Rip rap is large angular rock placed on banks, culvert outlets and shorelines to stop erosion. The stones must be heavy enough that fast-flowing water cannot move them. The Isbash equation, used by the U.S. Army Corps of Engineers and FHWA, relates the median stone size to the velocity, using a coefficient of 0.86 for highly turbulent flow and 1.20 for low turbulence.
How to use the Rip Rap Calculator
- Water velocity
- Specific gravity of rock
- Isbash coefficient
- Length of area
- Width of area
- Rock price
- Every result field is editable: type into Median stone diameter D₅₀ and Water velocity plus every other field update to match.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the design velocity, the specific gravity of the rock, the turbulence level and the area to protect. The calculator finds D₅₀ and the median stone weight, sets the layer thickness to twice D₅₀ and estimates the volume and tonnage with 40% voids.
Inputs explained
| Field | What to enter |
|---|---|
| Water velocity | Units: m/s, ft/s, km/h, mph |
| Specific gravity of rock | A number |
| Isbash coefficient | Choose one: 0.86 for high turbulence, 1.20 for low turbulence |
| Length of area | Units: ft, m, in, yd, cm |
| Width of area | Units: ft, m, in, yd, cm |
| Rock price | Units: /US ton, /t, /lb, /kg |
What each result means
- Median stone diameter D₅₀ = [Water velocity]^2÷(2×9.80665×[Isbash coefficient]^2×([Specific gravity of rock] – 1))
- Median stone weight W₅₀ = pi÷6×[Median stone diameter D₅₀]^3×[Specific gravity of rock]×1000
- Layer thickness (2 × D₅₀) = 2×[Median stone diameter D₅₀]
- Rock volume = [Length of area]×[Width of area]×[Layer thickness (2 × D₅₀)]
- Rock tonnage = [Rock volume]×[Specific gravity of rock]×1000×0.6
- Cost = [Rock tonnage]×[Rock price]
Example values
How the main result changes when Water velocity changes and everything else stays at the example values above:
| Water velocity (m/s) | Median stone diameter D₅₀ (in) |
|---|---|
| 1.5 | 3.7 |
| 2.25 | 8.33 |
| 3 | 14.8 |
| 3.75 | 23.13 |
| 4.5 | 33.31 |
| 6 | 59.22 |
Formula
D₅₀ = V² ÷ (2 g C² (S − 1))
W₅₀ = π/6 × D₅₀³ × S × ρ_water
Layer thickness = 2 × D₅₀; tonnage = area × thickness × bulk density
Worked example
Inputs: Water velocity: 3 m/s; Specific gravity of rock: 2.65; Isbash coefficient: 0.86 – high turbulence; Length of area: 30 ft; Width of area: 10 ft; Rock price: $50 /US ton.
Results: Median stone diameter D₅₀ = 14.8 in; Median stone weight W₅₀ = 162.6 lb; Layer thickness (2 × D₅₀) = 29.6 in; Rock volume = 27.41 yd³; Rock tonnage = 36.74 US ton; Cost = $1,836.81.
Key terms
- D₅₀
- The stone diameter that half of the rock (by weight) is smaller than.
Frequently asked questions
What is rip rap?
Large, angular stone placed to armour banks and outlets against erosion.
What size rip rap do I need?
It depends on the velocity: about 6 in D₅₀ for 6 ft/s and 12 in for 8–9 ft/s in turbulent flow. Use the calculator for your velocity.
Why is the layer twice D₅₀?
A layer about 1.5–2 times the median stone size lets stones interlock and protect the filter below.