Here is a list of common math calculation that a Cartographer should know and do from time to time

Latitude and longitude Issues

Degrees Minutes Seconds and Decimal Degrees

Latitude and longitude values are report in several formats

• Degrees Minutes Second - DMS
• Decimal Degrees - D.D
• Decimal Minutes - DM.s
• and others

Computers like Decimal Degrees but many times on maps we want DMS written out

Decimal Degree(D.d) to DMS

• you will just move the D. to the D of DMS - D. = D
• take the .d and multiple it by 3600 to get the number of seconds .d X 3600 = total number of seconds
• take the total number of seconds and divide by 60 the result of this is a quotient
• this quotient is Minute decimal seconds or M.s
• the M. is the M in DMS M. = M
• the .s must be converted to seconds again so you multiple the .s X 60 and you have S - .s X 60 = S

Example

• D.d = 45.6539
• D. = 45 - D = 45
• .d = 0.6539
• .d X 3600 = total seconds - .6539 X 3600 = 2354.04 total seconds
• M.s is the quotient of total seconds / 60 2354.04 / 60 = 39.2341667 M.s = 39.2341667
• M. = M - M. = 39 - M = 39
• at this point D = 45, S = 39
• convert the decimal of the quotient to seconds .s = .2341667 .s X 60 = seconds .234166 X 60 = 14.05 seconds
• answer is D = 45, M = 39, S = 14.05 or 45 39' 14.05'

DMS to Decimal Degree(D.d)

• The D in DMS is equal to the D. in D.d so D = D.
• The .d is equal to the total seconds / 3600
• .d = (M X 60 + S) / 3600
• D.d = D. + .d

Example

• -121 45' 8" to D.d
• D = -121 - D = sign D. - D. = - 121
• .d = (M X 60 + S)/3600 .d = (45 X 60 + 8) /3600 .d = 2708/3600 - .d = .75222
• D.d = sign |D.| + .d - D. = -121 - D.d = - |-121| + .7522 = -121.7522

Rectangler and Polar Coordinatees

Rectanglur (x,y) to Polar (R, Theta)

Basic forumlas R = SQRT(x^2 + y^2) and theta = arctan(y/x)

Example

• 4, 8 to R,theta(degrees)
• r = SQRT(4^2 + 8^2) = SQRT(16+64) = SQRT(80) = 8.944 = R
• theta = arctan(8/4) = arctan(2) = 63.43494882
• R, theta(degrees) = 8.944, 63.4349882 angle in Degrees
• you can also have the theta in units of Radians
• R, Theta(radians) = 8.944, 1.107148718

Polar (R, Theta(units) to rectanglur x,y

Basic Formulas x = R cos(Theta) and y = R sin(Theta)

Examples

• R, Theta = 18, 175 degrees
• x = R cos(theta) - x = 18 cos(175) - x = 10.7727
• y = R sin(theta) - y = 18 cos(175) - y = -14.420
• if your theta value in in radians make sure your calculater is set to RAD

Great Cirle Calculation

basic forumla

Angle of Distance = arcCOS(sin(lat1)sin(lat2)+cos(long1)cos(long2)cos(long1 - long2)

the average distance of a degree on the earth is 69.09 miles or 111.18958km

Angle of Distance * miles or km constant = great circle distance

Examples

• points (Long1, Lat1) = 43.28, 10.88 and (long2, Lat2) = 88.22, -32.43
• Angle of Distance = arcCOS(sin(10.88)sin(-32.43) + cos(43.28)cos(88.22)cos(44.94))
• angle of distance =