# Calculating longitude length in miles?

Suppose I have geographic coordinates of "Saratoga, California, USA" as

``````Latitude:   37°15.8298′ N
Longitude: 122° 1.3806′ W
``````

I know from here that in case of latitude `1° ≈ 69 miles` and that longitude varies:

``````1° longitude = cosine (latitude) * length of degree (miles) at equator.
``````

My question is how many miles is 1° longitude at `longitude: 122°1.3806′ W`?

• what is the distance in km of 30 latitude north? what is the distance in km of 30 latitude south? – user78466 Jul 23 '16 at 19:08
• The distance between 40 N latitude and 41 ° N latitude is 69 mi. What is this distance in km? (Hint: 1 km 0.621 mi) – user83926 Oct 6 '16 at 14:27
• Note that because the Earth is an ellipsoid, not a sphere, 1° latitude is not a constant distance. See this answer for the ellipsoid calculations involved. Based on that answer, `1° latitude = M * 2Π / 360` and `1° longitude = r * 2Π / 360`. – meustrus Apr 5 '17 at 13:11

It doesn't matter at what longitude you are. What matters is what latitude you are.

Length of `1 degree of Longitude` = `cosine (latitude in decimal degrees) * length of degree (miles) at equator`.

Convert your latitude into decimal degrees ~ 37.26383

Convert your decimal degrees into radians ~ 0.65038

Take the cosine of the value in radians ~ 0.79585

1 degree of Longitude = ~0.79585 * 69.172 = ~ 55.051 miles

More useful information from the about.com website:

Degrees of latitude are parallel so the distance between each degree remains almost constant but since degrees of longitude are farthest apart at the equator and converge at the poles, their distance varies greatly.

Each degree of latitude is approximately 69 miles (111 kilometers) apart. The range varies (due to the earth's slightly ellipsoid shape) from 68.703 miles (110.567 km) at the equator to 69.407 (111.699 km) at the poles. This is convenient because each minute (1/60th of a degree) is approximately one [nautical] mile.

A degree of longitude is widest at the equator at 69.172 miles (111.321) and gradually shrinks to zero at the poles. At 40° north or south the distance between a degree of longitude is 53 miles (85 km)

Note that the original site (about.com) erroneously omitted the "nautical" qualifier.

• I've been trying to follow these instructions, but always end up with lat/lng that are ~1.5 miles away from the initial location instead of 1 mile. cos(37.26383) is 0.79585587, so the answer to the question would be 55.05094223964 miles for 1 degree. Throwing it 0.2 miles out for every mile. – JackalopeZero Oct 5 '16 at 11:42
• Shouldn't you do 90-decimal degrees before converting to radians? – dewd Aug 14 '17 at 13:46
• @dewd - No. Latitude is zero at equator; cos(0) = 1, so the formula gives maximum length at equator. At N pole, cos(90 degrees) = 0, so formula gives zero length, as expected. – ToolmakerSteve Nov 14 '18 at 19:02
• Converting 37.26383 to radian shouldn't be 0.65037 instead of 0.79863?? This is a big difference... – pierre23 May 31 at 17:15

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