# Calculating how long arc second is for given long/lat? [closed]

I am wondering what area is covered by a dataset which is one arc second wide.

• Neither your title nor your body state clearly what you're after, and they even ask for different things. – Martin F Nov 16 '14 at 3:23

At sea level at the equator:

One degree of longitude is about 111km

One minute of longitude is one sixtieth of that: about 1.85km

One second of longitude is one sixtieth of that amount: about 31 meters or 100 feet.

However:

Arc-seconds of latitude remain nearly constant, while arc-seconds of longitude decrease in a trigonometric cosine-based fashion as one moves toward the earth's poles.

Arc seconds aren't really a great way to measure distance. Is there no possibility of using a ruler tool in your GIS or any kind of distance function?

Sources:

http://en.wikipedia.org/wiki/Arc_minute

http://www.esri.com/news/arcuser/0400/wdside.html

• Filled in some missing data -- hope you don't mind. – Martin F Nov 16 '14 at 3:34

1 nautical mile is one minute of arc. At equatorial sea level, this is equivalent to 1852m/60 = 30.86666667m (the equatorial arc-second).

As noted above, this distance will become smaller as one moves towards the poles.

At 33.6º latitude South, cos 33º = 0.83292, cos 33.6 * 30.866666667m = 25.709m for arc-second of longitude at this latitude (33.6º, approximately)

• As a bash script: DEGS_TO_RADS=0.017453293 EQUAT_ARC_SECOND_METERS=30.866666667 \$ seq 90 -5 1 | while read D ; do echo "\$EQUAT_ARC_SECOND_METERS * c(\$DEGS_TO_RADS * \$D)" | bc -l | sed "s|^|\$D degrees : |;s|\$| meters per arc seconds|" ; done 90 degrees : 0 meters 85 degrees : 2.690030000 meters 80 degrees : 5.359688000 meters 75 degrees : 7.988602000 meters – jmullee Feb 20 at 15:12