The Wetted Surface Area Calculator estimates the area of a boat hull that is below the waterline — the area you paint with antifouling and the area that creates skin-friction drag.
It uses the Mumford formula, S ≈ L × (1.7T + Cb × B), from waterline length, beam, draft and block coefficient. If you know the displacement instead, the Denny–Mumford form S ≈ 1.7LT + ∇ ÷ T is used. Both are empirical estimates for displacement hulls.
Wetted Surface Area Calculator
Estimate a boat hull’s wetted surface area for antifouling paint and drag calculations (Mumford / Denny formulas).
Formula
From dimensions (Mumford):
S ≈ L × (1.7 × T + Cb × B)
From displacement (Denny–Mumford):
S ≈ 1.7 × L × T + ∇ ÷ T
Where:
- S = wetted surface area
- L = waterline length (LWL)
- B = waterline beam
- T = hull draft (canoe body, excluding keel and rudder)
- Cb = block coefficient = underwater volume ÷ (L × B × T)
- ∇ = displaced volume = boat weight ÷ water density
How the Calculation Works
Step 1: The term 1.7 × T approximates the hull sides below the waterline.
Step 2: The term Cb × B approximates the bottom, scaled by how full the hull is.
Step 3: Multiplying by the waterline length gives the estimated wetted area. In the displacement form, ∇ ÷ T replaces L × Cb × B, since ∇ = Cb × L × B × T.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| L | Waterline length | ft, m |
| B | Waterline beam | ft, m |
| T | Hull draft | ft, m |
| Cb | Block coefficient (fullness) | — |
| ∇ | Displaced volume | ft³, m³ |
| S | Wetted surface area | ft², m² |
Example Calculation
From dimensions
Given: LWL = 30 ft, beam = 10 ft, draft = 2 ft, Cb = 0.4
Calculation: S ≈ 30 × (1.7 × 2 + 0.4 × 10) = 30 × (3.4 + 4)
Result: S ≈ 222 ft²
From displacement
Given: LWL = 30 ft, draft = 2 ft, displaced volume = 240 ft³
Calculation: S ≈ 1.7 × 30 × 2 + 240 ÷ 2 = 102 + 120
Result: S ≈ 222 ft²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10.7639 ft² |
| 1 ft² | 0.0929 m² |
Engineering Assumptions
- Both formulas are empirical approximations for displacement hulls, not exact geometry. Planing hulls, catamarans and unusual shapes can differ.
- Draft is the hull (canoe body) draft only. Keels, rudders, skegs and other appendages must be added separately — they can be a large share of a sailboat’s wetted area.
- Displaced volume = boat weight ÷ water density; seawater is slightly denser than fresh water, so the same boat displaces a little less volume in the sea.
Material Estimation Notes
Bottom paint quantity
Divide the wetted area (plus the boot-top or any area above the waterline you also paint) by the antifouling paint’s coverage per coat from the manufacturer, then multiply by the number of coats. Coverage varies between products.
Frequently Asked Questions
What is wetted surface area?
The area of the hull in contact with the water. It determines friction drag and how much bottom paint you need.
How do you calculate the wetted surface area of a boat?
A common estimate is S ≈ LWL × (1.7 × draft + Cb × beam).
What is the block coefficient?
The ratio of the hull’s underwater volume to the box L × B × T that surrounds it. Fine, slender hulls have low values; boxy hulls such as barges have high values.
How much bottom paint do I need?
Wetted area × coats ÷ coverage per unit of paint. Check the paint label for its coverage rate.
Does wetted surface area include the keel?
Not in these formulas. Add keel and rudder areas (both sides) separately.
