Inputs
Example data table
Use these sample inputs to validate your workflow and exports.
| Scenario | Method | Hs (m) | T (s) | Slope (V:H) | tanα | SWL (m) | Typical use |
|---|---|---|---|---|---|---|---|
| Beach A | Stockdon | 1.8 | 7.5 | 1:15 | 0.0667 | 0.4 | Sandy shoreline |
| Revetment B | EurOtop-style | 2.5 | 9.0 | 1:2 | 0.5000 | 0.8 | Rock slope |
| Jetty C | Simple | 3.0 | 10.0 | 1:1.5 | 0.6667 | 1.1 | Quick screening |
| Beach D | Stockdon | 1.2 | 6.0 | 1:25 | 0.0400 | 0.2 | Gentle foreshore |
| Revetment E | EurOtop-style | 4.0 | 12.0 | 1:3 | 0.3333 | 1.6 | Higher-energy site |
Formula used
This calculator estimates the 2% exceedance runup, noted as Ru2%, using one of three approaches.
Deep-water parameters
Computed for all methods:
- L0 = gT² / (2π)
- s0 = Hs / L0
- ξ = tanα / √s0
Stockdon approach
Used for open coasts and beach profiles:
Structure scaling
Two practical options:
- EurOtop-style: Ru2% = 1.65 γb γf γβ ξ Hs
- Simple: Ru2% = 1.75 ξ Hs
How to use this calculator
- Select the unit system that matches your inputs.
- Choose a method aligned with your shoreline or structure.
- Enter Hs, T, and slope as ratio or tanα.
- For sloping structures, enter γf, γb, and γβ when needed.
- Add SWL to estimate the total runup level on your datum.
- Optionally add a crest level to evaluate freeboard.
- Press Calculate to view results above the form.
- Use the export buttons to download CSV or PDF outputs.
Wave runup design brief
1) Why runup matters on sites
Runup is the uprush of waves above still water level and often governs overtopping risk. On coastal structures, even small changes in slope or wave period can shift runup by 10–30%. This calculator focuses on the 2% exceedance level, a common engineering metric for crest checks.
2) Typical inputs used in practice
Significant wave height Hs and a representative period T are usually sourced from hindcasts, buoy records, or design standards. Foreshore slope is typically taken from surveys over the active runup zone. For concept work, slopes between 1:10 and 1:30 are common on sandy coasts.
3) Deep-water wavelength and steepness
The calculator derives deep-water wavelength using L0 = gT²/(2π). For T = 8 s, L0 is about 100 m, while T = 12 s gives roughly 225 m. Steepness s0 = Hs/L0 helps indicate breaking tendency and controls the Iribarren number.
4) Interpreting the Iribarren number
The Iribarren number ξ = tanα/√s0 links slope and wave shape. Values below about 0.5 often align with spilling breakers, while values above 2 can indicate plunging to surging behavior. Use ξ as a sense-check when comparing methods.
5) Method selection guidance
The Stockdon approach is widely used for open-coast beaches and provides a runup estimate driven by β and √(HsL0). For sloping armoring and revetments, a factor-based approach can better reflect roughness, berm influence, and wave angle effects on runup.
6) Structure factors and common ranges
Roughness factors γf typically range from about 0.55 for very rough rock to near 1.00 for smooth faces. Berm factors γb often stay close to 1.00 unless a pronounced berm alters uprush. Obliquity factors γβ commonly vary from 0.60 to 1.00 depending on approach angle.
7) Linking runup to crest levels
Total runup level is reported as SWL + Ru2%. If you enter a crest elevation, the calculator returns freeboard = crest − total runup level. Negative freeboard indicates the crest is below the estimated exceedance runup level and may require geometry or armor adjustments.
8) Recommended workflow and QA checks
Start with conservative offshore conditions, then refine slope and factors as survey and material data improve. Compare at least two methods for sensitivity, and document assumptions in the Notes field for your exports. For final design, confirm local guidance, storm water levels, and breaking regime with specialist review.
FAQs
1) What does “2% exceedance runup” mean?
It is the runup level exceeded by only about 2% of runup events in a sea state. Engineers use it to check crest elevation and overtopping screening for design conditions.
2) Which wave period should I enter?
Use the period that matches your wave data source and design intent, often peak period. If only significant period is available, use it consistently and note it in the export report.
3) Should Hs be offshore or nearshore?
Prefer deep-water or offshore Hs when using deep-water wavelength relationships. If you use nearshore transformed Hs, ensure the wavelength assumptions remain reasonable and document the transformation basis.
4) How do I choose slope for tanα?
Use the representative foreshore or structure slope over the active uprush zone. For beaches, survey profiles near the design cross-section. For revetments, use the armored face slope.
5) What if the Eurotop factors are unknown?
Start with γf = γb = γβ = 1.0 for a conservative baseline, then reduce γf for rough rock or units. Update factors once material type, berm geometry, and wave approach angle are defined.
6) Why do methods give different results?
Each method targets different conditions and datasets. Beach-based formulas capture setup and swash behavior, while structure scaling focuses on slope and correction factors. Differences are useful for sensitivity checks.
7) Does this replace a full overtopping assessment?
No. It provides screening-level runup and crest checks. Detailed overtopping, structural stability, and local code compliance should be assessed using appropriate guidance, calibrated data, and engineering judgment.