Mileage by Map

Measured a route on a paper map with a ruler, string or map wheel? This calculator turns centimeters on the sheet into ground distance and adds an allowance for bends you could not trace.

How the calculation works

A scale of 1 : M means 1 cm on the map equals M cm on the ground, which is M / 100,000 km. Straight-line distance is therefore S = map length (cm) × M / 100,000. On a 1 : 100,000 map, 1 cm is exactly 1 km; on 1 : 50,000 it is 0.5 km; on a USGS 1 : 24,000 topo it is 0.24 km.

Roads and trails rarely run straight, and a series of straight segments misses small wiggles. The calculator multiplies by a winding (tortuosity) factor k: ground distance = S × k. Hikers and drivers commonly use 1.1–1.3 for roads, more for switchbacks. You can set k between 1 and 2; the default is 1.2.

Inputs: length on the map in centimeters (0.1–200), the scale denominator M (1,000 to 10,000,000) and k. If you measured in inches, multiply by 2.54 first. Results: ground distance in km, the straight-line distance, how many kilometers 1 cm represents, and the total in miles (1 mi = 1.609344 km).

Worked example

A route on a 1 : 100,000 map measures 10 cm. Straight line: 10 × 100,000 / 100,000 = 10 km, so 1 cm equals 1 km. With a winding factor of 1.2 the ground distance is 12 km, about 7.46 miles.

Things to keep in mind

• Trace the actual line of the road, not a straight line between endpoints. A map wheel or a piece of string laid along the curves lets you use a smaller k, around 1.05–1.1.
• On mountain routes, elevation gain affects travel time far more than the extra distance; add time for climbs separately.
• Double-check the scale printed on the sheet. Mixing up 1 : 24,000, 1 : 50,000 and 1 : 100,000 multiplies the error.
• Photocopies and printouts are often resized. Calibrate against the graphic scale bar on the map rather than the stated ratio.