# What is the distance between the tropics?

What is the distance between the tropic of cancer and the tropic of capricorn here on Earth?

Now this would seem like I could simply google the answer to it and know the exact distance in miles (please provide imperial units) but I have been researching this and cant find an answer... I also don't know how to do the calculations myself so, yeah. Providing a number is definitely not what I am wanting, I would rather be told a bit more information that would allow me to fact-check your answers by doing some simple addition (like how big a degree is and how many degrees there are total (though I can probably find the size of degrees on google).

I am specifically talking about when you follow the curvature of the earth.

• 46.874 degrees x 111.3 km/degree = 5217 km ; see here: earthscience.stackexchange.com/questions/6843/… – farrenthorpe Mar 27 '18 at 21:11
• How much precision are you looking for? Straight line? Or following the surface of the earth? – Camilo Rada Mar 27 '18 at 21:51
• Might be more applicable to a Geography SE, but unfortunately that's still only in proposal stages. A nice question, as while it's easy for some, it's not obvious to others, and will help people find useful information in the future. Hopefully someone takes the time to expand farrenthorpe's answer into a complete one (if you are talking along the surface of the Earth... as Camilo notes, it's "shorter" to cut through the inside of the Earth) :-) – JeopardyTempest Mar 28 '18 at 1:23

Both the tropics of Capricorn and Cancer are 23.43692 degrees from the equator. So the angular distance between the two is 46.8738 degrees (2 x 23.437) of latitude.

One nautical mile is defined as one minute of latitude. This is equivalent to one 1/60 of a degree.

Thus, the distance between the tropics, along the surface of the earth is 60 x 46.8738 = 2812.4304 minutes of latitude.

Also, one nautical mile is 1.852 km and 1.1508 miles.

Thus, 2812.43 minutes of latitude is 5208.6 km or 3236.5 miles

Let's start by the quick rule of thumb, I'll follow the way I do it mentally as I think the mnemonics I use could help you too.

First, the tropics are at 23.5° of latitude. And remembering that the original definition of meter is "A ten-millionth of an Earth's quadrant", it means the perimeter of Earth is 40,000 km, that consist on 360° of latitude, then:

$1^\circ = \frac{40,000 \, km}{360^\circ}= 111.11 \, km/^\circ$

Now, the distance between the tropics in a first approximation would be

$\text{Distance} = 2 \times 23.5^\circ \times 111.1 \, km/^\circ = 5221.7 \, km$

Now there are a few sources of error in this calculation. First, the actual latitude of the tropics is 23.43692° (or 23°26′12.9″). Second, the perimeter of Earth is not exactly 40,000 km (it is 40,075.017 km along the equator and 40,007.86 km along a meridian). And third, Earth is not a sphere, therefore not all the degrees of latitude cover the same distance. Taking all those factors into account the actual distance is 5,185.9 km (Calculated using a GIS software).

If you want more accuracy than a few hundred meters, you have to specify the date, because the actual latitude of the tropics oscillates between 22.1 and 24.5 degrees on a 41,000-year cycle. And it is currently changing at a rate of about 0.5 arc seconds of latitude per year, that translates in a displacement of about 14 meters every year.

NOTE: To make the answer more readable to everyone I decided to keep it in metric units (it also makes sense for the mnemonics I use to derive the length of a degree of latitude), so I leave the transformation to imperial units to you.

• IIRC, metric units are preferred on SE sites, even. (But I could not re-find the meta post saying that). – Jan Doggen Mar 28 '18 at 7:47