Calculate the angle of repose, pile height, or pile radius for a conical pile using height plus radius or base diameter.
Advanced options
How to use our Angle of Repose Calculator
- Choose Solve for to pick the value you want: angle, height, or radius.
- Set Length input mode to Radius if you measured from the center to the edge, or Base diameter if you measured across the whole pile.
- Select Length unit so all visible length inputs use the same unit.
- Enter the visible known values: Pile height, then either Pile radius or Base diameter, or enter Angle of repose when solving for height or radius.
- Open Advanced options if you want angle results in degrees, radians, or both, and if you want to change Number display or Significant figures.
- Click Calculate.
- Read Calculated value first, then check Radius used in calculation and Equivalent base diameter to confirm the pile size matches how you measured it.
- Sanity-check the result: a bigger Height-to-radius ratio means a steeper pile, and an angle near 0 deg should give a very wide pile while an angle near 90 deg should give a very narrow one.
Definitions
Solve for: The value the calculator will find for you: angle, height, or radius.
Length input mode: Chooses whether the pile size is entered as Pile radius or Base diameter.
Pile height: The vertical distance from the flat ground to the top of the pile.
Pile radius: The horizontal distance from the center of the base to the edge.
Base diameter: The full width across the base through the center. Diameter is 2 times radius.
Angle of repose: The surface slope of the pile measured upward from horizontal ground.
Height-to-radius ratio: Height divided by radius. Larger values mean a steeper pile.
Radius used in calculation: The effective radius after any base-diameter conversion.
Equivalent base diameter: The full base width that matches the radius used in the math.
Common mistakes and quick fixes
Mistake: Entering the full pile width into Pile radius when you really measured across the base.
Fix: Change Length input mode to Base diameter and enter that value in Base diameter , or divide the width by 2 before using Pile radius .
Mistake: Mixing units, such as typing Pile height in cm and Pile radius in m.
Fix: Use one shared Length unit for every visible length input before you calculate.
Mistake: Entering 0, a negative number, or 90 in Angle of repose .
Fix: Use an angle greater than 0 deg and less than 90 deg so the geometry works correctly.
Mistake: Reading Calculated value without noticing what mode is selected in Solve for .
Fix: Check Solve for first, then interpret Calculated value as angle, height, or radius for that mode.
Mistake: Ignoring Radius used in calculation after entering Base diameter .
Fix: Confirm that Radius used in calculation is half of the entered Base diameter so you know the conversion matched your measurement setup.
Mistake: Treating Assumption note as optional when comparing different materials or test setups.
Fix: Read Assumption note to remember the result is based on a simple conical pile geometry, not a full material-flow test.
Limitations & Key Assumptions / Boundary Conditions
- This calculator assumes a conical pile with a circular base and a straight surface slope.
- It assumes the pile sits on a flat horizontal base plane.
- The geometry uses a static surface shape, so it does not model pouring speed, vibration, moisture, particle size, packing, or other material effects that can change real measured angles.
- All visible length inputs must use the same Length unit or the result will be wrong.
- Angle of repose must be greater than 0 deg and less than 90 deg. Results become very sensitive to small input errors when the angle is close to 90 deg.
- Very small angles can produce very large radius results when solving for Radius; that is expected from the geometry.
- Hidden inputs are not part of the calculation. For example, when Length input mode is Base diameter, the active size input is diameter, not radius.
- The result should not be treated as a complete material property by itself; real test methods and material state can give different values.
Methodology
Core geometry
This calculator uses right-triangle geometry for a conical pile. The side view of the pile forms a triangle where height is the vertical side and radius is the horizontal side.
θ (angle in degrees) = arctan(h / r) x 180 / π
h (height) = r x tan(θ x π / 180)
r (radius) = h / tan(θ x π / 180)
r = d / 2
θ (angle in radians) = θ (degrees) x π / 180
height-to-radius ratio = h / r
What each mode does
When Solve for is set to angle, the calculator reads Pile height and the active length input, converts diameter to radius if needed, and then computes the angle. When set to height, it uses the active radius and the entered angle. When set to radius, it uses height and angle, then also reports the matching diameter.
Worked mini-example
If Pile height is 2 m and Base diameter is 4 m, the radius used is 2 m.
r = 4 / 2 = 2
θ = arctan(2 / 2) x 180 / π = 45 deg
ratio = 2 / 2 = 1
That means the pile surface is moderately steep, with height equal to radius.
Interpretation
A larger angle or a larger Height-to-radius ratio means a steeper pile. A smaller angle means a flatter, wider pile. The diameter output is included so users who measure across the whole base can verify the geometry quickly.
Assumptions behind the result
This is a geometry calculator, not a full bulk-material test model. It assumes a conical pile, a flat base, and a single stable surface slope. Real measured angle of repose can change with the material, how the pile was formed, and the test setup [2].