In short: buoyant force equals fluid density × gravity × displaced volume (Archimedes' principle). One liter of fresh water displaced at room temperature produces about 9.79 N (2.20 lbf) of upward force — roughly the weight of that same liter of water. Saltwater and colder water push a little harder; warmer water a little less.
These figures are planning aids based on published density data. For structural, diving or safety-critical work, confirm with a licensed engineer.
How to calculate buoyant force
Buoyant force comes from Archimedes' principle: any object submerged or floating in a fluid experiences an upward push equal to the weight of the fluid it displaces. The object's own weight, material and shape never enter the equation directly — only the volume it pushes out of the way and the density of the fluid doing the pushing.
This calculator converts your displaced volume to cubic meters, looks up the density of water at the temperature and type you selected, and returns the buoyant force in newtons, kilonewtons, pounds-force, kilogram-force, gram-force and dynes.
Worked example. A rock displaces 2.5 liters of fresh water at 20 °C. That's 0.0025 m³. Water at 20 °C has a density of 998.2 kg/m³. Multiply: 998.2 × 9.80665 × 0.0025 = 24.47 N, which is about 5.50 lbf (2.50 kgf). That upward push is what the water exerts on the rock, regardless of how heavy the rock itself is.
Buoyant force vs. floating. Buoyant force alone does not tell you whether something floats. Compare it to the object's actual weight: if the buoyant force at full submersion exceeds the object's weight, it floats and rises until the two balance; if not, it sinks. Use the Water Displacement Calculator to work out volumes for floating objects.
Why fluid density changes the answer
Because buoyant force is directly proportional to fluid density, anything that changes density changes the force. Two things matter most for water: temperature and dissolved salt. Water reaches its maximum density at about 4 °C (39 °F); above and below that point it becomes less dense, so the same displaced volume produces slightly less buoyant force. Between 4 °C and 100 °C, buoyant force for a fixed volume drops by roughly 4%.
Salinity works the other way: dissolved salt adds mass without adding much volume, so seawater is denser than fresh water — about 2.5–2.7% at typical ocean salinity — and produces proportionally more buoyant force. This calculator uses the Kell equation, the standard polynomial fit for the density of air-free water between 0 °C and 150 °C, with a linear salinity correction for seawater. Read the full method on our methodology page.
Buoyant force per liter, by temperature
The buoyant force produced by displacing exactly 1 liter of fresh water, from freezing to boiling. This is the same density data behind the calculator, expressed as a force so you can see how much it actually moves.
| Temperature | Density (kg/m³) | Force (N) | Force (lbf) |
|---|---|---|---|
| 0 °C / 32 °F | 999.84 | 9.81 | 2.20 |
| 4 °C / 39 °F (densest) | 999.97 | 9.81 | 2.20 |
| 10 °C / 50 °F | 999.70 | 9.80 | 2.20 |
| 20 °C / 68 °F (room) | 998.20 | 9.79 | 2.20 |
| 25 °C / 77 °F | 997.04 | 9.78 | 2.20 |
| 37 °C / 99 °F (body) | 993.33 | 9.74 | 2.19 |
| 60 °C / 140 °F | 983.20 | 9.64 | 2.17 |
| 80 °C / 176 °F | 971.80 | 9.53 | 2.14 |
| 100 °C / 212 °F (boiling) | 958.36 | 9.40 | 2.11 |
Quick reference: buoyant force by displaced volume
Fresh water at room temperature (20 °C / 68 °F). Handy when you just need a number without opening the calculator.
| Displaced volume | Force (N) | Force (lbf) | Force (kgf) |
|---|---|---|---|
| 1 liter | 9.79 | 2.20 | 1.00 |
| 5 liters | 48.94 | 11.00 | 4.99 |
| 10 liters | 97.88 | 22.01 | 9.98 |
| 1 US gallon | 37.06 | 8.33 | 3.78 |
| 1 cubic foot | 277.19 | 62.32 | 28.27 |
| 1 cubic meter | 9,789.0 | 2,200.6 | 998.2 |
Worked examples
A rock in a lake
4.90 N
A rock displacing 500 mL of lake water at 10 °C feels about 4.90 N (1.10 lbf) of buoyant force — roughly what it would take to hold up a small apple.
A beach ball in the ocean
401.5 N
A beach ball displacing 40 liters of seawater at 25 °C feels about 401.5 N (90.3 lbf) of buoyant force — seawater's extra salinity adds roughly 2.5% more push than fresh water would.
A small steel ball, fully submerged
0.147 N
A steel ball displacing 15 mL of water at 20 °C feels only about 0.147 N (15.0 gf) of buoyant force — far less than its own weight, which is why it sinks.
What else affects the result
Shape and material don't matter. Buoyant force depends only on the volume of fluid displaced, not on what the object is made of or what shape it is. A ball and a cube of the same volume, fully submerged in the same fluid, feel exactly the same buoyant force.
Depth is nearly irrelevant for rigid objects. Water is almost incompressible, so its density — and therefore the buoyant force on a fixed-volume object — barely changes with depth. Depth matters far more for compressible objects (a diving float, a partially filled ballast tank) whose volume itself shrinks under pressure.
Local gravity. This calculator uses standard gravity, 9.80665 m/s². Buoyant force scales with local gravitational acceleration, so it would be very slightly different at high altitude or on another planet.
Dissolved air and impurities. Ordinary tap water carries tiny amounts of dissolved gas and minerals. The effect on density — and therefore buoyant force — is well under a tenth of a percent, which is why the calculator models pure, air-free water.
Frequently asked questions
What is buoyant force and how is it calculated?
Buoyant force is the upward push a fluid exerts on anything submerged or floating in it. Archimedes' principle gives the formula: buoyant force equals the density of the fluid, times gravity, times the volume of fluid displaced (F = ρ·g·V). It does not depend on the object's own weight, material or shape — only on how much fluid it pushes out of the way.
Does an object's weight affect the buoyant force on it?
No. Buoyant force depends only on the volume of fluid displaced and the fluid's density. An object's own weight determines whether it floats or sinks — by comparing to that fixed buoyant force — but it does not change the buoyant force itself.
Why does buoyant force change with temperature?
Warmer water is less dense, and buoyant force is directly proportional to fluid density. Displacing the same volume of warmer water therefore produces a slightly smaller buoyant force — around 4% less at 100 °C than at 4 °C for the same displaced volume.
Does buoyant force change with depth?
For a rigid object of fixed volume in water, no — water is nearly incompressible, so its density barely changes with depth, and buoyant force stays essentially constant. This is different from a compressible object like a diving float, whose volume — and therefore its buoyant force — can shrink under pressure at depth.
Does the shape of an object affect its buoyant force?
No. Only the volume of fluid displaced matters. A flat sheet of metal and a ball of the same material and mass displace different volumes if one floats and one sinks, but for any two objects that displace the same volume of the same fluid, the buoyant force is identical regardless of shape.
How much more buoyant force does saltwater provide than freshwater?
Seawater is roughly 2.5–2.7% denser than fresh water at the same temperature because of dissolved salt, so it produces a proportionally larger buoyant force for the same displaced volume — one reason it is easier to float in the ocean than in a freshwater lake.
Sources & references
- Archimedes' Principle — the foundational law of fluid statics, underlying all buoyancy calculations.
- Kell, G. S. (1975). Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C. Journal of Chemical & Engineering Data, 20(1), 97–105.
- National Institute of Standards and Technology (NIST). Thermophysical Properties of Fluid Systems.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)