The Maidenhead locator system divides the earth into fields, squares, and subsquares. The first two characters in a Maidenhead locator specify the square. These are letters A through R representing 20 degrees of longitude or 10 degrees of latitude. Latitude A runs from the South Pole to 80*°* south of the equator. Latitude R runs from 80*°* north of the equator up to the North Pole.

The area of a field depends on latitude. The previous post was a lemma for this post, solving the general problem of finding the area of a region bounded by longitudes θ_{1} and θ_{2} and latitudes φ_{1} and φ_{2}. Working in degrees, the area is

*A* = π *r*² (sin φ_{1} − sin φ_{2}) (θ_{1} − θ_{2}) / 180.

So area of the *i*th field above or below the equator is

*A* = π *r*² (sin 10*i° *− sin 10(*i*−1)° ) / 6.

Fields whose second character is I or J are nearest to the equator and have the largest area. This area is

π *r*² sin 10*° */ 6

If we take *r* to be 3959 miles (6371 km) this gives an area of about 950,000 square miles or 2,500,000 square kilometers.

Let’s do a quick check to see whether this result is reasonable. The circumference of the earth is about *C* = 40,000 km [1]. The fields on either side of the equator are roughly Euclidean rectangles C/18 wide and C/36 tall. This also gives an area of about 2.5 million km².

For fields nearest the poles, fields with second character A or R, the area is

π *r*² (sin 90*° *− sin 80° ) / 6

which works out to be 83,000 square miles or 215,000 square kilometers.

Here’s a complete list of field areas based on the second letter.

|-------+----------+---------| | Field | sq miles | sq km | |-------+----------+---------| | A | 83119 | 215250 | | B | 246831 | 639211 | | C | 403044 | 1043750 | | D | 547010 | 1416575 | | E | 674356 | 1746359 | | F | 781211 | 2023080 | | G | 864330 | 2238330 | | H | 921187 | 2385571 | | I | 950054 | 2460326 | | J | 950054 | 2460326 | | K | 921187 | 2385571 | | L | 864330 | 2238330 | | M | 781211 | 2023080 | | N | 674356 | 1746359 | | O | 547010 | 1416575 | | P | 403044 | 1043750 | | Q | 246831 | 639211 | | R | 83119 | 215250 | |-------+----------+---------|

The area of a Maidenhead square is approximately 1/100 of the area of the field it is in. The area of a square also depends on latitude, but not as much as the area of a field does.

The area of a Maidenhead subsquare is approximately 1/24² = 1/576 of its square.

A typical Maidenhead field has area around 800,000 square miles or 2,000,000 square kilometers. (By “typical” I mean well populated areas. Much of the world’s population lives at around 30 or 40 degrees latitude.) So a typical square has area 8,000 square miles or 20,000 square kilometers. A typical subsquare will be around 14 square miles or 35 square kilometers.

## Related posts

[1] It isn’t a coincidence that this is such a round number. The meter was initially defined as 1/10,000,000 of the distance from the North Pole to the equator.