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Conical Heap Slope Angle, Height & Radius

Relate height and radius of an ideal conical heap to slope angle and a simple friction-equivalent ratio.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

A heap 1 m high with a 1 m base radius has slope ratio 1 and slope angle 45° from horizontal.

Slope ratio = height / base radius; slope angle = arctan(slope ratio)

Enter these known values and leave the other values blank.

Height, radius and slope ratio must be positive. The angle is strictly between 0° and 90°.
The geometry assumes a straight conical side. Interpreting tan(angle) as a friction coefficient requires the ideal noncohesive limiting-equilibrium model.
Measured granular repose angle can depend on grain shape, moisture, packing and measurement method. The geometry alone does not establish a material property or safe slope.

Enter radius, half the base diameter. Using the full diameter would halve the height-to-radius ratio.

No. It computes a geometric ratio and its angle. A material friction measurement or stability assessment requires additional information.

Bookify requires a positive slope ratio for the positive conical-heap geometry.