Buoyancy Calculator — Buoyant Force & Floating Depth

What This Calculator Does

Using Archimedes’ principle, buoyant force equals the weight of displaced fluid: \( F_b=\rho g V \). If a waterplane area \(A_{wp}\) is provided (e.g., barge length × beam), draft is \( h = V/A_{wp} \). For an unknown displacement, provide object mass \(m\) (or weight \(W\)) and we solve the equilibrium displacement volume \( V_{eq} \) where weight equals buoyancy; then draft is \( h = V_{eq}/A_{wp} \).

• SI units throughout: ρ (kg/m³), V (m³), g (m/s²), A_wp (m²), m (kg), W (N), F_b (N), h (m).
• Assumes a roughly constant waterplane area near the operating draft (good for barges, boxes, simple pontoons).
• Educational tool — not a substitute for full hydrostatic curves (curves of form) on complex hulls.

Buoyancy & Draft — Quick Primer

Archimedes’ principle. A floating body displaces a volume of fluid whose weight equals the body’s weight. In symbols, buoyant force is \( F_b = \rho g V_{\text{disp}} \). At equilibrium on calm water, \( F_b = W \) (the object’s weight), so the displaced volume is \( V_{\text{eq}} = \dfrac{W}{\rho g} = \dfrac{m}{\rho} \). Notice that \(g\) cancels if you enter mass, which is why using mass or weight gives the same equilibrium displacement in this tool.

Draft and waterplane area. The draft \(h\) is the vertical distance from the waterline to the lowest point of the hull. For simple floaters (rectangular barge, pontoon, box) the waterplane area \(A_{\text{wp}}\) is roughly constant with depth, so displaced volume increases linearly with draft: \( V \approx A_{\text{wp}}\,h \) and \( h \approx \dfrac{V}{A_{\text{wp}}} \). For fine ship hulls and submarines, \(A_{\text{wp}}\) changes with immersion, making \(h(V)\) non-linear. In that more general case you can treat \(A_{\text{wp}}\) as the local slope, \( A_{\text{wp}} \approx \dfrac{dV}{dh} \), near your operating draft.

Densities & environments. Fresh water is about \(998~\text{kg/m}^3\) at \(20^\circ\text{C}\), typical seawater is \( \sim 1025~\text{kg/m}^3 \), and colder/saltier water is denser. A higher \( \rho \) means more buoyant force for the same volume, so a boat rides higher in salt water than in fresh. Gravity \(g\) varies by world: Earth \( \approx 9.80665~\text{m/s}^2 \), Moon \( \approx 1.62~\text{m/s}^2 \). Lower \(g\) reduces buoyant force for a given \(V\), but equilibrium displacement still follows \( V_{\text{eq}} = m/\rho \).

When things sink. If an object’s average density (mass divided by its total external volume) exceeds the fluid density, no partially submerged equilibrium exists—it will sink unless an external force or trapped air changes the average density. Hollow hulls float because the hull + enclosed air yields a low average density.

What this calculator assumes. We assume hydrostatic balance, calm water, and either a known displaced volume \(V\) or an equilibrium condition using mass/weight. Draft calculations assume a constant or locally constant \(A_{\text{wp}}\). Real vessels use curves of form (displacement vs. draft) to capture hull nonlinearity, trim, and list; those are beyond this educational scope but the \(A_{\text{wp}}\) approach is a good first estimate.

Design workflow. Start with your fluid (fresh/sea), enter \( \rho \) and \( g \). If you know the footprint area, use it as \( A_{\text{wp}} \). Enter mass \(m\) (or weight \(W\)) to get \( V_{\text{eq}} \) and the corresponding draft \( h = V_{\text{eq}}/A_{\text{wp}} \). If you already know the displaced volume from geometry or experiments, enter \(V\) directly and get buoyant force and draft.

Tip: If you know target draft and footprint, set \(A_{\text{wp}}\) to the footprint area and back out the required displacement \(V = A_{\text{wp}} h\). Then check whether that displacement is compatible with your mass: you’ll float at that draft in fluid density \( \rho \) when \( m \approx \rho V \).