RASC Calgary Centre - Latitude and Longitude
By: Larry McNish
Page last updated November 5, 2018
(Page originally created April 2, 2005)
The Shape of the Earth
The Earth is not a Sphere - it is an "Oblate Spheroid" - it is 134.397 km further around the Equator than it is around the Poles.
The following diagram is exaggerated to show what we mean. (The blue line is a circle.)
| Earth's Equatorial Radius, RE | 6378.14 km | (3963.19 miles) |
| Earth's Polar Radius, RP | 6356.75 km | (3949.90 miles) | (99.66 % of the Equatorial radius) |
| Earth's Mean Radius = (RE2 x RP)1/3 | 6371.00 km | (3958.76 miles) |
How "far" is 1° of Longitude or 1° of Latitude on the Earth's Surface?
The answer is that it depends on your Latitude (but not your Longitude).
(In reality it does depend on your local terrain. To go one degree West you might have to climb a mile high mountain, but we're going to ignore that and assume the surface of the Earth is smooth.)
Distance Between Longitudes:
Longitude At the Equator (0° latitude):
| | 1° of Longitude (1/360th of the Earth's equatorial circumference) is | 111.3195 km | (69.17073 miles)
| | | 1' (1 minute) of Longitude (1/60th of 1°) is | 1.8553 km | (1.1528 miles)
| | | 1" (1 second) of Longitude (1/3600th of 1°) is only | 30.9221 m | (101.45 feet)
| | | 0.1" (1/10th second) of Longitude (1/36000th of 1°) is only | 3.09221 m | (10.145 feet)
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Longitude At the Poles (90° latitude):
| | At the Poles - all lines of Longitude converge to a point - there is no distance between them.
You can go through all lines of Longitude just by turning around in a circle without going any distance.
Therefore, at the Poles there is no distance between longitudes.
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Longitude At Other Latitudes:
| | At other Latitudes, the distance between longitudes decreases the further North (or South) you go.
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The Formula for Longitude Distance at a Given Latitude (theta) in km:
1° of Longitude = 111.41288 * cos(theta) - 0.09350 * cos(3 * theta) + 0.00012 * cos(5 * theta)
Distance Between Latitudes:
Latitude At the Equator (0°):
| | 1° of Latitude (1/360th of the Earth's Polar circumference) is | 110.5743 km | (68.70768 miles)
| | | 1' (1 minute) of Latitude (1/60th of 1°) is | 1.8429 km | (1.1451 miles)
| | | 1" (1 second) of Latitude (1/3600th of 1°) is only | 30.7151 m | (100.771 feet)
| | | 0.1" (1/10th second) of Latitude (1/36000th of 1°) is only | 3.07151 m | (10.0771 feet)
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Latitude At the Poles (90°):
| | 1° of Latitude (1/360th of the Earth's Polar circumference) is | 111.6939 km | (69.40337 miles)
| | | 1' (1 minute) of Latitude (1/60th of 1°) is | 1.8616 km | (1.1567 miles)
| | | 1" (1 second) of Latitude (1/3600th of 1°) is only | 31.0261 m | (101.792 feet)
| | | 0.1" (1/10th second) of Latitude (1/36000th of 1°) is only | 3.10261 m | (10.1792 feet)
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Note that the distance between Latitudes increases towards the poles - this is because the Earth is "flatter" the further you are from the Equator.
The Formula for Latitude Distance at a Given Latitude (theta) in km:
1° of Latitude = 111.13295 - 0.55982 * cos(2 * theta) + 0.00117 * cos(4 * theta)
So, how does this change as you go from the Equator to the Pole?
Or, The incredible shrinking Longitude and expanding Latitude!
Calculating the Distance between two points on the Earth
To calculate the distance between two points of Latitude and Longitude on the Earth's surface, See one of the following:
http://www.gpsvisualizer.com/calculators
http://www.movable-type.co.uk/scripts/latlong.html
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