Free Buoyancy Experiment Calculator

The Buoyancy Experiment: Measuring Unknown Liquid Density Using Archimedes' Principle

This online buoyancy experiment calculator helps you determine the density of an unknown liquid—for example, dish soap—by applying Archimedes' principle. The method requires only a few household items and a simple procedure. By observing how a small ball floats between two distinct liquid layers, the tool can compute the unknown density from your measurements.

Understanding the Archimedes Principle

According to Archimedes' principle, any body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. The magnitude of this force is given by

$$F_B = \rho_{\text{fluid}} \times V_{\text{displaced}} \times g$$

where $F_B$ is the buoyant force, $\rho_{\text{fluid}}$ is the fluid density, $V_{\text{displaced}}$ is the volume of the displaced fluid, and $g$ is the acceleration due to gravity. Whether an object sinks or floats depends on density: if the object is denser than the fluid, it sinks; if it is less dense, it floats. In a system with two immiscible liquids of different densities, an object can come to rest at the interface when its density lies between those of the two liquids—the scenario exploited in this experiment.

Although buoyancy also occurs in gases, the effect is negligible for small objects in air, so the experiment focuses purely on liquids.

Items You Will Need

• Dish soap (or the liquid you want to measure)
• Table salt and water (to prepare a saltwater solution of known density)
• A golf ball, or any small spherical object that floats in saltwater but sinks in dish soap
• A tall, transparent container
• A ruler or measuring tape
• A digital scale

Step‑by‑Step Procedure

1. Measure the ball's density
   Weigh the ball and record its mass. Measure its diameter, then compute the volume using the sphere formula $V = \dfrac{4}{3}\pi r^{3}$. Divide the mass by the volume to obtain $\rho_{\text{ball}}$. For a standard golf ball weighing 1.62 oz with a diameter of 1.68 in, the density comes out to about 0.6525 oz/in³ (or roughly 1129 kg/m³).

2. Prepare a saltwater solution of known density
   Dissolve a controlled amount of salt in water. For instance, to produce a 20 % (200‰) solution, mix 200 g of salt with 800 g of water. You can find the resulting density by using a water density calculator that accepts the salt and water masses, or by consulting a density‑salinity table.

3. Assemble the two‑liquid system
   Pour the saltwater into the container. Gently lower the ball into the saltwater—it should float on the surface. Next, slowly pour the dish soap along the side of the container so that it forms a separate layer above the saltwater without mixing. The ball will become suspended between the two layers.

4. Record the immersion depth
   Measure the height $h$ of the part of the ball that extends into the upper liquid (the dish soap). This is often called the cap height.

5. Let the calculator work
   Enter the ball's density (or its mass and volume), the density of the saltwater, and the measured cap height. The buoyancy experiment calculator uses the balance of buoyant forces from both liquids to solve for the unknown density of the dish soap.

6. Read the result
   The tool displays the unknown liquid's density. For the golf‑ball example with a cap height of 0.5 in and a 20 % saltwater solution, the dish soap density is computed as 0.5883 oz/in³, which equals approximately 1017.8 kg/m³.

Practical Hints

• If the ball does not remain at the interface—that is, it sinks to the bottom or floats entirely on the top—adjust the saltwater concentration. The density of the saltwater must fall between the ball's density and the unknown liquid's density. Increase salinity to raise the density, or dilute to lower it.
• The calculator also provides an optional breakdown of how much each liquid contributes to the total buoyant force (available in the additional parameters panel).
• The same experimental design can be adapted to measure the density of other household liquids such as cooking oil, ethanol, or milk, provided you have a reference liquid of known density.

This Archimedes principle–based buoyancy force calculator turns a simple at‑home experiment into a reliable tool for discovering unknown liquid densities.