Riprap Stone Size Calculator

Designing Riprap for Channel and Bank Protection

Riprap is a layer of rock placed on channel beds, banks, shorelines, or around structures to resist erosion from flowing water. Correctly sizing the stone is critical. If the pieces are too small, they may be displaced during floods, exposing the underlying soil and potentially leading to progressive failure of the bank or structure. If the pieces are much larger than required, construction becomes more difficult and costly, and the roughness may overly increase water levels or reduce conveyance.

The calculator on this page applies the Isbash formula to estimate a median riprap stone size for a given design flow velocity, rock density, stability coefficient, and safety factor. It is intended as a preliminary design aid or educational tool, not as a substitute for detailed hydraulic design by a qualified engineer.

The Isbash Formula for Riprap Stone Size

The Isbash method is based on balancing the hydraulic forces acting on an individual stone with its submerged weight. For fully submerged conditions in uniform flow, the relationship between the characteristic flow velocity and the required median stone diameter can be expressed in SI units as:

where:

• D₅₀ = median stone diameter (m)
• V = design flow velocity at the riprap location (m/s)
• K = stability coefficient (dimensionless)
• g = acceleration due to gravity (9.81 m/s²)
• ρ_s = rock density (kg/m³)
• ρ_w = water density (typically 1000 kg/m³)

The calculator computes an initial D₅₀ from the Isbash formula and then multiplies it by the user-specified safety factor to give a conservative design diameter. It also estimates a corresponding median stone weight by assuming approximately spherical particles:

W50 = (ρs · π · D503) / 6

Because flow forces scale with velocity squared, even modest increases in design velocity can lead to large increases in required stone size. Choosing a realistic but adequately conservative design velocity is therefore one of the most important decisions in riprap design.

Choosing Input Values

The calculator requires four main inputs. The brief notes below provide context for each value and typical ranges seen in practice.

Design Flow Velocity V (m/s)

This is the representative depth-averaged velocity at the location where riprap is to be placed, under the selected design event (for example, a 10-year or 50-year flood). It is normally obtained from hydraulic calculations or models rather than guessed. Typical ranges include:

• Low-energy channels and gentle slopes: approximately 0.5–1.5 m/s
• Moderate alluvial streams: approximately 1.5–3.0 m/s
• Steep channels, spillways, and culvert outlets: often 3.0–6.0 m/s or higher

As V increases, the required D₅₀ rises rapidly. Doubling V increases V² by a factor of four, which quadruples the required stone size under otherwise identical conditions.

Rock Density ρ_s (kg/m³)

The rock density reflects the specific gravity of the riprap material. Denser rock has greater submerged weight for a given size, which improves stability. Some indicative values are:

If laboratory test data are available, use the tested bulk density. Otherwise, use a typical value from design manuals for the selected rock type.

Stability Coefficient K

The Isbash coefficient K accounts for stone shape, angularity, placement quality, and interlocking. Lower K values indicate greater stability for a given velocity (because a smaller numerator V² is sufficient), while higher values indicate less stable configurations. Representative values include:

Use values recommended by the relevant design standard for your jurisdiction if available, and align the selected K with the actual construction method and rock quality.

Safety Factor

The safety factor multiplies the computed D₅₀ to provide a more conservative design size. It is meant to cover uncertainties in input values (such as velocity, rock density, or K), future channel changes, and construction variability. Typical ranges are:

• Preliminary or conceptual design with good data: 1.1–1.2
• Standard applications with moderate uncertainty: 1.2–1.3
• High-consequence structures or highly uncertain conditions: 1.3–1.5

Increasing the safety factor raises both the stone size and stone weight. This generally improves stability but increases cost and may make handling more difficult.

Interpreting the Calculator Results

After entering your inputs and running the calculator, you will obtain a median stone diameter and an estimated median stone weight. These outputs should be interpreted as follows:

• Median stone diameter D₅₀ (m or mm): This is the size for which 50% of the stones (by weight) are smaller and 50% are larger. Actual riprap specifications typically define a gradation band (for example, D₁₅, D₅₀, D₈₅) rather than a single size.
• Median stone weight W₅₀ (kg): This is the approximate weight of a stone with diameter D₅₀, assuming a roughly spherical shape. Real stones are irregular, but the estimate is usually adequate for planning and for checking unit weights against standard riprap classes.
• Comparison to standard classes: Many agencies publish standard riprap classes defined by minimum and maximum stone sizes or weights. Compare the calculated D₅₀ and W₅₀ to these tables and select the nearest riprap class that provides equal or greater stability.

If your calculated D₅₀ is close to the upper limit of a standard class, it is often prudent to step up to the next larger class, especially in high-risk locations or where hydraulic conditions may worsen over time.

Worked Example

The following example illustrates how to use the calculator and how to interpret the results.

Problem: A straight, lined drainage channel conveys stormwater from an urban catchment. Hydraulic analysis for the design event indicates a depth-averaged velocity of 2.5 m/s at the downstream end. The designer plans to use angular granite riprap with density 2650 kg/m³, placed as a flexible layer. Determine an appropriate median stone size using the Isbash method with a stability coefficient K = 0.86 and a safety factor of 1.2.

1. Enter design velocity V: V = 2.5 m/s.
2. Enter rock density ρ_s: ρ_s = 2650 kg/m³.
3. Enter stability coefficient K: K = 0.86 (angular, well-graded rock).
4. Enter safety factor: SF = 1.2.
5. Compute base D₅₀ using Isbash: the calculator evaluates the formula above to obtain an initial D₅₀ (without safety factor). For these values, the base result will fall in the cobble–small boulder range.
6. Apply the safety factor: the base D₅₀ is multiplied by 1.2 to produce the design D_50,design.
7. Compute estimated stone weight: using ρ_s and D_50,design, the calculator returns W₅₀ in kilograms.
8. Compare to standard gradations: consulting agency guidelines, the designer checks which riprap class has a median size close to or larger than D_50,design and selects that class for specification.

In practice, the designer would also verify that the selected class provides adequate thickness and that the underlying filter layer or geotextile is compatible with both the stone size and the protected soil.

Comparison of Key Design Influences

The table below summarizes how the main input parameters qualitatively influence the required median stone size.

Assumptions, Limitations, and Good Practice

The Isbash method and this calculator are based on simplifying assumptions. They are not suitable for all situations. The main assumptions include:

• Uniform, steady flow: The formula assumes that flow conditions are approximately steady over the design event and uniform over the length of the protected reach. Rapidly varied flow, hydraulic jumps, or strong secondary currents can generate forces beyond those represented by a single depth-averaged velocity.
• Fully submerged riprap: The derivation presumes that the stones are fully surrounded by water. Conditions with intermittent submergence, wave action, or frequent wetting and drying may require different design approaches or additional checks.
• Relatively straight alignment: The method is most applicable in straight or gently curving channels. Sharp bends, transitions, and constrictions can cause localized accelerations and turbulence that increase required stone size.
• Stable bed and banks beneath the riprap: The calculator does not address piping, internal erosion of the foundation material, or undermining due to scour below the riprap layer.
• Representative input data: Reliability of the results depends directly on the accuracy of the design velocity, rock density, and selected K value.

Important limitations and cautions are:

• Not a full hydraulic design: The tool does not compute flow depths, freeboard, overtopping, or structural stability. It only addresses stone sizing under specified hydraulic conditions.
• No automatic compliance with local standards: National and regional agencies (for example, transportation departments, flood control districts, or environmental regulators) often publish riprap design criteria that may differ from Isbash or introduce additional requirements such as minimum layer thickness and filter design.
• Simplified stone weight estimate: Actual stone shapes and gradations vary, so the weight calculation should be treated as approximate and used alongside standard riprap class tables.
• Site-specific effects: Ice, debris impact, wave action, vegetation, and long-term channel evolution are not explicitly modeled but can materially affect performance.

Professional Use and Disclaimer

This calculator is intended for preliminary sizing, feasibility studies, and educational exploration of how velocity, rock properties, and safety factors influence riprap design. It does not replace the need for:

• Detailed hydraulic and geotechnical analysis for the project site
• Compliance with applicable design manuals, codes, and regulations
• Review and approval by a qualified professional engineer, especially for dams, levees, flood control works, bridge foundations, or other safety-critical structures

Users are responsible for verifying all inputs, reviewing the applicability of the Isbash method to their specific conditions, and confirming that the final design meets local requirements and safety objectives.