How to Calculate Buoyant Force

Buoyant force is the force exerted on an object submerged in a fluid, acting in the opposite direction of gravity. When an object is placed in a fluid, its weight pushes down on the fluid (whether liquid or gas), while the buoyant force pushes the object upwards, counteracting gravity. In general, the buoyant force can be calculated using the equation F_b = V_s × D × g, where F_b is the buoyant force, V_s is the volume of the submerged part, D is the density of the surrounding fluid, and g is the gravitational force. To learn how to calculate the buoyant force of an object, start with Step 1 below.

Find the volume of the submerged part of the object. The buoyant force acting on an object is directly related to the volume of the object that is submerged. In other words, the more submerged a solid object is, the greater the buoyant force acting on it. This means that even if an object is fully submerged in a liquid, buoyant force still acts on it. To begin calculating the buoyant force on an object, the first step is typically to determine the submerged volume. In the buoyant force equation, this value should be written in m³.

• For an object completely submerged in a fluid, the submerged volume will equal the total volume of the object. For an object floating on the surface of a fluid, only the volume beneath the fluid surface is considered.
• For example, let’s say we want to find the buoyant force on a rubber ball floating in water. If the ball is a perfect sphere with a diameter of 1 m and it floats with exactly half submerged under water, we can find the submerged volume by calculating the total volume of the ball and then halving it. Since the volume of a sphere is (4/3)π(radius)³, the volume of the ball would be (4/3)π(0.5)³ = 0.524 m³. Dividing by 2, we get 0.262 m³ submerged.

Find the density of the fluid. The next step in determining buoyant force is to calculate the density (in kg/m³) of the surrounding liquid. Density is a quantity measured as the ratio of the mass of a substance to its corresponding volume. When two objects have the same volume, the one with higher density will weigh more. The general principle is that the higher the density of the fluid, the greater the buoyant force acting on an object submerged in it. For fluids, the easiest way to determine density is often by referencing reliable sources.

• In the example above, the ball floats in water. Consulting study materials tells us that the density of water is 1,000 kg/m³.
• The densities of many common fluids are listed in technical references. You can find this list here.

Determine the gravitational force (or downward force). Whether an object is submerged or floating in a fluid, it is always subject to the force of gravity. In fact, the constant downward force is approximately 9.81 Newtons per kilogram. However, if there are additional forces acting on the fluid and the object, such as centrifugal forces, these must also be considered when calculating the total 'downward' force for the system.

• In the example above, if we have a standard static system, we can assume that the only downward force acting on the fluid and the object is the standard gravitational force — 9.81 Newtons per kilogram.

Multiply the volume by density and gravitational force. When you have the values for the volume of the object (in m³), the density of the fluid (in kg/m³), and the gravitational force (or downward force in Newtons per kilogram), finding the buoyant force becomes simple. Just multiply these three quantities together to calculate the buoyant force in Newtons.

• For example, to solve the problem, substitute the values into the equation F_b = V_s × D × g. F_b = 0.262 m³ × 1,000 kg/m³ × 9.81 N/kg = 2,570 Newtons. The other units cancel out, leaving only Newtons.

Determine if the object will float by comparing with its weight. Using the buoyant force equation, you can easily determine the force pushing an object out of the liquid. However, you can also find out whether the object will float or sink in the fluid by taking an additional step. First, find the buoyant force acting on the entire object (using its full volume V_s), then calculate the gravitational force pulling the object downward with the formula G = (mass of the object)(9.81 m/s²). If the buoyant force is greater than the gravitational force, the object will float. Conversely, if the gravitational force is larger, the object will sink. If both forces are equal, the object is said to be in neutral buoyancy.

• An object in neutral buoyancy will neither rise to the surface of the water nor sink to the bottom, but instead will remain suspended within the fluid, floating between the surface and the bottom.
• For example, suppose we want to determine if a wooden cylindrical barrel weighing 20 kg with a diameter of 0.75 m and a height of 1.25 m will float in water. We must follow several steps to solve this problem:
  • First, calculate the volume using the formula for the volume of a cylinder V = π(radius)²(height). V = π(0.375)²(1.25) = 0.55 m³.
  • Next, using the standard gravitational force and the density of water, we calculate the buoyant force acting on the barrel. 0.55 m³ × 1,000 kg/m³ × 9.81 N/kg = 5,395.5 Newtons.
  • Now, calculate the gravitational force on the barrel. G = (20 kg)(9.81 m/s²) = 196.2 Newtons. This result is much smaller than the buoyant force, so the barrel will float.

Use similar calculations when the fluid is a gas. When solving buoyant force problems, don't forget that the fluid doesn't necessarily have to be a liquid. Gases are also considered fluids, although they have much smaller densities compared to other substances, and gases can still displace objects floating in them. Helium balloons are proof of this. Since the density of helium gas is lower than the surrounding fluid (air), the balloon will rise!

Place a small bowl inside a larger one. With just a few household items, you can easily observe the effect of buoyant force in real life. In this experiment, we demonstrate that when an object is submerged, it experiences a buoyant force because it displaces an amount of fluid equal to the volume of the submerged part of the object. During the experiment, we also show how to calculate the buoyant force acting on the object. First, place an open container, like a bowl or cup, inside a larger container, such as a big bowl or water tank.

Fill the smaller container with water up to the rim. You must fill the container almost to the edge without letting any water spill over. Be careful during this step! If the water spills over, you will need to empty the large container and start over.

• For this experiment, assume that the water has a density of 1,000 kg/m³. Unless you are using saltwater or a completely different liquid, most types of water have a density close to this reference value, so the results will not be affected.
• If you have a dropper, you can use it to carefully add water to the smaller container until the water reaches the edge.

Submerge a small object. Next, find an object that fits inside the smaller container but will not be damaged by the water. Measure its mass in kilograms (it is best to weigh it in grams and then convert to kilograms). Slowly submerge this object into the water without getting your fingers wet until it begins to float or you can no longer hold it, then release it. You will observe some water spilling over the edge of the smaller container into the larger one.

• For this example, suppose we are submerging a toy car weighing 0.05 kg into the smaller container. We do not need to know the volume of the toy car to calculate the buoyant force, as we will determine it in the next step.

Collect and measure the spilled water. When you submerge an object in water, it displaces a certain amount of water — otherwise, there would be no room to submerge it. As it displaces the water, the water pushes back, creating the buoyant force. Collect the water that spills out of the smaller container and pour it into a measuring cup. The volume of water in the cup should equal the volume of the submerged object.

• In other words, if the object floats, the volume of the spilled water will be equal to the volume of the submerged part of the object. If the object sinks, the volume of spilled water will be equal to the volume of the entire object.

Calculate the mass of displaced water. Since you know the density of water and can measure the volume of displaced water in the measuring cup, you can compute the mass of water. Convert the volume to m³ (you can use an online conversion tool such as this one to assist with this) and multiply it by the density of water (1,000 kg/m³).

• In the example provided, let’s assume the toy car sinks in the smaller container and displaces about 2 tablespoons of water (0.00003 m³). To find the mass of the water, multiply this value by the density: 1,000 kg/m³ × 0.00003 m³ = 0.03 kg.

Compare the mass of displaced water to the mass of the object. Now that you know both the mass of the submerged object and the mass of the displaced water, compare these two values. If the object's mass is greater than the mass of the displaced water, it will sink. Conversely, if the mass of the displaced water is greater, the object will float. This principle of buoyancy is how floating works in real life — for an object to float, it must displace a mass of water greater than its own mass.

• Thus, lightweight objects with a large volume float best. This explains why hollow objects float so well. Consider a canoe: it floats because it is hollow inside, allowing it to displace a lot of water while not being too heavy. If the canoe were solid, it would not float as effectively.
• In the above example, the toy car has a mass of 0.05 kg, which is greater than the mass of the displaced water at 0.03 kg. This matches what we observed: the toy car sank.

• Use a scale that resets to zero after each use to ensure precise measurements.

• Small cup or bowl
• Large bowl or container
• Small object that can be submerged in water (like a rubber ball)
• Measuring cup