Density Calculator

The formula this calculator uses

Density = mass / volume (rho = m / V)

m

Mass of the sample, in grams or kilograms

V

Volume the sample occupies, in cm3 or m3

rho

Density — mass per unit volume, the quantity you are solving for

rho water

Density of water, 1.0 g/cm3 or 1000 kg/m3, the reference for specific gravity

How to check the result by hand

1. 1

   Establish the mass of the sample

   Use a balance, which measures mass directly and reads in grams or kilograms. If you only have a spring scale you are measuring weight, so divide by the gravitational acceleration of about 9.81 m/s2 to recover the mass before going any further. A balance compares masses, so it gives the same reading on the Moon as on Earth, which is exactly the property density relies on.

2. 2

   Find the volume in a known unit

   For a regular solid, multiply its dimensions; for a liquid, read the graduated cylinder; for an irregular solid, use displacement. Whatever route you take, record the volume as cm3 or m3 and write the unit down, because the next step inherits it.

3. 3

   Divide mass by volume

   500 g divided by 250 cm3 gives 2 g/cm3. The units of the answer are simply the units of the inputs combined, so feeding in grams and cubic centimetres yields grams per cubic centimetre with no extra work. Carrying the units through the division is a habit worth forming, because it makes a mistake in the setup visible before you trust the number.

4. 4

   Convert to SI when the context demands it

   Multiply the g/cm3 figure by 1000 to reach kg/m3, turning 2 into 2000. Multiplying by 100 is the classic error, and it produces an answer that is ten times too small yet still plausible enough to pass a glance.

5. 5

   Check the result against a known material

   Water is 1.0, aluminium 2.70, steel about 7.85 and gold 19.32 g/cm3. If your answer lands far outside the range spanned by real materials, the cause is almost always a unit slip rather than a measurement problem.