Map Slope Calculator
Work out the average grade, angle and slope ratio between two points on a topographic map from the contour interval, the contours crossed and the map distance.
Reading height from contour lines
Contour lines join points of equal elevation. The contour interval, printed in the map margin, is the height difference between neighbouring lines: 40 ft on many USGS 1:24,000 quadrangles in hilly terrain, 20 ft in flatter areas, and 10 m on Ordnance Survey and most European 1:25,000 maps, with 5 m on some. Every fifth line, the index contour, is drawn thicker and labelled. To find the rise between two points, count the contour lines crossed and multiply by the interval. The run is the map distance multiplied by the scale. Grade is rise ÷ run × 100%; the angle is the arctangent of rise ÷ run.
A worked example
On a 1:24,000 quadrangle with a 40 ft interval, a trail climbs from a creek to a saddle, crossing 8 contour lines over 1.5 inches on the map. The rise is 8 × 40 = 320 ft and the run is 1.5 × 24,000 = 36,000 inches, or 3,000 ft. The average grade is 320 ÷ 3,000 = 10.7%, an angle of 6.1° and a slope ratio of 1 in 9.4. For comparison, US Interstate design standards keep grades to about 6% even in mountainous terrain, a steep paved road is 15% to 20%, and a trail above about 15% average feels very steep on foot. If the same 8 lines were crossed in only 0.5 inch, the grade would be 32%, an angle of 17.7°.
Percent grade is not degrees
The most common mistake is to treat grade and angle as the same number. A 100% grade means a rise equal to the run, which is 45°, not vertical. A 10% grade is 5.7°, 25% is 14.0° and 50% is 26.6°. Avalanche terrain is usually described in degrees, with most slab avalanches on slopes of 30° to 45°, which is 58% to 100% grade; road signs and trail guides usually use percent. When contour lines are very close together, measure across a short distance and use the map’s slope-angle gauge if it has one, because a small error in a short map distance becomes a large error in grade.
The limits of an average
The result is the average slope between the two points you chose. Contour lines can hide anything less than one interval: a 30 ft cliff can sit between two 40 ft contours and not appear at all. Map accuracy standards allow contours to be off by up to half an interval at well-defined points, so short measurements carry large uncertainty. When no contour lines are crossed, the calculator reports an upper bound, because the rise must be less than one interval. For route planning, measure the steepest section separately rather than averaging it into a long gentle approach.
How to use it
- Find the contour interval in the map margin and choose feet or metres.
- Count the contour lines crossed between the two points.
- Measure the straight-line map distance and enter the map scale.
- Read the grade, angle and slope ratio, and measure steep sections separately.
Questions from the map table
How do you calculate slope from a topographic map?
Multiply the number of contour lines crossed by the contour interval to get the rise, convert the map distance to ground distance with the scale to get the run, and divide rise by run. Eight 40 ft contours over 1.5 inches at 1:24,000 is 320 ft over 3,000 ft, a 10.7% grade.
Is a 100% grade vertical?
No. A 100% grade means the rise equals the horizontal distance, which is a 45° angle. A vertical cliff would have an infinite grade. Grade in percent is rise ÷ run × 100, while the angle is the arctangent of rise ÷ run, so the two numbers diverge quickly as slopes steepen.
What is the contour interval on USGS and Ordnance Survey maps?
USGS 1:24,000 quadrangles commonly use 10, 20 or 40 ft depending on the terrain, with some mountain sheets at 80 ft. Ordnance Survey Explorer maps at 1:25,000 use 5 m in most of lowland Britain and 10 m in mountain areas. The interval is always printed in the map margin.
Why does my GPS track show a steeper section than the map slope?
Because the map gives an average between two points and contours cannot show features smaller than one interval. A short steep pitch, a step or a small cliff between two contour lines is averaged away. Measure the closest-spaced contours separately to find the steepest part of a route.
Disclaimer: Map results are calculations on the WGS84 datum from the coordinates and measurements you enter. They are not a navigation device, a land survey or a safety assessment. Carry a map and compass outdoors, check the datum of your map, apply the current magnetic declination, and rely on deeds and licensed surveyors for property boundaries and areas.