How to Find Density of a Cube: Step-by-Step Guide (2025)

Finding the density of a cube is a straightforward calculation: measure its mass, measure one edge to find its volume, then divide mass by volume. The formula is density = mass / volume, and for a cube volume = edge length cubed.

What You Need Before Starting

Density tells you how much mass is packed into a given volume. For a cube, the math is simpler than for irregular objects because its shape is perfectly regular. The standard unit for density in science is grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

The National Institute of Standards and Technology provides the official definitions for SI units used here, including the kilogram and meter, which form the basis for density measurements in most countries.

Before you begin, gather three things: a scale (preferably digital, accurate to at least 0.1 grams), a ruler or caliper (accurate to 0.1 millimeters), and the cube itself. If the cube has any coating, paint, or absorbed moisture, those will affect the density reading. Dry, clean samples give the most accurate results.

Step 1: Measure the Mass

Place the cube on the scale and record its mass. If your scale has a tare function, use it to zero out any container. For small cubes, a precision scale is essential because even a few milligrams of error can throw off the density calculation.

Write down the mass in grams. For example, suppose the cube weighs 270 grams.

Step 2: Measure the Edge Length and Calculate Volume

A cube has equal length, width, and height. Measure any one edge with your ruler or caliper. Take the measurement at the center of the edge, not at a corner, because corners can be slightly rounded from manufacturing.

Record the length in centimeters. If your ruler uses millimeters, convert to centimeters by dividing by 10 (for instance, 30 mm = 3.0 cm).

Calculate the volume

The volume of a cube is edge length raised to the third power:

Volume = edge x edge x edge = edge³

Using a cube with an edge of 3.0 cm:

Volume = 3.0 cm x 3.0 cm x 3.0 cm = 27 cm³

Step 3: Apply the Density Formula

Now put the two measurements together:

Density = mass / volume

Using the example numbers:

Density = 270 g / 27 cm³ = 10 g/cm³

That result (10 g/cm³) is close to the density of silver (about 10.49 g/cm³ according to Encyclopedia Britannica). Your cube might be a silver alloy or a different material entirely. The calculation gives you a number you can compare against known densities to identify the material.

Common density values for reference

If your calculated density falls near one of these values, the cube is likely made of that material or a close alloy. If it falls between two values, the cube might be a mixture or have internal voids.

Step 4: Check for Accuracy and Common Mistakes

A few things can throw off your density calculation.

Measurement precision. If your ruler reads only to the nearest millimeter, your volume calculation could be off by several percent. A caliper that reads to 0.1 mm gives much better accuracy.

Air bubbles or hollow spots. A cube that looks solid might have internal cavities from casting. This makes the volume appear larger than the actual material volume, so density comes out too low. If you suspect voids, use water displacement (Archimedes’ method) to find the true volume.

Surface contamination. Oil, dirt, or moisture adds mass without adding volume, making density appear higher. Clean the cube with a lint-free cloth before measuring.

Scale calibration. Check that your scale reads zero when empty. A drift of even 0.5 grams on a 270-gram cube changes density by about 0.02 g/cm³. That is small but noticeable for precise work.

When to Use Water Displacement Instead

The direct measurement method works only for perfect cubes. If your cube has rounded corners, dents, or an irregular shape, measuring the edge alone will not give the true volume. In that case, use water displacement: submerge the cube in a graduated cylinder filled with water, and the rise in water level equals the cube’s volume. Then divide mass by that volume.

This method also works for cubes that are too large to measure with a ruler, or for oddly shaped objects that are roughly cubic. The trade-off is that you need a container large enough to hold the cube and enough water to cover it completely.

Working Through a Second Example with Different Units

Suppose you have a larger cube made of aluminum. You measure its edge as 10 centimeters and find its mass on a kitchen scale is 2,700 grams. The volume is 10 cm x 10 cm x 10 cm = 1,000 cm³. Density is 2,700 g / 1,000 cm³ = 2.70 g/cm³. That matches the known density of pure aluminum.

Now convert that to SI units. One cubic meter equals 1,000,000 cm³, so 1,000 cm³ is 0.001 m³. Mass in kilograms is 2.7 kg. Density in kg/m³ is 2.7 kg / 0.001 m³ = 2,700 kg/m³. Aluminum’s density is often given as 2,700 kg/m³ in technical handbooks.

This conversion matters if you work in fields like aerospace or automotive design, where densities are typically expressed in kg/m³. The calculation itself stays the same. Only the units change.

Key Takeaways

• Density of a cube equals its mass divided by its volume, where volume = edge length cubed.
• Use a precise scale and caliper for accurate measurements; small errors in length get cubed in the volume calculation.
• Compare your result against known density values to identify the material or check for internal flaws.
• For imperfect cubes, use water displacement instead of the edge-measurement method.
• Always clean the cube and zero your scale before starting to avoid contamination errors.