# Convert sexagesimal to decimal

I've been studying astronomy and I've encountered 3 different (sexagesimal) ways to write angles.

1. hh mm ss - hours minutes and seconds

2. dd '' '''' - degrees, arcminutes and arcseconds.

3. +/- dd mm ss -

For example most sources give the right ascension of an object in the first format while the declination is given in the third.

Why are two coordinates that usually come together given in two different ways?

How can one convert each one of the formats in to decimal degrees?

Start at the left: 60 s = 1 m so to convert decimal minutes

dm := m + s/60 where := is the usual 'is assigned to' and dm is decimal minutes.

Repeat for decimal degrees

dd = d + dm/60

This works for declination too.

easier to calculate

dd = d + m/60 + s/3600

Right ascension is different, because it's using time as it's unit instead of degrees. However both hours and degrees are divided into minutes and seconds, but they aren't the same size.

Since it's 24 hours around, an hour is equal to 15 degrees. A minute of hour angle = 1/60 of 15 degrees = 1/4 degrees, and a second of hour angle =
1/240 degree. So if RA is given in h m s

decimal ra = 15 * h + m/4 + s/240

• What about the plus and minus sign on the declination? – user3636673 Oct 15 '18 at 12:04
• Sign is carried over. It's in effect -1 * (hh:mm:ss) or -1 *(dd.ddddddd) – Sherwood Botsford Oct 16 '18 at 19:33