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Riprap Isbash Scale and Material Budget

Explore the classical Isbash stone-diameter relation and estimate bulk layer volume, mass and cost using explicit assumptions.

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Calculator inputs

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How to use this calculator

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

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Formula and method

For the classical relation with 2 m/s velocity, relative solid density 3, g = 10 m/s² and low-turbulence coefficient 1.2, the calculated diameter scale is approximately 6.944444 cm.

D = V²/[2gK²(S−1)]; bulk volume = area × depth; ordered volume = volume × (1+waste%).

Worked example

Enter these known values and leave the other values blank.

I want to find the...
average rock diameter (D₅₀)
Water velocity (V)
2 m/s
Specific gravity (S)
3
Gravitational acceleration (g)
10 m/s²
Isbash constant (C)
Low turbulence (1.2)
Average rock diameter (D₅₀)
6.944 cm

Assumptions and limitations

  • The classical Isbash scale assumes fully submerged stone and a selected empirical stability coefficient. It omits bank slope, bends, local turbulence corrections, depth, filters, scour, gradation and installation checks. It is an educational relation and quantity allowance; it does not establish site-specific riprap design.
  • Coefficient choices 0.86 and 1.20 are retained classical high- and low-turbulence conventions described in USACE EM 1110-2-1601 Appendix F. Bulk density is the installed rock-layer bulk density including voids, distinct from the solid-rock specific gravity used by the diameter relation.
  • Depth is a user planning input and is not derived from calculated diameter. Prices replace defaults; added waste increases ordered bulk volume.
  • Clear an unknown before solving backward. Currency controls represent the chosen denomination without exchange rates; prices must use the selected denominator units.

Common questions

What is included in this estimate?

The classical Isbash scale assumes fully submerged stone and a selected empirical stability coefficient. It omits bank slope, bends, local turbulence corrections, depth, filters, scour, gradation and installation checks. It is an educational relation and quantity allowance; it does not establish site-specific riprap design.

References

Enforce the documented geometric domains and positive whole counts.

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