dip: the visible horizon is below the true horizontal; subtract 1.76′ × √(height of eye in metres).
- This gives the apparent altitude Ha, which is used to enter the altitude correction tables.
- Refraction (always subtracted), semi-diameter (+ for the lower limb, − for the upper limb) and parallax (significant for the Moon) give the observed altitude Ho.
Example: Sun, lower limb
Hs 34°27.5′, index error 2.0′ on the arc, height of eye 3 m, semi-diameter 16.1′: Hs − 2.0′ − dip 3.0′ = Ha 34°22.5′; − refraction 1.5′ + SD 16.1′ + parallax 0.1′ = Ho 34°37.2′.
Refraction uses the Nautical Almanac formula for standard conditions (10 °C, 1010 hPa). Results agree with the almanac tables to about 0.1′; for an exam, always show the corrections from the almanac.
Arc and time
The Earth turns 360° in 24 hours, so 15° of longitude equals 1 hour, 1° equals 4 minutes and 1′ equals 4 seconds of time. That conversion is used to turn a longitude into a time difference, for example to find the time of meridian passage at your position.
Frequently asked questions
How do I add degrees and minutes?
Add the degrees and the minutes separately. If the minutes reach 60 or more, subtract 60 and add 1 to the degrees: 20°40′ + 10°35′ = 30°75′ = 31°15′.
How do I subtract degrees and minutes?
If the minutes you subtract are larger, borrow 1° as 60′: 30°10′ − 12°25′ = 29°70′ − 12°25′ = 17°45′.
Is index error on the arc added or subtracted?
Subtracted. An error on the arc makes the sextant read too high, so it is taken off; an error off the arc is added (“if it's on, take it off; if it's off, put it on”).
How is dip calculated?
Dip in minutes is about 1.76 × √(height of eye in metres), or 0.97 × √(height in feet). At 3 m it is 3.0′, at 10 m 5.6′.
How do I convert decimal degrees to degrees and minutes?
Multiply the decimal part by 60: 34.275° = 34° + 0.275 × 60′ = 34°16.5′.
For training and checking your working. Always navigate with official almanac data and keep a reserve for errors.