Shoaling Coefficient Calculator

This calculator uses linear wave theory to compute the shoaling coefficient:

• Dispersion relation: ω² = g k tanh(kh), where ω = 2π/T.
• Wavelength: L = 2π/k, and C = L/T.
• Group coefficient: n = 0.5(1 + 2kh/sinh(2kh)).
• Group velocity: Cg = nC. In deep water, n0 = 0.5.
• Shoaling coefficient: Ks = √(Cg0/Cg).
• Height transform (optional): H = Ks × H0.

Assumptions: straight-crested waves, no refraction, no breaking, and no bottom friction. For exposed sites, always cross-check with engineering standards and local guidance.

1. Select your preferred unit system.
2. Enter wave period T and water depth h.
3. Optionally enter deep-water height H0 for height estimates.
4. Click Calculate to see results below the header.
5. Review wavelength and group velocity to sanity-check inputs.
6. Download CSV for logs, or PDF for reporting.

1) Where this coefficient fits on site

Nearshore works can see larger waves as depth reduces. Ks estimates that depth-driven height change for straight-crested waves, supporting early checks around cofferdams, trestles, seawalls, and floating plant. It is a planning tool for comparing options and documenting assumptions.

2) Typical input ranges you can defend

Wind-wave periods often fall near 3–12 s, while swell commonly sits around 12–20 s. Working depths for coastal construction may range from 0.5–30 m (or the equivalent in feet). Gravity is typically 9.80665 m/s² (32.174 ft/s²).

3) What Ks values usually indicate

In deep water, Ks approaches 1.00. As depth decreases, group velocity generally drops and Ks rises above 1.00. Many practical comparisons fall roughly between 1.00 and 1.60. Much higher values can appear in very shallow water, but breaking limits often control first.

4) Converting height with H = Ks × H0

If you have deep-water height H0, the calculator estimates H at the chosen depth using H = Ks × H0. Example: H0 = 1.5 m and Ks = 1.20 gives H ≈ 1.80 m. Use this for access limits, deck freeboard checks, and plant selection.

5) Sensitivity and quick validation

Ks depends strongly on period and depth. Longer-period waves interact with the seabed at greater depths, so Ks can increase earlier as depth reduces. Run two nearby depths (such as 4 m and 5 m) and confirm a smooth trend before using results in decisions.

6) Solver reliability and convergence

The wave number is solved from ω² = gk tanh(kh). Shallow depths paired with long periods can need more iterations. If you see a convergence note, raise the iteration limit and re-run. Stable Ks and wavelength values are good indicators the solution is usable.

7) Using exports for reporting

Capture the period, depth, gravity, and Ks used in planning notes. CSV export helps teams compare multiple depths and scenarios in one sheet. PDF export suits daily logs, method statements, and review packs, especially when you need consistent records across shifts. Keep versions dated so input changes and depth assumptions remain traceable during audits.

8) Limitations to state in your method

This approach assumes linear behavior with no refraction, currents, bottom friction, or breaking. Treat Ks as a screening estimate for planning. For exposed sites or final design, combine this with local standards, wave breaking checks, bathymetry effects, and specialist analysis.

1) What is the shoaling coefficient in simple terms?

It is a multiplier that estimates how wave height changes as water depth changes, under linear wave theory. When depth decreases, Ks often rises above 1.0, indicating potential wave height growth.

2) Do I need deep-water wave height to calculate Ks?

No. Ks is computed from wave period and depth. Deep-water height (H0) is only needed if you want the calculator to estimate wave height at the selected depth using H = Ks × H0.

3) Why does Ks increase in shallow water?

As waves enter shallower areas, group velocity typically decreases. To conserve energy flux in linear theory, wave height increases, which is captured by a higher Ks value.

4) What Ks range is common for planning?

Many practical nearshore comparisons fall around 1.0 to 1.6, depending on period and depth. Very shallow cases can exceed this, but wave breaking and other effects may control before extreme growth.

5) How do I know if my inputs are unrealistic?

Check that period and depth are credible for your site and conditions. Compare two nearby depths; results should change smoothly. Sudden jumps often indicate a depth outside the intended range or unit confusion.

6) Can I use this for final design of a seawall?

Use it for screening and documenting assumptions, not as the sole design basis. Final design typically requires local standards, breaking limits, wave direction effects, and detailed coastal analysis.

7) What should I include in a report export?

Include T, depth, gravity, Ks, and the derived height if used. Adding wavelength and group velocity helps reviewers validate the calculation and compare alternatives across different depths.