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Density Calculator

Find density, mass or volume from the other two in any units, and see whether the object would float or sink in water.

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Density tells you how tightly packed a material is: how much mass fits in each unit of volume. Know any two of density, mass and volume and this calculator finds the third, in whatever units your lab uses, and tells you whether the object would float in water.

How to Use It

  1. Choose what to Find: Density, Mass or Volume.
  2. Enter the other two values and pick each one’s unit.
  3. Choose the unit for the answer in Answer In.
  4. Press Calculate to see the answer and whether the object floats or sinks in water.

How It Works

Density is mass divided by volume:

ρ=mV\rho = \frac{\vA{m}}{\vB{V}}

Rearranging gives the other two: m=ρVm = \rho V and V=mρV = \frac{m}{\rho}. The calculator converts every value to kilograms and cubic meters first, so you can mix units, such as grams and milliliters.

Water’s density, about 1 g/cm³ (1000 kg/m³), is the dividing line: anything less dense floats in it, anything denser sinks.

Worked Example

A block has a mass of 540 g and a volume of 200 cm³:

ρ=540 g200 cm3=2.7 g/cm3\rho = \frac{540 \text{ g}}{200 \text{ cm}^3} = 2.7 \text{ g/cm}^3

That’s the density of aluminum. At 2.7 times the density of water, the block sinks.

Tips and Common Mistakes

  • Keep units consistent. Grams with cm³ gives g/cm³; kilograms with m³ gives kg/m³. The calculator handles mixed units for you.
  • 1 mL = 1 cm³. So g/mL and g/cm³ are the same number.
  • Measure irregular volumes by displacement. The rise in water level in a graduated cylinder is the object’s volume.
  • Mass isn’t density. A big log can be heavy yet still float, because it’s less dense than water.
  • Temperature matters a little. Most materials get slightly less dense as they warm up.

Frequently Asked Questions

What is the density formula?

Density = mass ÷ volume (ρ = m/V). Rearranged, mass = density × volume and volume = mass ÷ density.

What units is density measured in?

In chemistry, usually g/cm³ or g/mL (the same thing). In physics, kg/m³. 1 g/cm³ = 1000 kg/m³.

How does density tell me if something floats?

An object floats in water if it's less dense than water (about 1 g/cm³) and sinks if it's denser. Ice (0.92 g/cm³) floats; aluminum (2.7 g/cm³) sinks.

How do I find the volume of an irregular object?

Use water displacement: note the water level in a graduated cylinder, lower the object in, and the rise in level is its volume.

Does density change with temperature?

Slightly, for most materials: they expand when warmed, so their density drops. Water is densest at about 4 °C.

Is density the same as weight?

No. A kilogram of feathers and a kilogram of lead have the same mass, but lead is far denser, so it takes up much less space.

Sources

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