Tutorial: Angles in Degrees Minutes and Seconds

Angles in Degrees Minutes and Seconds

Introduction

The DMS system is a number system used for angles. A full circle is still divided up into 360 degrees, but the individual degrees are then split into 60 minutes of arc, and each minute divided into 60 seconds of arc.

The notation for X degrees, Y minutes and Z seconds is XºY'Z", for example 24º30'59".

If the angle has precision to more than the arc-second, the fractions of the second revert back to the decimal system, as in 180º1'1.57". This can happen at high zooms.

All the trig scales ( but not the hyperbolic scales ) are available either in dms or with degree divisions as regular decimal numbers.

Most disciplines use decimal angles these days, but DMS angles are still around in astronomy and cartography. It's time consuming to convert dms to decimal, adding minutes/60 to seconds/3600, so it makes sense to populate your slide rule with the number system you're going to use.

Scale divisions

There is 60' in a degree, so when two ticks mark off an angle of 1º, the ticks in between them will represent halves, thirds, or sixths of a degree, representing 30', 20', or 10', respectively. 1 dms degree will never be divided into fifths or tenths like the other scales, and this makes them look a bit strange. The same divisions apply between ticks marking off one minute of arc, dividing it into 30", 20" or 10".

Converting between dms and decimal

There are textbook formulas for doing this but they require many operations. If you have to convert frequently, another way is to include side by side S2 and S2_D scales:

Suppose we want to convert 48.16370º to dms. Zoom in on a degree near the high-precision left end of the S2 scale, say, to 1.1637º, and read the minutes and seconds directly off the S2_D: 1º9'49.32", so the answer is 48º9'49.32".

For highest precision, use the S2,ST, or T2 scales for this purpose, not S or T. This method obviously works equally well converting back to decimal, and it is far faster than using the slide rule to multiply out the conversion formulas.