SME
Cartography · Problem type
Degrees, minutes and seconds
Use this for “Write the latitude 40° 26′ 46″ N in decimal degrees.”
This is an example. Type your own values to start a new problem.
d
°
m
′
s
″
=
x
°
Formulas
x
=
d
+
m
60
+
s
3,600
40.4461
=
40
+
26
60
+
46
3,600
Assumptions
•
A degree has 60 minutes (′) and a minute has 60 seconds (″), so a degree has 3,600 seconds.
•
A south latitude or west longitude gets a minus sign on the whole decimal: 40° 26′ 46″ S is −40.4461°.
•
Four decimal places of a degree pin a place to about 11 m on the ground.
Step-by-step
WE KNOW
d = 40, m = 26, s = 46
FIND
decimal degrees (x)
Step 1 · Find decimal degrees (x)
Use x = d + m ÷ 60 + s ÷ 3,600
Minutes are sixtieths of a degree and seconds are 3,600ths, so turn each into degrees and add.
x
=
40
+
26
60
+
46
3,600
26
60
=
0.4333
46
3,600
=
0.0128
40 + 0.4333 + 0.0128 = 40.4461
x
=
40.4461
Check
Put the numbers back in. Both sides should match.
40.4461
=
40
+
26
60
+
46
3,600
✓
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