Buoyant Force Calculator

Calculation method Archimedes (density × gravity × displaced volume) Weight difference (air vs submerged reading) Floating estimate (mass + object volume)

Tip: use Archimedes when you know displaced volume.

Gravity

m/s² ft/s²

Use 9.80665 m/s² for standard gravity.

Fluid density

kg/m³ g/cm³ lb/ft³ slug/ft³

Examples: water ≈ 1000 kg/m³, seawater ≈ 1025 kg/m³.

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Displaced volume

Enter directly or compute from a shape.

Volume source Direct volume From shape dimensions

Displaced volume value

m³ L mL cm³ ft³ in³ US gal

Shape Rectangular box Cylinder Sphere

Length unit m cm mm ft in

Length

Width

Height

Radius

Height

Radius

These dimensions estimate displaced volume for a fully submerged shape.

Air vs submerged reading

Use mass-equivalent readings from a scale or balance.

Reading in air

Reading submerged

Mass unit kg g lb slug

Apply optional air-buoyancy correction (advanced)

This needs an object volume estimate and air density.

Air density

kg/m³ g/cm³ lb/ft³

Volume for correction uses the displaced-volume fields above.

Floating estimate

Compute fraction submerged from object density.

Object mass

kg g lb slug

Object volume source Direct volume From shape dimensions

Object volume value

m³ L mL cm³ ft³ in³ US gal

Shape Rectangular box Cylinder Sphere

Length unit m cm mm ft in

Length

Width

Height

Radius

Height

Radius

If fraction submerged exceeds 1, the object sinks.

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Output force unit N kN lbf

Reset Calculate

• Archimedes: F_b = ρ_f · g · V_disp
• Weight difference: F_b = W_air − W_sub, where W = m · g
• Floating estimate: ρ_obj = m / V, fraction ≈ ρ_obj/ρ_f, and at equilibrium F_b = W

1. Select a calculation method that matches your data.
2. Enter gravity and the fluid density in your preferred units.
3. Provide volume (directly or using the shape tool).
4. For weight difference, enter air and submerged readings.
5. Click Calculate to view results and extra outputs.
6. Use Download CSV or Download PDF for reporting.

1) Archimedes principle in one line

Buoyant force equals the weight of the displaced fluid: F_b=ρ·g·V. If you displace 0.010 m³ of seawater (ρ≈1025 kg/m³) at g=9.80665 m/s², the lift is about 100.6 N, which is roughly 22.6 lbf.

2) Typical fluid densities you can enter

Freshwater is commonly 1000 kg/m³, seawater about 1020–1030 kg/m³, and engine oil often 850–920 kg/m³. Mercury is around 13,534 kg/m³. Air near sea level is about 1.2 kg/m³, so buoyancy in air is small but measurable for large volumes and precision scales.

3) Choosing a volume method

If you know displaced volume from a tank or overflow measurement, use “Direct volume.” If you only know dimensions, use the shape tool. For a cylinder with r=5 cm and h=20 cm, volume is πr²h≈0.001571 m³, producing about 15.4 N of buoyancy in water. For irregular objects, measure displacement by water overflow, then enter the collected volume directly accurately.

4) Weight-difference measurements

With a spring scale, the difference between the reading in air and the submerged reading equals buoyant force. Example: 10.0 kg in air and 8.5 kg submerged implies Δm=1.5 kg, so F_b=Δm·g≈14.7 N. The optional air correction refines this for high accuracy when the object volume is large.

5) Floating and fraction submerged

For a floating object, buoyancy balances weight. The fraction submerged is approximately ρ_obj/ρ_fluid. A 1.2 kg object with 0.0015 m³ volume has ρ≈800 kg/m³, so it floats in water with about 0.80 of its volume below the surface.

6) Unit conversions and output checks

This calculator converts inputs to SI internally, then shows results in N, kN, and lbf. A quick sanity check: doubling displaced volume doubles buoyant force, and increasing fluid density from 1000 to 1025 kg/m³ increases buoyancy by 2.5% for the same volume. Remember 1 lbf ≈ 4.448 N.

7) Practical tips for real experiments

Ensure the object is fully submerged for the Archimedes method, remove trapped air bubbles, and measure dimensions carefully. For liquids with temperature variation, density can change noticeably; even a 1% density change alters buoyant force by 1%, which matters in calibration and design work.

1) What does buoyant force represent?

It is the upward force from a fluid on an object. Numerically, it equals the weight of the fluid displaced by the object’s submerged volume, so higher density fluids and larger displaced volumes produce more lift.

2) Does the object need to be fully submerged?

Only for the “displaced volume” method when you treat the whole object as displaced volume. If the object floats, only the submerged portion displaces fluid, and the calculator’s floating estimate uses density ratio to approximate that fraction.

3) Can I use this calculator for gases?

Yes. Enter gas density (for example, air ≈ 1.2 kg/m³) and the displaced volume. The resulting buoyant force is usually small, but it matters for balloons, large enclosures, and precision mass measurements.

4) Why can buoyancy be large, yet the object still sinks?

An object sinks when its weight exceeds the maximum buoyant force available at full submersion. In density terms, if ρ_obj > ρ_fluid, the required displaced volume would exceed the object’s own volume.

5) How do I estimate displaced volume for irregular shapes?

Use a displacement container. Submerge the object carefully and collect the overflow, then measure that collected volume with a graduated cylinder or scale. Enter the measured value in the “Direct volume” option for best results.

6) How accurate are the unit conversions and results?

Conversions use standard constants and SI internal math. Accuracy depends mostly on your inputs: density, gravity, and volume. Measure dimensions precisely and avoid trapped bubbles. For critical work, compare with a lab measurement or calibration mass.