Buoyant Force in Water: Formula and Calculation

This calculator finds the upward buoyant force water exerts on an object when you enter the volume of water it displaces. It returns force in newtons, using water’s standard density and gravity; the method also shows how to calculate other unit systems by hand.

Formula

Archimedes’ principle says that the buoyant force on a fully or partly submerged object equals the weight of the fluid it displaces. For water, the standard calculation is:

F_b = ρ_water × g × V_displaced

• F_b is buoyant force, in newtons (N).
• ρ_water is water density, taken here as 1,000 kilograms per cubic metre (kg/m³).
• g is gravitational acceleration, taken as 9.81 metres per second squared (m/s²).
• V_displaced is the volume of water displaced, in cubic metres (m³).

Since density multiplied by volume gives displaced-water mass, you can also write the formula as F_b = m_{displaced water} × g. The calculator’s first result is the buoyant force. Its second result, displaced-water mass, is an optional intermediate value. The calculator assumes fresh water at the standard density above; actual water density varies slightly with temperature and dissolved salt.

Worked Example

The calculator’s default displaced volume is 0.01 m³. Substituting that value into the same formula:

1. Calculate the mass of displaced water: 1,000 kg/m³ × 0.01 m³ = 10 kg.
2. Multiply that mass by gravity: 10 kg × 9.81 m/s² = 98.1 N.
3. Rounded to two decimal places, the buoyant force is 98.10 N.

The units reduce correctly: kg/m³ × m³ × m/s² = kg·m/s², which is a newton. This result is the upward force from the water, not necessarily the object’s total force or its apparent weight.

What You’ll Need

• The object’s displaced volume, measured or calculated in cubic metres for the calculator.
• A calculator, if working by hand.
• If you need a more precise result, the water’s density for its temperature and salinity.

Step-by-Step

1. Decide what force you want. Buoyant force is the upward force exerted by the water. It is different from net force, which also depends on gravity, tension, and other forces acting on the object.
2. Find the displaced volume. For a fully submerged object, use the volume of the part under water. For a floating or partly submerged object, use only the submerged portion. The volume of displaced water equals the submerged volume of the object, provided the object does not absorb water and its shape remains stable.
3. Convert the volume to cubic metres. The calculator accepts m³. For example, 1 litre = 0.001 m³, so 10 litres = 0.01 m³. For centimetres, convert cubic units carefully: 1 cm³ = 0.000001 m³. Do not enter a length in metres where a volume is required.
4. Enter the volume in the calculator. Type the displaced volume into the input field. The default is an example only; replace it with your measured or calculated value.
5. Read the buoyant force in newtons. The main result is the force the water pushes upward. The additional mass result indicates how much water that volume would contain at the assumed density.
6. For hand calculation, multiply in order. Use 1,000 kg/m³ × displaced volume in m³ × 9.81 m/s². Keep the units alongside the numbers so that errors are easier to spot.
7. Compare with weight only if needed. To determine whether an unsupported object rises, sinks, or is in balance, compare buoyant force with the object’s weight. Its weight is mass in kilograms × 9.81 m/s². Equal forces mean neutral balance in the ideal static case; buoyant force greater than weight gives an upward net force, and less gives a downward net force.

Common Mistakes

• Using the object’s total volume when only part is submerged. A floating object displaces water according to its underwater volume, not its entire outside volume.
• Confusing volume and mass. Litres and cubic metres measure volume; kilograms measure mass. Use density to relate them.
• Mixing units. Do not multiply a volume in litres directly by density in kg/m³. Convert first, or use a consistent unit system throughout.
• Using the wrong quantity for an irregular object. If its volume is difficult to calculate from dimensions, measure displaced water in a suitable container. Ensure the measurement reflects only the submerged part.
• Calling buoyant force the net force. Buoyant force acts upward, while weight acts downward. Other forces may also matter.
• Rounding too early. Keep extra digits during conversions and intermediate steps, then round the final force to a sensible precision.

Tips

• For a rectangular submerged section, calculate volume as length × width × submerged depth, with all dimensions converted to metres.
• For a fully submerged object in a measuring container, the rise in water level gives displaced volume if the container’s scale is suitable. Avoid trapping air bubbles, which add apparent displacement.
• In US customary units, use water density of about 62.4 lb/ft³ and multiply by displaced volume in ft³ to get buoyant force in pound-force (lbf). Alternatively, use density about 1.94 slug/ft³ and g about 32.2 ft/s². Do not mix pound-mass (lbm) with pound-force without the appropriate conversion.
• For salt water or unusually warm or cold water, use an appropriate density rather than 1,000 kg/m³ if the small difference matters.
• For a freely floating object at rest, buoyant force equals its weight. This gives a useful check on a measurement, but does not mean every submerged object experiences a force equal to its own weight.

Troubleshooting

• The answer seems far too large or small: Check whether the input is in m³. A volume entered in litres is numerically 1,000 times larger than its value in m³; convert litres by multiplying by 0.001.
• You have dimensions but no volume: Multiply the dimensions for a regular shape. For a complex shape, use water displacement or a reliable volume measurement. Subtract the starting water reading from the final reading.
• The object floats, but the calculated force seems too high: Recalculate using only the submerged volume. For an object floating at rest, its buoyant force should match its weight, subject to measurement accuracy and other support forces.
• Your measured displacement changes between trials: Check for bubbles, splashing, water absorbed by the object, movement of the container, or a meniscus-reading error. Let the water settle and repeat the measurement.
• You need a more exact result: Confirm the fluid density for its conditions and use a suitably precise value for gravity. The default calculation is a practical standard estimate, not a correction for every laboratory condition.

Frequently Asked Questions

What is the buoyant force in water?
It is the upward force water exerts on an immersed object. Its magnitude equals the weight of the water displaced.

How do I calculate buoyant force from volume?
Multiply water density by gravity and displaced volume: F_b = ρgV. With the calculator’s standard values, that is 1,000 × 9.81 × volume in m³, giving newtons.

Does a floating object displace its whole volume?
No. It displaces water equal to the volume of the part below the surface. At rest, its buoyant force balances its weight.

Can buoyant force be greater than an object’s weight?
Yes. If the object is free to move and the upward buoyant force exceeds its weight, it has an upward net force. A tether or other support can change its motion.

What is the unit of buoyant force?
The SI unit is the newton (N). In US customary calculations, the force is commonly expressed in pound-force (lbf), not simply pounds of mass.

Does water temperature affect the answer?
Yes, because water density changes with temperature. For ordinary estimates, 1,000 kg/m³ is convenient; use measured or tabulated density when greater accuracy is needed.

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in v | Displaced volume | m^3 | 0.01 | 0
out force | Buoyant force | N | 1000 * v * 9.81 | 2
out mass | Displaced water mass | kg | 1000 * v | 2