Built by a geologist

Slope and Gradient Calculator

Slope describes vertical change relative to horizontal distance. The dimensionless gradient equals rise divided by horizontal run. Percent slope or percent grade equals that gradient multiplied by 100. The slope angle equals the inverse tangent of the gradient, while a 1:N ratio under GeoMiner's explicit convention means one vertical unit for N horizontal units. A rise of 10 metres over a horizontal run of 100 metres is a 0.1 gradient, 10 percent grade, about 5.71 degrees, and 1:10 vertical:horizontal. A 100 percent grade is 45 degrees, not 100 degrees. Percent slope can exceed 100 when rise exceeds horizontal run; it approaches infinity toward a vertical face. Positive values rise in the stated direction, negative values fall, and zero is level. Always preserve direction because a magnitude alone cannot distinguish ascent from descent. Horizontal run is not distance travelled along the surface. For known rise and run, surface distance is the hypotenuse: the square root of rise squared plus run squared. A map, elevation model, or survey must supply compatible horizontal and vertical measurements before the formulas are meaningful. Coordinate reference system, horizontal and vertical datums, map scale, contour interval, raster resolution, interpolation, vegetation, rough terrain, measurement alignment, route curvature, and endpoints can all change the result. A single average grade can hide short steep sections, benches, breaks, transitions, and crossfall. Ratio notation is ambiguous between disciplines: some publish vertical:horizontal, others horizontal:vertical, and phrases such as one in four can be misunderstood. State the full convention every time. Conversion is geometry, not design. It cannot establish safe mine-ramp, haul-road, trail, accessibility, excavation, slope, stockpile, pit, quarry, foundation, or earthwork criteria. Material strength, discontinuities, soil and rock conditions, water, drainage, erosion, stability, equipment capability, braking, traction, curvature, crossfall, sight distance, weather, regulation, operating procedures, survey quality, and consequence require applicable standards and qualified work. GeoMiner keeps exact values in the browser. Analytics retain only bounded action, input-format, direction, and broad slope-band groups—never rise, run, percent, angle, ratio, distance, route, station, project, or location.