# Calculating Your Map Accuracy Using US National Map Accuracy Standards

Geospatial Technology September 27, 2011

Many people would like to assess the accuracy standards for mapping products. In the United States, standards for accuracy assessment have been developed.

The National Map Accuracy Standard (NMAS) provides insurance that maps conform to established accuracy specifications, thereby providing consistency and confidence in their use in geospatial applications.

The following information from the USGS National Geospatial Program Standards Web sitegenerally describes the NMAS.

With a view to the utmost economy and ease in producing maps which fulfill not only the broad needs for standard or principal maps but also the particular needs of individual agencies, standards of accuracy for published maps are defined as follows:

1. Horizontal accuracy. For maps on publication scales larger than 1:20,000, not more than 10 percent of the points tested shall be in error by more than 1/30 inch, measured on the publication scale; for maps on publication scales of 1:20,000 or smaller, 1/50 inch. These limits of accuracy shall apply in all cases to positions of well-defined points only. Well-defined points are those that are easily visible or recoverable on the ground, such as the following: monuments or markers, such as bench marks, property boundary monuments; intersections of roads, railroads, etc.; corners of large buildings or structures (or center points of small buildings), etc. In general what is well defined will be determined by what is plottable on the scale of the map within 1/100 inch. Thus, while the intersection of two road or property lines meeting at right angles would come within a sensible interpretation, identification of the intersection of such lines meeting at an acute angle would obviously not be practicable within 1/100 inch. Similarly, features not identifiable upon the ground within close limits are not to be considered as test points within the limits quoted, even though their positions may be scaled closely upon the map. In this class would come timber lines, soil boundaries, etc.

2. Vertical accuracy, as applied to contour maps on all publication scales, shall be such that not more than 10 percent of the elevations tested shall be in error more than one-half the contour interval. In checking elevations taken from the map, the apparent vertical error may be decreased by assuming a horizontal displacement within the permissible horizontal error for a map of that scale.

3. The accuracy of any map may be tested by comparing the positions of points whose locations or elevations are shown upon it with corresponding positions as determined by surveys of a higher accuracy. Tests shall be made by the producing agency, which shall also determine which of its maps are to be tested and the extent of the testing.

4. Published maps meeting these accuracy requirements shall note this fact on their legends, as follows: "This map complies with National Map accuracy Standards."

5. Published maps whose errors exceed those aforestated shall omit from their legends all mention of standard accuracy.

6. When a published map is a considerable enlargement of a map drawing (manuscript) or of a published map, that fact shall be stated in the legend. For example, "This map is an enlargement of a 1:20,000-scale map drawing," or "This map is an enlargement of a 1:24,000-scale published map."

7. To facilitate ready interchange and use of basic information for map construction among all Federal mapmaking agencies, manuscript maps and published maps, wherever economically feasible and consistent with the uses to which the map is to be put, shall conform to latitude and longitude boundaries, being 15 minutes of latitude and longitude, or 7.5 minutes, or 3-3/4 minutes in size.

Source: U.S. BUREAU OF THE BUDGET Issued June 10, 1941 Revised April 26, 1943 Revised June 17, 1947

Quick Method for Determining Accuracy

Depending on the scale of the map, the actual ground distance represented by 1/30th and 1/50th of an inch will vary. To determine the minimum standards for horizontal accuracy in actual ground meters, the following calculation must be performed.

• If larger than 1:20,000-scale, use this calculation: 0.03333 x scale x 2.54 / 100 = ground meters.

• If 1:20,000-scale or smaller, use this calculation: 0.02 x scale x 2.54 / 100 = ground meters.

Examples:

• For 1:100,000-scale maps: 0.02 x 100,000 x 2.54 / 100 = 50.8 meters (or 166 ft)

• For 1:24,000-scale maps: 0.02 x 24,000 x 2.54 / 100 = 12.2 meters (or 40 ft)

• For 1:10,000-scale maps: 0.03333 x 10,000 x 2.54 / 100 = 8.5 meters (or 28 ft)

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This work is supported by the USDA National Institute of Food and Agriculture, New Technologies for Ag Extension project.