Map Scale: Distance, Area, and Representative Fraction

A representative fraction of 1:24,000 means one unit on the map is 24,000 of the same units on the ground, and because the fraction is unitless the conversion to feet per inch is just a division by twelve -- which is why the standard 7.5-minute quadrangle gives 2,000 ft per inch, and where the old rule about an inch being roughly a third of a mile comes from. Area is where it goes wrong. Scale enters area SQUARED, so a map at twice the scale denominator does not cover twice the ground per square inch, it covers four times. On a 1:24,000 quadrangle one square inch is 91.83 acres; on a 1:100,000 sheet the same square inch is 1,594 acres, seventeen times more, for a scale that is only about four times smaller. Anyone estimating a burn area, a search segment, or a parcel off a map without squaring the scale will be off by a large multiple, and the error is always in the direction of underestimating the bigger sheet. Measuring 3.5 in along a route on a quadrangle is 7,000 ft or 1.33 mi, and a 2.4 sq in polygon planimetered off the same sheet is 220 acres -- but 3,826 acres off the 1:100,000 sheet, from the same pencil marks. A measurement aid; the map's own scale bar, its datum, and a GIS measurement govern anything that matters.

ft_per_inch = representative_fraction / 12; ground_distance_ft = map_distance_in x ft_per_inch; acres_per_sq_inch = ft_per_inch^2 / 43,560; ground_area_acres = map_area_sqin x acres_per_sq_inch.

Representative fraction to ground units, with area scaling as the SQUARE of the linear scale, by name; public map arithmetic. The 1:24,000 USGS 7.5-minute quadrangle at 2,000 ft per inch is named as the familiar case, not reproduced from any table. The map's own scale bar, its datum, and a GIS measurement govern anything that matters.

Multiplication and division on the map's stated scale and the user's own measurements.

Estimate. AHJ and licensed professional govern.

Field names used by the API: representative_fraction, map_distance_in, map_area_sqin, ft_per_inch, ground_distance_ft, acres_per_sq_inch, ground_area_acres

• Unitless fraction RF / 12 gives ground feet per map inch directlypublic map arithmetic
• Area is squared ground per square inch goes as the SQUARE of the linear scale; 43,560 sq ft per acrepublic map arithmetic
• Paper and datum the map's own scale bar governs; paper distortion and the sheet's datum are not modeledcartographic practice