# Buoyancy Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

This buoyancy calculator is a simple tool that lets you determine the buoyant force in a blink of an eye. All you have to do is provide the density of a fluid and the volume of an object that stays underwater, and it will use the buoyancy formula to estimate the force that keeps the object floating.

If you are wondering how to calculate the buoyant force by hand, don't worry – we've got you covered!

## What is the buoyant force?

Buoyancy, otherwise called the upthrust, is the force acting in a direction opposite to the gravitational force that prevents a floating object from sinking. When the object is immersed in water (or any other liquid), its weight pulls it downwards. Buoyancy opposes that weight and has a magnitude directly proportional to the volume of fluid that would otherwise occupy the space taken by the object – in other words, to the volume of the displaced liquid.

Another situation in which you can observe the phenomenon of buoyancy is when objects less dense than air float above the ground. Please take a look at our helium balloons calculator for a special case scenario 🎈

## Buoyant force equation

You can calculate the buoyant force with the following buoyancy formula:

B = ρ × V × g

where:

• ρ – Density of the liquid the object is immersed in, measured in kg/m³;
• V – Volume of the displaced liquid, measured in m³;
• g – Gravitational acceleration in m/s²; and
• B – Buoyant force.

Our buoyancy calculator has a default value for the gravitational acceleration set to 9.81 m/s². If you want to change this value, open the advanced mode of the calculator.

## How to calculate the buoyant force

If you would like to find the buoyant force with step-by-step calculations instead of using our buoyancy calculator, follow the instructions below:

1. Decide on the gravitational acceleration in the place you want to measure buoyancy. If you immerse the object in a liquid on Earth, you don't need to make any changes in default values. Let's assume, though, that you wish to perform an experiment on Mars. Then, the gravitational acceleration will be equal to 3.24 m/s².

2. Choose the liquid you want your object to be immersed in. Let's say it is salted water with a density of 1020 kg/m³. Our density calculator may come in handy if you need to find out the density of fluids.

3. Place the object in the water and measure the volume of the displaced liquid. For example, let's say it is equal to 0.03 m³.

4. Input all of these values into the buoyant force equation:

B = ρ × V × g = 1020 × 0.03 × 3.24 = 99.14 N

5. You can also calculate the weight of the displaced liquid. To find this result, simply multiply the volume by density:

W = ρ × V = 1020 × 0.03 = 30.6 kg

## FAQ

### What is the SI unit of buoyancy?

The SI unit of the buoyant force is Newton (N). One Newton is the force required to accelerate a mass of 1 kilogram to 1 meter per second squared from rest.

### What causes buoyancy?

The pressure of a fluid increases with its depth. This increasing fluid pressure causes an upward force to relieve the pressure, which we call the buoyant force.

### How much buoyancy do I need to save myself from drowning?

You need about 30-50 newtons of buoyant force to save yourself from drowning. This is why life jackets provide more than 33 N of buoyancy, which increases the more a person weighs.

### How do I measure my body's volume using buoyancy?

To estimate your body's volume at home:

1. Fill a regular-shaped bathtub to the brim with water.
2. Get into the bath and submerge yourself completely. The sides should overflow.
3. Get out of the tub and measure the volume of water left inside.
4. The change in volume of the water is your body's volume.
5. Have fun mopping up the mess!

### How do I estimate the buoyancy of a 1 L water bottle?

We estimate the buoyancy needed for an object using the formula B = ρ × V × g, where ρ and V are the object's density and volume, respectively, and g is the acceleration due to gravity. Water has a density of 1000 kg/m3. Thus, the buoyant force needed is 1000 kg/m3 × 1 L × 9.81 m/s2 = 9.81 N.

Bogna Szyk
Fluid type (optional)
Sea water
Fluid density (ρ)
lb/cu in
Volume (V)
cu ft
Buoyant force (B)
lbf
Mass of displaced fluid
lb
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