Dem Resolution to Ground Distance Calculator

Elevation data distributed on a geographic grid is spaced in angular units, not metres, and the ground size of a cell therefore depends on where it sits. One arc-second of latitude corresponds to a fixed north-south distance of about 30.87 m, obtained by taking the mean Earth radius of 6,371,000 m, multiplying by pi over 180 to get 111.19 km per degree, and dividing by 3600. East-west spacing shrinks with the cosine of latitude because meridians converge toward the poles, so the same one arc-second cell measures roughly 30.87 m across at the equator, 21.8 m at 45 degrees, and 15.4 m at 60 degrees. Cells are consequently rectangular almost everywhere, and cell area falls off with cosine of latitude as well, from about 953 square metres at the equator to under 500 at 60 degrees. This is why the familiar shorthand of calling one arc-second data 30 m and three arc-second data 90 m holds only near the equator. It matters in practice for area and volume calculations, for slope algorithms that assume square cells, and for any analysis spanning a wide latitude band, which is normally handled by reprojecting to an equal-area or local projected system before computing. The cosine relation also explains why high-latitude datasets are often distributed with widened longitudinal spacing to keep cells roughly square. Two caveats: the formula assumes a spherical Earth, so it differs from ellipsoidal values by a few tenths of a percent, and horizontal cell size says nothing about vertical accuracy, which is a separate property of the source sensor.

Dividing the circle into 360 degrees, each of 60 minutes and each minute of 60 seconds, is Babylonian sexagesimal practice inherited through Greek astronomy, and it was still the natural unit when geodesy became systematic. The metre itself was defined in the 1790s as a fraction of the meridian quadrant from pole to equator, which is why a degree of latitude works out near 111 km and the numbers in this conversion look tidy. Early topographic surveying worked in projected national grids, but global data had no such option and defaulted to latitude and longitude. The angular convention became universal with satellite elevation datasets. The USGS EROS Data Center released GTOPO30 in 1996, a global model at 30 arc-seconds, roughly one kilometre. The Shuttle Radar Topography Mission flew aboard Endeavour on mission STS-99 in February 2000, using C-band interferometry to map land between about 56 degrees south and 60 degrees north, distributed at 3 arc-seconds globally and 1 arc-second for the United States, with the full 1 arc-second product released worldwide in 2014 and 2015. ASTER GDEM, produced from stereo optical imagery by NASA and Japan's Ministry of Economy, Trade and Industry, followed in 2009 at 1 arc-second. The USGS 3D Elevation Program distributes lidar-derived data at 1/3 and 1/9 arc-second, continuing the same angular convention.