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Map scale calculator

Representative fraction to ground distance

A map scale calculator turns a ruler measurement into a ground distance. A representative fraction of 1:24,000 means one unit on the map is 24,000 of those units on the ground. USGS 7.5-minute topographic maps use 1:24,000. Measure the trail on the map in inches or centimeters, enter the denominator, and read feet, miles, meters, and kilometers. The page does not look at a map image. You bring the measurement.

Inputs

Result

Enter a scale and the distance you measured on the map.

Disclaimer: Straight arithmetic on the scale and the measurement you enter. Paper stretch, a bent trail, and a wrong scale will all throw it off.

After the map distance is in miles, unit cleanup can also happen on the ClearQuip unit converter.

How to use

  1. Read the scale printed on the map. Pick a preset or type the denominator. For 1:24,000 the denominator is 24000.
  2. Measure the route on the map with a ruler or a string, in inches or centimeters. A winding trail measured as a straight line will be short.
  3. Select the unit you measured.
  4. Press Calculate. Ground distance is the map distance times the denominator.

How it's calculated

Ground inches = map inches × denominator
Feet = ground inches ÷ 12
Miles = feet ÷ 5,280
Centimeters on the map are converted at 2.54 cm = 1 inch

The representative fraction has no units of its own. One inch times 24,000 is 24,000 inches on the ground, which is 2,000 feet. Three inches on a 1:24,000 map is 6,000 feet, or 6,000 ÷ 5,280 = 1.136 miles. A centimeter is 1/2.54 inch, so the page divides centimeter measurements by 2.54 before applying the scale.

Once you have miles, pace and time are the pace calculator and the Naismith calculator. This page does not read contour lines; elevation still has to be counted.

Worked example

Three inches on a 1:24,000 map: 3 × 24,000 = 72,000 inches on the ground. Divide by 12 to get 6,000 feet, then by 5,280 to get 1.136 miles. The same three inches on a 1:62,500 map is 62,500/24,000 times as far, about 2.96 miles. One centimeter on a 1:25,000 map is 25,000 cm, or 250 meters, or 0.25 km.

Assumptions and sources

USGS 7.5-minute quadrangles are published at 1:24,000, and older 15-minute maps at 1:62,500. Those denominators are map-series facts, not measurements of your trail. The inch is converted at 2.54 centimeters exactly. A trail that bends must be measured along its length; the calculator cannot see the paper. It also assumes the scale you typed is the scale of the copy you measured. An enlarged photocopy is a different scale.

FAQ

What does 1:24,000 mean in feet?

One inch on the map is 24,000 inches on the ground, and 24,000 ÷ 12 = 2,000 feet. So one inch represents about 2,000 feet.

Why is my trail longer than the straight-line result?

You measured a chord, not the path. Measure along the trail with a string or a map wheel, then enter that length.

Can I use a phone screenshot of a map?

Only if you know the scale of the image you measured. Zooming changes the scale. The printed representative fraction applies to the sheet, not to a cropped screenshot.

Does this give elevation?

No. It converts horizontal map distance. Count contours separately and use the elevation gain calculator.

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