Angle of repose is a term used in science and engineering and can have two related meanings. It is generally used to describe the maximum angle, measured upwards from the horizontal, at which a pile of a particular granular material will remain stable without any of the material sliding downward. It can also refer to a combination of a ramp or other slope and an object resting upon it. In this case, the angle of repose is the maximum angle at which the ramp or slope will support the object without it sliding downward. In either case, the angle of repose, or critical angle of repose as it is more properly known, will always be greater than 0 degrees and less than 90 degrees, and most materials will have an angle of repose of 45 degrees or less.

Any material of a granular nature, even when the individual units are very large, like chunks of broken concrete or boulder sized rocks, naturally forms a pile in the shape of a cone when deposited on a flat surface from a height. The natural profile of this cone will approximate the angle of repose for that particular material or mixture. Very small or smooth granules that exert little friction on each other will tend to form piles with shallower sides and, therefore, a lower angle of repose. Rougher granules or those that adhere to each other strongly tend to form piles with steeper sides and a higher angle of repose. Moisture content also significantly affects the angle of repose of most materials.

Geologists, as well as mining and civil engineers often employ angle of repose data. It can be used to analyze slopes and embankments for danger of collapse as well as helping to evaluate potential danger of avalanche. It is useful in designing storage and transportation machinery for granular materials as it can give an engineer insight into the appropriate size and shape of such devices for a particular material. Civil engineers use angle of repose data when designing and managing construction and land management projects, such as levees, dams, and raised roadbeds. Geologists and vulcanologists use it to predict the possible behavior of cinder cones and sand volcanoes as well as to study processes related to the weathering of rocks and deposition of sediments.

Engineers and scientists use a number of methods to calculate the angle of repose of a granular substance or mixture. Calculations and formulas that employ previously published data are one method, and several simple experiments exist for determining the angle for any substance with small enough grains to be easily handled. Depending on the method and the accuracy of possible measurements, angle of repose figures tend to be close approximations rather than exact values. This does not reduce or eliminate their usefulness, however.