Angle of Repose Calculator

We have all watched a rock slowly roll down a slightly steep hill. Use this tool to calculate the maximum steepness of an angle where granular material will not roll down.

Required Information

Angle of Repose:

What it is

What is Angle of Repose?

Create Date: October 15, 2024

Last Modified Date: November 15, 2024

Sometimes called the critical angle of repose, the angle of repose refers to the maximum slope of a hill or plane before granular material would begin to roll down.

How do you Calculate Angle of Repose?

Angle of repose can be calculated various ways but with the formula that we employ we only need two variables to get your result. The two variables required are:

  1. Height of hill

  2. Radius of hill
Once we have those values we can now use this formula to find our answer:
An image showing the formula for finding the angle of repose.
Where:
  1. AR = Angle of Repose

  2. Height = Hill Height (in meters)

  3. Radius = Hill Radius (in meters)

Understanding Your Results

Once you hit calculate you will get a single value returned to you as your answer which is the angle of repose. This value is displayed in degrees by default. You can use the result to then determine if granules would be able to roll down the slope or if they would need to be assisted with agitation or by other means.

How to Use the Angle of Repose Tool

If you are looking for a simple and easy-to-use angle of repose calculator you are in the right place. To use our tool you need to follow the following steps:

  1. Enter the total height of the hill or heap, or pile.

  2. Enter the radius of said hill, heap, or pile.

  3. Ensure the units of measurement for each field is properly set to align with your values.

  4. Hit calculate and get your angle of repose in under a second!

Example Calculation

Let's say you want to find the angle of repose for a hill that is 20 feet high and has a radius of 10 feet. You simply will enter 20 into the first field and then 10 into the second radius field. You will not have to change either of the units of measurement since they are in feet by default.

You can now hit calculate to get your answer. In this situation, we find that the angle of repose is 63.435 degrees. If needed, we can change the unit of measurement from degrees to another unit very easily by selecting it from the dropdown menu beside the answer.

Angle of Repose - Frequently Asked Questions

A high angle of repose can indicate granules that are sticky or a hill/slope made of something that is not very easy to roll down for some reason.

Irregular, angular gravel would likely have the greatest angle of repose since the pieces would easily interlock and would require more of a steep slope to break free and begin to fall down.

Angle of repose typically increases when the friction coefficient increases. The more friction between two objects, the harder it would be for it to begin to simply roll or fall down.

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