Latitude and Longitude Getting Started
Lines of latitude measure distance north or south of the equator. The latitude of a particular location is the distance, measured in degrees, between that place and the equator. This distance is measured along a meridian, or line of longitude. If the earth were a perfect sphere (which it isn’t), the distance, or the length, of 1o of latitude would be constant everywhere. In reality, the earth is slightly flattened at the poles, so the length of 1o of latitude at the poles is slightly more than at the equator. At the equator, the length of 1o of latitude is equal to 110.6 km (68.7 mi.) and at the poles, the length of 1o of latitude is equal to 111.7 km (69.4 mi.). For our purposes, we will assume the length of one degree of latitude is 111 km.
Lines of longitude, also called meridians, run north - south. Meridians are farthest apart at the equator, and converge at the North and South Poles. The prime meridian, which runs through Greenwich, England, is referred to as 0o longitude. Points are measured east or west of the prime meridian until one reaches the opposite side of the prime meridian, which is referred to as the International Date Line. This is considered 180o longitude, and is the highest value which longitude can take. In other words, values for longitude range from a minimum of 0o to a maximum of 180o.
Figure EG.13 Equator and Prime Meridian
(Source: Peter H. Dana, Coordinate Systems Overview, The Geographer’s Craft Project, )
Lines of longitude measure distance east or west of the prime meridian. The longitude of a particular location is the distance along a parallel, measured in degrees, between that place and the prime meridian. The prime meridian passes through the old Royal Observatory at Greenwich, England, and is sometimes referred to as the Greenwich meridian. Since meridians are farthest apart at the equator and converge at the poles, the distance in kilometers (or miles) of 1o of longitude varies from a maximum at the equator, to a minimum at the poles. At the equator the approximate length of 1o is approximately 111 km (69 mi.). At 60o north and south latitudes, the length of 1o of longitude is approximately 55.5 km (34.5 mi.), or half what it is at the equator.
An infinite number of parallels or meridians can be drawn on a globe. Thus, parallels and meridians exist for any point on the earth. Generally, only selected parallels and meridians are marked on maps and globes, and these are usually spaced equal distances apart. Parallels and meridians always intersect each other at right angles. In order to locate a particular point on the earth, a latitude and a longitude measurement is necessary. As stated above, these measurements are in degrees, but sometimes measurements smaller than degrees are necessary. In this case, minutes and seconds are used.
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.)
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Earth’s Equatorial Radius, RE |
6378.14 Km |
(3963.19 miles) |
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|
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) |
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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):
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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) |
|
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1″ (1 second) of Longitude (1/3600th of 1°) is only |
30.9221 m |
(101.45 feet) |
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0.1″ (1/10th second) of Longitude (1/36000th of 1°) is only |
3.09221 m |
(10.145 feet) |
Longitude At the Poles (90° latitude):
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At the Poles - all lines of Longitude converge to a point - there is no distance between them. |
Longitude At Other Latitudes:
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At other Latitudes, the distance between longitudes decreases the further North (or South) you go. |
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°):
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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) |
|
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1″ (1 second) of Latitude (1/3600th of 1°) is only |
30.7151 m |
(100.771 feet) |
|
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0.1″ (1/10th second) of Latitude (1/36000th of 1°) is only |
3.07151 m |
(10.0771 feet) |
Latitude At the Poles (90°):
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|
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) |
|
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1″ (1 second) of Latitude (1/3600th of 1°) is only |
31.0261 m |
(101.792 feet) |
|
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0.1″ (1/10th second) of Latitude (1/36000th of 1°) is only |
3.10261 m |
(10.1792 feet) |
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!
Click here to Calculate distance and bearing between two Latitude/Longitude points