Map Math Instruction Sheet

Converting Units � � � from to do this Examples � �

� milimeters meters 1,000mm = 1m An expanded mm m divide by 1000 4,321mm = 4.321m �

� meters milimeters 1m = 1,000mm

� tutorial on using m mm multiply by 1000 4.3m = 4,300mm map math � meters kilometers 1,000m = 1km � divide by 1000 � is available at m km 4,300m = 4.3km kilometers meters 1km = 1,000m � www.MapTools.com multiply by 1000 � km m 4.3km = 4,300m � inches feet 12 in. = 1 ft. � in. ft. divide by 12 48 in. = 4 ft. � � feet inches multiply by 12 1 ft. = 12 in.

� ft. in. 4 ft. = 48 in. � � Map scales feet miles 5,280 ft. = 1 mi. ft. mi. divide by 5280 7,392 ft. = 1.4 mi.

� grid tools, rulers, �

� miles feet 1 mi. = 5,280 ft. and other tools mi. ft. multiply by 5280 1.4 mi. = 7,392 ft. �

� for measuring inches milimeters 1 in. = 24.5mm � multiply by 24.5 map coordinates in. mm 12 in. = 294mm �

� milimeters inches divide by 24.5 24.5mm = 1 in. � are available mm in. 294mm = 12 in. miles kilometers multiply by 1 mi. = 1.6093km �

� mi. km 1.6093 5 mi. = 8.0465km kilometers miles divide by 1.6093 1.6093km = 1 mi. � km mi. 1km = 0.6213 mi. �

Check with your Map Distance v.s. Terrain Distance �

� local map store or visit Distances measured on a map assume a flat surface and do not account or the Map Math

� additional distance introduced as you climb up and down over the terrain. � www.MapTools.com ��

� Instruction � � MapTools �� Sheet

� �� 1755 La Honda Rd #95 Woodside, CA 94062 � � www.MapTools.com �

� “all weather” paper. � � � � �

Map Scale Scale Equations Some Examples � � � � � � Map scale is the relationship of When using these equations, On a 1:24,000 scale map, you have measured the distance along a trail with distances shown on the map to distances the map and ground distance your ruler as 57mm. What distance does that represent on the ground? over the ground. measurements must be Ground Distance = Map Distance X Scale Divisor

There are four ways to describe map in the same units. � scale: Ground Distance = 57mm X 24,000

Scale as a ratio Ground Distance = 1,368,000mm Scale Divisor = 1:63,360 or 1:24,000 Convert to meters by dividing by 1000 to get 1,368m Ground Distance / Map Distance Scale as a fraction or decimal value Convert to kilometers by dividing be 1000 to get 1.368km �

1/63,360 or 0.000015783 Convert to miles by dividing by 1.6093 to get 0.85 miles Map Distance = Scale as a divisor Ground Distance / Scale Divisor 63,360 On a 1:50,000 scale map, how far apart would 1km grid lines be? � Scale as an equivalence 1km = 1,000m = 1,000,000mm Ground Distance = 1 inch ⇔ 1 mile Map Distance = Ground Distance / Scale Divisor Map Distance X Scale Divisor In a scale ratio the first number Map Distance = 1,000,000mm / 50,000

represents a distance on the map. The � Map Distance = 20mm value of one is always used for the map It is usually inconvenient to measure distance. the map and ground distances in the same units. Thus we frequently will The second number is the distance What scale is a map where 1.5 inches ⇔ 1 mile? over the ground in the same units as convert a large number of millimeters measured on the map. into meters or kilometers. We would First get the units of measure to be the same convert inches into feet or miles. Refer � The ratio holds true no mater what to the back of this sheet for information 1 mile = 5280 feet = 63,360 inches units of measure are selected. However, about converting units. both map and ground distances must be Scale Divisor = Ground Distance / Map distance measured in the same units. Scale Divisor = 63,360 in. / 1.5 in.

Thus on a 1:24,000 scale map... � Scale Divisor = 42,240 one inch on the map The map scale is 1:42,240 is 24,000 inches on the ground.

one foot on the map is 24,000 feet on the ground. �