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Physics & Science Suite

Density Calculator

Calculate density, mass, or volume. Select from common material presets to autofill density, or enter your own values.

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Understanding Density and Buoyant Force

Density is defined as the mass of a substance per unit volume. It is a fundamental physical property that helps identify materials, explain why objects sink or float, and design objects ranging from aerospace parts to concrete foundations.

The Density Formula

The mathematical formula is straightforward:

Density (ρ) = Mass (m) ÷ Volume (V)

To find the other values, we rearrange the formula:

  • Mass (m): m = ρ × V
  • Volume (V): V = m / ρ

Floating and Sinking in Water

Archimedes' principle explains how buoyant force determines whether an object floats or sinks. Water has an average density of exactly 1 gram per cubic centimeter (1.0 g/cm3). If an object has a higher average density than 1.0 g/cm3, the gravity pulling it down exceeds the water's upward buoyant force, and it sinks. If it has a lower density, it floats.

Common Questions & Density Insights

What is density and how is it calculated?

Density represents how much mass is packed into a given volume. The formula is Density = Mass / Volume. For example, if a block of metal weighs 100 grams and occupies 50 cubic centimeters of space, its density is 2 grams per cubic centimeter.

How does water density determine if something floats?

Pure water has a density of approximately 1.0 g/cm3 (or 1 g/mL). Any object with a density less than 1.0 g/cm3 will float in water, while objects with a density greater than 1.0 g/cm3 will sink. This is why heavy steel ships float (because their hollow shape makes their average density lower than water) but a solid steel nail sinks.

What units are used for density?

In science, the standard metric units are grams per cubic centimeter (g/cm3), grams per milliliter (g/mL), or kilograms per cubic meter (kg/m3). In US imperial measurements, pounds per cubic foot (lb/ft3) is commonly used.

How do you calculate mass or volume from density?

If you know the density and volume, multiply them to get mass (Mass = Density × Volume). If you know mass and density, divide mass by density to get volume (Volume = Mass / Density).

Why does density change with temperature?

As temperature increases, most substances expand and occupy a larger volume while their mass remains the same. Because volume increases, the density decreases. Water is a famous exception when it freezes—ice is less dense than liquid water, which is why ice cubes float.

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