Buoyancy Calculator

Introduction

Buoyancy is the upward force that a fluid pushes on an object placed in it. This force is what makes boats float and heavy steel ships stay on top of water. Our Buoyancy Calculator helps you quickly find the buoyant force acting on any object submerged in a fluid. It uses Archimedes' Principle, which states that the buoyant force equals the weight of the fluid displaced by the object. All you need to know is the fluid's density, the volume of fluid displaced, and the acceleration due to gravity. Whether you are a student solving homework problems or just curious about why things float or sink, this tool gives you fast and accurate results.

How to use our Buoyancy Calculator

Enter the details about your object and the fluid it is placed in. The calculator will find the buoyant force acting on the object and tell you whether it sinks or floats.

Fluid Density: Type in the density of the fluid the object is submerged in. This is measured in kilograms per cubic meter (kg/m³). For example, fresh water has a density of about 1000 kg/m³ and salt water is about 1025 kg/m³.

Object Volume: Enter the total volume of the object that is submerged in the fluid. This is measured in cubic meters (m³). If the object is fully underwater, use its entire volume.

Object Mass: Type in the mass of the object in kilograms (kg). This value is used along with the buoyant force to figure out if the object will sink or float.

Gravitational Acceleration: This is set to 9.81 m/s² by default, which is the standard value for gravity on Earth. You can change it if you need to calculate buoyancy on another planet or at a different location.

Understanding Buoyancy

Buoyancy is the upward force that a fluid pushes on any object placed in it. When you drop a ball into a pool, the water pushes up on that ball. This pushing force is what we call the buoyant force. It is the reason some things float and other things sink.

Archimedes' Principle

Over 2,000 years ago, a Greek scientist named Archimedes discovered a simple but powerful rule: the buoyant force on an object equals the weight of the fluid it pushes aside. This is known as Archimedes' Principle, and it is written as:

B = ρ × V × g

• B is the buoyant force, measured in newtons (N). You can also explore how forces work more broadly with our Force Calculator.
• ρ (rho) is the density of the fluid, or how heavy the fluid is for its size, measured in kg/m³.
• V is the volume of fluid that the object displaces (pushes out of the way), measured in m³.
• g is the acceleration due to gravity, which is about 9.81 m/s² on Earth. For a deeper look at gravitational acceleration, see our Acceleration Calculator.

If you know any three of these four values, you can solve for the missing one. The Buoyant Force tab in the calculator above does exactly that.

What Makes an Object Float or Sink?

Whether an object floats or sinks depends on how its density compares to the density of the fluid around it. Density is simply how much mass is packed into a given volume. Here are the three possible outcomes:

• Floats: The object's density is less than the fluid's density. The fluid can support the object's full weight before the object is fully submerged. A wooden log floats in water because wood is less dense than water.
• Sinks: The object's density is greater than the fluid's density. Even when fully submerged, the buoyant force is not strong enough to hold the object up. A steel bolt sinks because steel is much denser than water.
• Neutrally buoyant: The object's density matches the fluid's density exactly. The object neither rises nor sinks and stays suspended wherever you place it. Submarines control their buoyancy to achieve this state.

The net force on a submerged object is the difference between the buoyant force pushing up and the object's weight pulling down. Understanding this balance ties directly into concepts like momentum and impulse, which describe how forces change an object's motion over time.

How Much of a Floating Object Sits Below the Surface?

When an object floats, only part of it sits underwater. The fraction that is submerged equals the ratio of the object's density to the fluid's density:

Fraction submerged = ρ_object ÷ ρ_fluid

This is why about 90% of an iceberg is hidden below the ocean surface. Ice has a density of roughly 920 kg/m³, and seawater has a density of about 1,025 kg/m³. Dividing 920 by 1,025 gives approximately 0.90, or 90%. The remaining 10% is the part you can see above the water. The Volume Above Surface tab uses this formula to show you exactly how much of any floating object stays above and below the waterline.

Why Fluid Density Matters

Different fluids have different densities, and this changes buoyancy results significantly. Fresh water has a density of about 998 kg/m³, while seawater is denser at around 1,025 kg/m³. The Dead Sea, famous for letting people float effortlessly, has a density of roughly 1,240 kg/m³. Mercury, a liquid metal, has a density of 13,546 kg/m³ — so dense that even a lead brick would float in it. The denser the fluid, the stronger the buoyant force it produces for the same displaced volume. Understanding fluid behavior at the molecular level also connects to topics like pressure and temperature relationships explored in our Ideal Gas Law Calculator.

Real-World Applications

Buoyancy plays a role in countless areas of everyday life and engineering. Ship designers use buoyancy calculations to make sure vessels can carry heavy cargo without sinking. Hot air balloons float because the warm air inside is less dense than the cooler air outside. Hydrometers measure fluid density by observing how deep a calibrated float sinks. Geologists use buoyancy principles to understand why Earth's tectonic plates float on the denser mantle below. Even fish use a swim bladder — a small internal air sac — to adjust their density and control whether they rise, sink, or stay at the same depth.

Buoyancy is also closely related to other fundamental physics concepts. The Gravitational Force Calculator can help you understand the weight component that opposes buoyancy, while the Potential Energy Calculator lets you explore how energy changes as an object rises or sinks in a fluid. If you are studying objects in free fall before they enter a fluid, our Free Fall Calculator shows how gravity accelerates them, and the Kinetic Energy Calculator reveals how much energy they carry at the moment of impact with the surface.

Frequently Asked Questions

What is the buoyancy formula used in this calculator?

This calculator uses Archimedes' Principle: B = ρ × V × g. Here, B is the buoyant force in newtons, ρ is the fluid density in kg/m³, V is the displaced volume in m³, and g is gravitational acceleration in m/s². If you know any three of these values, the calculator solves for the fourth one automatically.

How do I switch which variable the calculator solves for?

In the Buoyant Force tab, the calculator solves for whichever field you leave empty or edit last. For example, if you type values into fluid density, displaced volume, and gravity, the calculator will solve for buoyant force. If you clear the volume field and fill in the other three, it will solve for volume instead. A small ← Computed label appears next to the field being calculated.

What units does the buoyancy calculator support?

The calculator supports many units for each input:

• Density: kg/m³, g/cm³, g/m³, kg/cm³, lb/ft³, lb/yd³, oz/in³, g/L, and slug/ft³
• Volume: m³, cm³, mm³, mL, L, US gal, US fl oz, imp gal, in³, ft³, and yd³
• Gravity: m/s², × g (multiples of standard gravity), and ft/s²
• Force: N, kN, lbf, dyn, kgf, and poundal

Pick your preferred units from the dropdown menus next to each field.

What is the difference between the three tabs in this calculator?

Each tab solves a different buoyancy problem:

• Buoyant Force: Calculates any one of the four variables in B = ρ × V × g when you provide the other three.
• Sink / Float: Compares the object's density to the fluid's density and tells you whether the object will float, sink, or be neutrally buoyant. It also shows object weight, buoyant force, and net force.
• Volume Above Surface: For floating objects, it shows what percentage of the object sits above the waterline and what percentage is submerged, along with a visual bar.

How does the Sink/Float tab determine if an object floats?

It compares the object's density to the fluid's density. If the object's density is less than the fluid's density, it floats. If it is greater, it sinks. If the two densities are nearly equal (within 0.1%), the object is considered neutrally buoyant, meaning it stays suspended at whatever depth you place it.

Can I use this calculator for gases instead of liquids?

Yes. Archimedes' Principle works for any fluid, including gases. For example, you can calculate the buoyant force on a helium balloon in air. Just enter the density of air (about 1.225 kg/m³ at sea level) as the fluid density and the balloon's volume as the displaced volume. The formula works the same way for gases as it does for liquids.

Why does the calculator show displaced fluid mass?

Displaced fluid mass tells you how much fluid the object pushes out of the way. It is calculated as ρ × V (fluid density times displaced volume). This value is useful because, by Archimedes' Principle, the weight of that displaced fluid equals the buoyant force. Knowing the displaced mass helps you understand how much fluid is involved in supporting the object.

What does net force mean in the Sink/Float results?

Net force is the difference between the buoyant force (pushing up) and the object's weight (pulling down). If the net force is upward, the buoyant force wins and the object floats or accelerates upward. If the net force is downward, the object's weight wins and it sinks. A net force of zero means the object is neutrally buoyant.

How accurate is this buoyancy calculator?

The calculator uses precise unit conversion factors and computes results to 7 significant figures internally. It is accurate for standard physics and engineering problems. However, it assumes uniform density for both the fluid and the object, and it does not account for factors like temperature changes, fluid compression at great depths, or irregular object shapes that might trap air pockets.

What does the visual bar in the Volume Above Surface tab show?

The colored bar shows the fraction of a floating object that sits below the surface versus above it. The purple section on the left represents the submerged portion, and the remaining space on the right represents the part above the surface. The percentage is labeled directly on the bar so you can see the split at a glance.

Can I calculate buoyancy on other planets?

Yes. Change the gravitational acceleration value to match the planet you are interested in. For example, use 3.72 m/s² for Mars or 1.62 m/s² for the Moon. The buoyant force changes directly with gravity, so a lower gravity means a weaker buoyant force for the same fluid and volume.

What happens if I enter zero or a negative number?

The calculator requires positive values for density, volume, and gravity. If you enter zero or leave multiple fields blank, the results will display a dash (—) to indicate that a valid calculation cannot be done. The Sink/Float tab will show an Invalid Input warning asking you to enter positive values.

How do I find the volume of an irregular object for this calculator?

Use the water displacement method. Fill a graduated container with a known volume of water, then submerge the object completely. The rise in water level equals the object's volume. For example, if the water rises from 500 mL to 750 mL, the object's volume is 250 mL (or 250 cm³). Enter that value into the calculator.

Does the fluid density preset update my calculation automatically?

In the Buoyant Force tab, selecting a preset fills in the density field and recalculates the result instantly. In the Sink/Float and Volume Above Surface tabs, the preset fills in the density field, but you need to click the Calculate button to update the results.