Contour Interval Calculator

Choosing a contour interval is a compromise between vertical detail and horizontal legibility. The raw arithmetic is trivial, dividing the elevation range by the number of lines wanted, but the answer must then be snapped to a conventional value from the sequence 1, 2, 5, 10, 20, 25, 50, 100, 200, 250, 500, and 1000 metres so that readers can count lines and interpolate mentally. A 2000 m range at roughly 20 lines gives a raw interval of 100 m, already a standard value. Interval and scale are coupled because the printed spacing between lines, not the vertical step, is what limits readability. A useful rule of thumb sets the interval in metres near one-thousandth of the scale denominator, so 1:25000 suits 25 m and 1:50000 suits 50 m in moderate relief. Several conventions ride on the chosen value. Every fifth line is drawn heavier as an index contour and labelled, so a 20 m interval produces index contours every 100 m. Supplementary contours at half the interval, drawn dashed, are added selectively in flat ground where the standard lines would be hundreds of metres apart on the map. The first and last drawn contours are the whole multiples of the interval falling inside the elevation range, with true summits and depressions given as spot heights instead. The main limitation is that a single interval must serve the whole sheet, so any map with both alpine and floodplain terrain will be crowded in one area and sparse in the other. Accuracy standards conventionally allow error of half the contour interval.

Contours began underwater. Depth soundings joined into lines of equal depth appear on Dutch charts from the late sixteenth century, and in 1727 the engineer Nicolaas Cruquius mapped the bed of the river Merwede using isobaths, producing what is generally regarded as the first true contour map. Philippe Buache applied the same idea to the English Channel in 1752. Extending the technique to dry land was proposed by Marcellin du Carla-Boniface in 1782, and in 1791 Jean-Louis Dupain-Triel published a contour map of France, establishing the method for terrestrial relief. Military and national survey organisations turned the practice into standards during the nineteenth century, since artillery and route planning demanded consistent relief depiction. The French Corps of Engineers and later the British Ordnance Survey adopted fixed intervals tied to map scale, along with the heavier labelled index line and hachured depression contours. In the United States the Geological Survey, founded in 1879, built its topographic quadrangle programme on these conventions, and its 7.5-minute series at 1:24000 scale used contour intervals of 10, 20, or 40 feet depending on relief. National map accuracy standards adopted in the 1940s codified the requirement that 90 percent of tested points fall within half a contour interval of true elevation. Contour generation is now automated from elevation grids, typically by marching-squares style cell tracing followed by curve smoothing.