Turn centimeter dimensions into volume, multiply by density, and convert grams to kilograms. A building block animation explains cubic units and how hollow space changes the answer.
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The calculation
Solid block mass (kg) = length × width × height (cm³) × density (g/cm³) ÷ 1,000
Worked example
A 10 × 5 × 2 cm solid block has a volume of 100 cm³. At an assumed density of 2 g/cm³, its mass is 200 g = 0.2 kg. If 20 cm³ of material is removed, the remaining 80 cm³ has a mass of 160 g = 0.16 kg at the same density.
Length is not mass, and centimeters are not cubic centimeters. Use the actual density and actual material volume; the density of 2 g/cm³ is an illustrative assumption.
Video chapters
- 0:00 — A length does not determine a mass
- 0:16 — Build length, width and height
- 0:31 — cm³ means volume, not length
- 0:49 — Each cm³ contributes 2 grams
- 1:06 — 200 g ÷ 1,000 = 0.2 kg
- 1:22 — Subtract empty space before multiplying
- 1:38 — A different density unit needs conversion
- 1:57 — Dimensions → volume → mass → kilograms
Read the full transcript
A measurement of ten centimeters cannot, by itself, tell you a mass in kilograms. A thin strip and a solid block can share that length. To calculate the mass of a uniform solid, we need its volume and density. Dimensions are the first step, not the complete conversion.
Take a rectangular solid ten centimeters long, five centimeters wide, and two centimeters high. Multiply length by width to get fifty square centimeters for the base. Then multiply by the two-centimeter height to get one hundred cubic centimeters of volume.
The units explain the change: centimeters times centimeters gives square centimeters; multiply by centimeters again and you get cubic centimeters. One cubic centimeter is a cube one centimeter on each edge. Do not treat a centimeter measurement as though it were already a volume.
Suppose the material density is two grams per cubic centimeter. This is a hypothetical value. Each cubic centimeter contributes two grams, so one hundred cubic centimeters times two gives two hundred grams. The cubic-centimeter units cancel, leaving a mass rather than another volume.
One kilogram is one thousand grams. Divide two hundred grams by one thousand to get zero point two kilograms. A check is to multiply zero point two kilograms by one thousand: you recover two hundred grams. The object has not changed; only the mass unit has.
What if the object is hollow? Its outside dimensions include space with no material in it. Suppose twenty cubic centimeters are removed from our hundred-cubic-centimeter block. Eighty remain. At the same density, that is one hundred sixty grams, or zero point one six kilograms.
Always match the volume unit to the density unit. A density in kilograms per cubic meter cannot be multiplied directly by a volume in cubic centimeters. There are one million cubic centimeters in one cubic meter, because the length conversion is cubed. Convert consistently before multiplying, and use the actual material value.
Calculate the material volume, multiply by a matching density, and convert the resulting mass to kilograms if needed. Account for hollow space and label assumed densities. Our ten-by-five-by-two-centimeter solid, at two grams per cubic centimeter, has a mass of zero point two kilograms.