Buoyancy Calculator - Archimedes Principle, Buoyant Force, Float or Sink
Use Archimedes' principle to calculate buoyant force, solve for displaced volume or density, and check whether an object will float, sink, or stay neutrally buoyant. Add boat or barge dimensions to estimate draft with the constant waterplane-area assumption. Private by design: everything runs locally in your browser.
Inputs
Enter fluid density and displaced volume to calculate buoyant force.
Fluid and force
Leave blank to derive volume from object mass and volume when possible.
Object
Boat / barge draft
Draft uses \(h = V/A_{wp}\), which assumes constant waterplane area. It is best for boxy hulls, pontoons, and barges; curved hulls need hydrostatic curves.
Result units
Status-
Buoyant force-
Submerged-
Draft-
Results
Mode answer
-
-
Float / Sink
-
Enter mass and total volume.
Buoyant Force
Fb = -
-
Object Density
ρobj = -
Fluid ρ = -
Weight and Apparent Weight
W = -
Wapp = -
Net Force
-
Positive is upward, negative is downward.
Submerged Fraction
-
Submerged volume: -
Displaced Volume
Vdisp = -
Equilibrium V: -
Draft (Boat / Barge)
h = -
Enter A_wp or length × beam.
Equations: \( F_b = \rho g V_{\text{disp}} \), \( \rho_{\text{obj}} = m/V_{\text{obj}} \), \( W_{\text{app}} = W - F_b \), floating fraction \( = \rho_{\text{obj}}/\rho \), and \( h = V/A_{wp} \).
Buoyancy Diagram
Worked Examples
Wood block floating in water
A 0.50 m³ block with mass 300 kg has density \(300/0.50 = 600~\text{kg/m}^3\).
In fresh water, submerged fraction \(600/998 \approx 0.601\), so about 60.1% is underwater and \(V_{\text{disp}} \approx 0.301~\text{m}^3\).
Steel object sinking
A 10 L steel object with density near \(7850~\text{kg/m}^3\) has mass about 78.5 kg.
Fresh water can provide only \(998 \cdot 9.80665 \cdot 0.010 \approx 97.9~\text{N}\), far below the object's weight, so it sinks.
Boat / barge draft
A 12 m × 4 m boxy barge has \(A_{wp}=48~\text{m}^2\). With 20,000 kg total mass in fresh water, \(V=m/\rho \approx 20.04~\text{m}^3\).
Draft \(h=V/A_{wp}\approx 0.417~\text{m}\), assuming the sides are nearly vertical over that range.
Apparent weight in water
A 50 kg object displacing 0.020 m³ weighs about 490.3 N on Earth.
In fresh water, \(F_b \approx 195.7~\text{N}\), so its apparent weight while submerged is about 294.6 N.
Buoyancy and Draft 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 float at that draft in fluid density \( \rho \) when \( m \approx \rho V \).
Buoyancy FAQ
What is Archimedes' principle?
Archimedes' principle says an object in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
What is the buoyant force formula?
The formula is \(F_b = \rho g V_{\text{disp}}\), where \(\rho\) is fluid density, \(g\) is gravity, and \(V_{\text{disp}}\) is displaced fluid volume.
How do you know if an object floats?
Compare average object density with fluid density. If object density is lower, it floats; if higher, it sinks; if almost equal, it is neutrally buoyant.
How do you calculate volume displaced?
For a known buoyant force, \(V_{\text{disp}} = F_b/(\rho g)\). For a floating object at equilibrium, \(V_{\text{disp}} = m/\rho_{\text{fluid}}\).
Why do ships made of steel float?
A ship's average density includes its hollow volume and enclosed air. The combined hull, cargo, and air can be less dense than water even though solid steel is much denser.
Does depth affect buoyant force?
For an incompressible fluid, depth does not change buoyant force once displaced volume is fixed. Buoyant force depends on fluid density, gravity, and displaced volume.
What is apparent weight?
Apparent weight is the support force needed while submerged: \(W_{\text{app}} = W - F_b\). A submerged object feels lighter because buoyancy offsets part of its weight.
