What is the formula for buoyant force?

Archimedes' principle gives the buoyant force as F = ρ·V·g, where ρ is the fluid density in kg/m³, V is the volume of fluid the object displaces in m³, and g is gravity, about 9.81 m/s². For example, a fully submerged object that pushes aside 0.001 m³ (1 litre) of fresh water feels an upthrust of 1000 × 0.001 × 9.81 = 9.81 N, the weight of that displaced litre. Scale V up to 1 m³ and the force becomes 9810 N.

How do I know if an object will float or sink?

Compare average densities. An object floats when its average density is less than the fluid's, sinks when it is greater, and hovers in neutral buoyancy when they are equal. Oak at about 700 kg/m³ floats on water (1000), while steel at 7850 sinks. A steel ship still floats because its average density, counting all the air inside the hull, is far below 1000 kg/m³. Switch this tool to float mode and enter the object density, or its mass and volume, to get the verdict.

Why is the density of water 1000 kg/m³?

By definition, 1 litre of fresh water has a mass of almost exactly 1 kilogram at 4°C, and 1 m³ holds 1000 litres, so its density is 1000 kg/m³. This round number is the reference point for buoyancy problems and for the whole metric system of mass. Sea water is denser at about 1025 kg/m³ because of dissolved salt, and air is far thinner at 1.225 kg/m³, which the presets in this calculator fill in with one click.

Why does a ship float higher in sea water than in a river?

Because sea water is denser, about 1025 kg/m³ versus 1000 for fresh water, so the same displaced volume produces more upthrust: F = ρ·V·g rises with ρ. A ship therefore needs to displace less volume to balance its weight, and it rides higher. This is the Plimsoll line story: ships are marked with load limits that differ between fresh and salt water. Put 0.01 m³ into this tool at 1000 then 1025 and watch the buoyant force climb.

What is apparent weight under water?

Apparent weight is what a submerged object seems to weigh once buoyancy helps hold it up: W_app = m·g − ρ·V·g, the true weight in air minus the upthrust. A 10 kg rock with volume 0.001 m³ weighs 98.1 N in air but only about 88.3 N under water, because the displaced litre of water lifts with 9.81 N. This is why lifting a stone is easier underwater. In mass-and-volume float mode this tool prints both the air weight and the apparent weight.

Does buoyancy depend on the object's shape or depth?

Not directly. Buoyant force depends only on the volume of fluid displaced, the fluid density and g, not on the object's shape, material or how deep it sits, as long as it stays fully submerged and the fluid density is constant. A flat plate and a sphere of the same volume feel the same upthrust. Depth changes the pressure on each face but the net buoyant force stays ρ·V·g. Shape matters only for how much volume a floating object can displace before water spills over its sides.

Solve a physics homework problem step by step

The textbook asks for the buoyant force on a 2 litre block fully submerged in water. Switch to force mode, set ρ to 1000 with the fresh water preset, type 2 with the litre unit selected, leave g at 9.81, and read 19.62 N. The on-screen steps spell out ρ·V·g so you can copy the working into your answer and show how you got there, not just the final number.

Decide whether a design will float before building it

Designing a raft, a buoy or a foam float, you need to know it will sit on top of the water, not under it. Put in the average density of your assembly, or its total mass and volume, against water at 1000, and the verdict and density ratio appear at once. Tweak the volume until the tool flips from sinks to floats and you have the displacement your design needs.

Show a class why a steel ship floats

Steel is 7850 kg/m³, nearly eight times denser than water, yet ships float. Enter a hull's total mass and its enclosed volume in mass plus volume mode and watch the average density drop below 1000, so the verdict reads floats. Share the URL with the class and every student opens the same scenario, then raise the mass until it sinks to find the loading limit live.

Estimate the apparent weight of a salvage load

Lifting a sunken object, you want to know how much it will seem to weigh underwater before it breaks the surface. Enter its mass and volume in float mode and the tool prints both the true weight in air and the apparent weight while submerged, the difference being the buoyant help. That apparent figure is the load your hoist actually feels until the object clears the water.

Buoyancy Force Calculator — Archimedes' Principle (F = ρ·V·g)

F = ρ·V·g · Archimedes' principle · will it float or sink · fresh/sea water + air presets · apparent weight · 100% browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

What do you want to do?

Fluid density ρ

kg/m³

Object density

kg/m³

Object mass

Displaced volume V

Gravity g

m/s²

Result

Buoyant force9.81 N

Formula steps

F_b = ρ · V · g
F_b = 1,000 × 0.001 × 9.81
F_b = 9.81 N

What this tool does

Free buoyancy calculator built on Archimedes' principle: the upthrust on a submerged or floating object equals the weight of the fluid it pushes aside, F = ρ·V·g. Enter the fluid density ρ in kg/m³, the displaced volume V in cubic metres or litres, and the gravitational acceleration g (default 9.81), and the tool returns the buoyant force in newtons with every step of the formula shown so you can check the arithmetic by hand. A second mode answers the question every physics class asks, will it float, by comparing the object's average density against the fluid: lighter than the fluid and it floats, heavier and it sinks, equal and it hovers in neutral buoyancy. Describe the object by its density directly, or by its mass and volume and the tool works out the density for you, then reports the true weight in air and the apparent weight while submerged. Density presets cover fresh water 1000, sea water 1025 and air 1.225 kg/m³, which is why a ship floats higher at sea than on a river. Everything runs in your browser and a shareable URL reproduces the exact problem. 100% client-side, no upload, no account.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Buoyancy Force Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Solve a physics homework problem step by step
The textbook asks for the buoyant force on a 2 litre block fully submerged in water. Switch to force mode, set ρ to 1000 with the fresh water preset, type 2 with the litre unit selected, leave g at 9.81, and read 19.62 N. The on-screen steps spell out ρ·V·g so you can copy the working into your answer and show how you got there, not just the final number.
Decide whether a design will float before building it
Designing a raft, a buoy or a foam float, you need to know it will sit on top of the water, not under it. Put in the average density of your assembly, or its total mass and volume, against water at 1000, and the verdict and density ratio appear at once. Tweak the volume until the tool flips from sinks to floats and you have the displacement your design needs.
Show a class why a steel ship floats
Steel is 7850 kg/m³, nearly eight times denser than water, yet ships float. Enter a hull's total mass and its enclosed volume in mass plus volume mode and watch the average density drop below 1000, so the verdict reads floats. Share the URL with the class and every student opens the same scenario, then raise the mass until it sinks to find the loading limit live.
Estimate the apparent weight of a salvage load
Lifting a sunken object, you want to know how much it will seem to weigh underwater before it breaks the surface. Enter its mass and volume in float mode and the tool prints both the true weight in air and the apparent weight while submerged, the difference being the buoyant help. That apparent figure is the load your hoist actually feels until the object clears the water.

Common pitfalls

Using the object's volume instead of the displaced fluid volume. For a fully submerged object they are equal, but a floating object only displaces the part of its volume that is under the surface. Feeding the whole volume into F = ρ·V·g overstates the buoyant force on a floater. Use the submerged volume, or work in float mode by density.
Plugging in the object's density instead of the fluid's density. The ρ in F = ρ·V·g is the density of the fluid being pushed aside, not the object. Mixing these up is the most common slip, since water is 1000 while a floating wood block is 700, and only the 1000 belongs in the force formula.
Forgetting to convert litres to cubic metres. The formula is in SI, so 1 litre is 0.001 m³, not 1. Typing a litre value into a cubic-metre field inflates the force by a thousand. This tool gives you a litre unit so the conversion happens for you, but check the unit picker before you trust the number.

Privacy

Every calculation here, the buoyant force, the float-or-sink verdict, the density ratio, the unit conversions and the formula steps, is plain JavaScript that runs in your browser tab. No densities, volumes, masses or results ever leave the page, and nothing you type is logged. The one caveat: the shareable URL encodes your inputs in the query string, so a share link pasted into chat records those numbers in the recipient server's access log. For ordinary physics problems that is harmless; if your figures are sensitive, use the copy button and paste the text instead of the URL.

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Buoyancy Force Calculator — Archimedes' Principle (F = ρ·V·g)

Result

Formula steps

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Buoyancy Force Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Solve a physics homework problem step by step

Decide whether a design will float before building it

Show a class why a steel ship floats

Estimate the apparent weight of a salvage load

Common pitfalls

Privacy

FAQ

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