Size a circular-culvert riprap apron with FHWA HEC-14 Equations 10.4 and 10.5. The calculator reports the equation result, selects the next adequate Table 10.1 riprap class, and calculates the class-specific apron length, end width, and thickness.
Use this tool for the protection apron—not the culvert barrel
This page starts with a known circular-culvert discharge, diameter, tailwater, and flow regime, then applies HEC-14 to the downstream riprap apron. It does not solve inlet control, outlet-control headwater, barrel losses, or the receiving channel's water-surface profile.
- 1. Solve the culvert Check HDS-5 outlet control
- 2. Screen scour Evaluate outlet velocity and bed stability
- 3. Design protection Use the HEC-14 apron calculator below, then confirm constructability and local criteria.
Ready to Design
Enter the circular culvert and design-flow data.
For educational purposes only. Not a substitute for professional engineering judgment.
Interactive model
Interactive riprap apron design
See how culvert diameter, discharge, tailwater, selected HEC-14 riprap class, and the resulting apron dimensions fit together downstream of a circular outlet.
Open full model (opens in a new tab)HEC-14 calculation sequence
1. Adjust the rise for supercritical flow
For subcritical flow, use the circular diameter D. For supercritical flow, use D' = (D + yn)/2 from Equation 10.5.
2. Apply the tailwater bounds
Equation 10.4 uses 0.4D' ≤ TW ≤ D'. An input outside that range is bounded and clearly reported rather than applying a discontinuous reduction factor.
3. Calculate the required median stone size
D50 = 0.2D' [ Q / (sqrt(g) D'2.5) ]4/3 (D'/TW)
4. Select a class and size the apron
The next Table 10.1 class whose nominal D50 meets the equation result is selected. Class controls length and thickness; Figure 10.4 gives the apron end width as W = 3D' + (2/3)L.
HEC-14 Table 10.1 apron classes
Dimensions use the selected class D50, not the unrounded equation result.
| Class | Nominal D50 | Apron length | Blanket thickness |
|---|---|---|---|
| Class 1 | 5 in / 125 mm | 4D | 3.5D50 |
| Class 2 | 6 in / 150 mm | 4D | 3.3D50 |
| Class 3 | 10 in / 250 mm | 5D | 2.4D50 |
| Class 4 | 14 in / 350 mm | 6D | 2.2D50 |
| Class 5 | 20 in / 500 mm | 7D | 2.0D50 |
| Class 6 | 22 in / 550 mm | 8D | 2.0D50 |
These numbered classes and multipliers belong specifically to the HEC-14 circular-culvert apron method. They are not interchangeable with every state DOT or NRCS riprap class. For other applications, use the riprap sizing calculator and check the specified rock gradation.
FHWA worked-example checks
Customary-units example
Q = 85 cfs, D = 5 ft, and TW = 1.6 ft. Equation 10.4 uses TW = 0.4D = 2 ft and gives D50 = 0.431878 ft (5.18254 in). The design therefore uses Class 2: D50 = 0.5 ft, L = 20 ft, thickness = 1.65 ft, and end width = 28.3333 ft.
SI example
Q = 2.33 m³/s, D = 1.5 m, and TW = 0.5 m. The bounded TW is 0.6 m and the required D50 is 0.130854 m. Class 2 gives D50 = 0.15 m, L = 6 m, thickness = 0.495 m, and end width = 8.5 m.
Frequently asked questions
How is the required riprap D50 calculated?
The calculator implements FHWA HEC-14 Equation 10.4 for circular culverts: D50 = 0.2D[Q/(sqrt(g)D^2.5)]^(4/3)(D/TW). It uses discharge, culvert diameter, and tailwater directly; an outlet-velocity or Froude-number shortcut is not substituted for the published equation.
How does HEC-14 handle low or high tailwater?
For Equation 10.4, the tailwater used is limited to the range 0.4D through D. If the entered depth is below 0.4D, the calculator uses 0.4D. If it exceeds D, the calculator uses D and warns that HEC-14 Figure 10.3 and Section 10.3 should also be evaluated for a submerged outlet.
What changes when culvert flow is supercritical?
HEC-14 Equation 10.5 replaces the culvert rise with D' = (D + yn)/2, where yn is normal depth. The adjusted rise is then used in Equation 10.4 and in the apron dimensions.
Can Equation 10.4 be used for a box or arch culvert?
No. HEC-14 limits this riprap-apron relationship to circular culverts, principally those with diameters no greater than 60 inches (1.5 m). A hydraulic-radius or equivalent-diameter conversion is not part of the method. Use the application-specific open-bottom-culvert tool or a project-specific energy-dissipator design for noncircular outlets.
Standards & related tools
FHWA HEC-14 (2006)
Hydraulic Design of Energy Dissipators for Culverts and Channels.
Riprap Sizing by Application
Channel, bridge, overtopping, open-bottom culvert, wave, and filter designs.
Culvert Outlet Control
Solve HDS-5 headwater, barrel losses, tailwater, and outlet velocity first.
Outlet Velocity & Scour
Screen the receiving bed for scour before selecting protection.
What This Solves
Designs riprap aprons and outlet protection pads at culvert and pipe outlets using FHWA HEC-14 methodology to prevent scour from high-velocity discharge.
Best Used When
- You need to design a riprap apron at a culvert outlet to prevent downstream erosion
- You want to determine the required stone size (D50), blanket thickness, and apron dimensions
- You are evaluating whether existing outlet protection is adequate for the design flow
Do NOT Use When
- You need a formal energy dissipation structure (stilling basin) rather than a riprap apron — Use Energy Dissipator Calculator
- You need to size riprap for channel bank protection along a reach, not at an outlet — Use Riprap Sizing Calculator
Key Assumptions
- Riprap sizing follows FHWA HEC-14 relationships for pipe and culvert outlets
- The apron is placed on a stable subgrade with appropriate filter fabric or bedding
- Tailwater depth affects the required stone size and apron length
- Riprap is angular, well-graded stone meeting standard gradation specifications
- No significant debris or ice loading on the riprap apron
Input Quality Notes
Outlet velocity and tailwater depth are the key inputs. Calculate outlet velocity from pipe flow analysis and tailwater from downstream channel conditions. Use conservative (low) tailwater for riprap sizing.
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Last verified: August 2026