Water, one liter
School order for water: 1 kg in 0.001 m³. The quotient 1 / 0.001 is 1,000 kg/m³, or 1 g/cm³. This is the reference example on this page.
ρ = 1,000 kg/m³
Density Calculator
Enter mass in kilograms and volume in cubic meters. The calculator finds density with ρ = m/V and also shows grams per cubic centimeter and the volume of one kilogram. For 1 kg and 0.001 m³ the result is 1,000 kg/m³. The model does not include specific weight γ = ρg or a temperature correction for gases.
Result
Enter a mass and a volume. Density, grams per cubic centimeter, and the ρ(V) chart will appear here.
On the neighboring pages density is an input, not the result: buoyant force uses F = ρ·V·g, and hydrostatic pressure uses p = ρ·g·h.
How it works
m1 kg
V0.001 m³
ρ1,000 kg/m³
Density is mass per volume. The formula ρ = m/V divides mass by volume. The SI unit is the kilogram per cubic meter. For 1 kg and 0.001 m³, one liter, the quotient is 1,000 kg/m³. That same number is 1 g/cm³ and 1 kg per liter. One kilogram of that sample occupies 0.001 m³.
The calculator uses mass m in kilograms and volume V in cubic meters. Enter 1 L as 0.001, and 1 cm³ as 0.000001. One hundred liters is 0.1 m³. 250 ml is 0.00025 m³. A comma and a period are the same decimal separator. Volume does not switch to cubic feet.
What the result panel shows. Besides density in kg/m³, the calculator shows the same value in g/cm³, the volume of one kilogram equal to 1/ρ, the mass used in the division, and the volume in cubic meters. For 1 kg and 0.001 m³ the panel shows 1,000 kg/m³, 1 g/cm³, and 0.001 m³ per kilogram. The chart draws ρ against volume at that same mass, from one quarter of the entered volume to four times that volume. The middle point is the pair you entered.
Limits of the model. The result is the quotient of the numbers you entered. It is not a measurement of temperature, moisture, or porosity. Water in school problems is on the order of 1,000 kg/m³. Near 4 °C it is close to 1,000 kg/m³, and near 20 °C it is closer to 998 kg/m³. The calculator does not apply that correction. The concrete example, 2.4 kg in 0.001 m³, gives 2,400 kg/m³ as a school order for ordinary concrete, not as a mix certificate. Lightweight concrete and reinforced concrete sit in other ranges.
Density does not depend on g. Specific weight is ρ·g, force per volume. Buoyant force F = ρ·V·g is on the buoyant-force page, and fluid-column pressure p = ρ·g·h is on the hydrostatic-pressure page. There, ρ is an input. If you already know ρ and V, mass is m = ρ·V. This calculator goes the other way and has no field for a ready-made density.
The unit switch in the header changes mass to pounds and converts a number already entered in the mass field. It does not convert volume: volume stays in m³. Density stays in kg/m³. Figures in the text stay in SI as the reference. The button “Fill this example” enters the mass in the header unit and refreshes the panel and the chart. The fields start empty.
Formula
ρ = m / V
[ρ] = kg / m³; 1 g/cm³ = 1,000 kg/m³ = 1 kg/L
Model: the definition of density as mass per volume. No single author wrote ρ = m/V. Vitruvius describes comparing densities by the volume of water displaced, in the story of Archimedes. This calculator returns only ρ. Order of operations: mass in kilograms, volume in cubic meters, then the quotient.
Theory, units, and materials
Definition and the kilogram per cubic meter
The density of a uniform body is ρ = m/V. It is mass per volume, not a force and not a pressure. The SI unit kg/m³ follows from the kilogram and the meter. Those unit definitions are in the SI Brochure (BIPM, 9th edition). In the United States, NIST SP 330 is the guide to the SI. 1,000 kg/m³ is 1 g/cm³ and also 1 kg per liter, because 1 m³ = 1,000 L = 1,000,000 cm³.
For 1 kg and 0.001 m³ the path is short. Step 1: the mass is 1 kg. Step 2: the volume is 0.001 m³. Step 3: the quotient 1 / 0.001 = 1,000 kg/m³. The volume of one kilogram is then 1/ρ = 0.001 m³.
Archimedes and displaced water
In De architectura, Vitruvius tells that Archimedes compared a crown with a lump of gold of the same mass by the water each one displaced. That story is about equal volumes, and therefore about density, but it is not the algebraic line ρ = m/V. The calculator does not measure a water level and does not estimate the makeup of a crown. It uses the mass and the volume you enter.
School orders of magnitude for materials
The examples on this page are quotients of specific numbers, not a laboratory certificate. Water: 1 kg in 0.001 m³ gives 1,000 kg/m³. Ice: 0.92 kg in 0.001 m³ gives 920 kg/m³. Oil: 0.9 kg in 0.001 m³ gives 900 kg/m³. Air: 1.2 kg in 1 m³ gives 1.2 kg/m³, the order of dry air at room temperature. Wood: 0.6 kg in 0.001 m³ gives 600 kg/m³. Concrete: 2.4 kg in 0.001 m³ gives 2,400 kg/m³. Aluminum: 2.7 kg in 0.001 m³ gives 2,700 kg/m³. Steel: 7.8 kg in 0.001 m³ gives 7,800 kg/m³. Copper: 8.9 kg in 0.001 m³ gives 8,900 kg/m³. One gram of water in one cubic centimeter is 0.001 kg in 0.000001 m³ and is 1,000 kg/m³ again.
A real sample depends on composition, moisture, and temperature. Ordinary concrete is often in this 2,400 kg/m³ range, but lightweight concrete is clearly lighter and reinforced concrete is heavier. Tool steel and structural steel do not share one number either. The calculator does not open a materials table.
Specific weight, buoyancy, and pressure
Specific weight γ = ρ·g has the unit N/m³. At g = 9.81 m/s², water at 1,000 kg/m³ has a specific weight of about 9,810 N/m³. This form does not compute that product. Buoyant force and the pressure of a liquid column use density as an input. They are on separate pages. Specific gravity relative to water at 1,000 kg/m³ equals the number of g/cm³: concrete at 2.4 g/cm³ is 2.4 times as dense as that school value for water.
Sources
The definition and the unit come from textbooks and from metrology: D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, the chapter on density and pressure; H. D. Young and R. A. Freedman, University Physics, the chapter on fluids; Vitruvius, De architectura, the story of Archimedes; BIPM, SI Brochure, 9th edition; NIST Special Publication 330. This page is for educational purposes.
How to use
- Enter the mass in kilograms, for example 1 for a liter of water or 2.4 for a liter in the concrete range. After the header switches to US, the field accepts pounds.
- Enter the volume in cubic meters, for example 0.001. 1 L is 0.001. 1 cm³ is 0.000001. One hundred liters is 0.1.
- Click Calculate or wait for the live result. For 1 kg and 0.001 m³ the calculator shows 1,000 kg/m³.
- Check the panel: g/cm³, the volume of one kilogram, and the mass and volume used in the division. The chart is the curve ρ(V) at that mass.
- Clearing the form removes the numbers you entered and hides the panel. The examples enter mass and volume pairs for water, ice, oil, air, wood, concrete, aluminum, steel, and copper.
Symbol glossary
ρ is density, m is mass, and V is volume. For 1 kg and 0.001 m³ the result is 1,000 kg/m³.
- ρ
- Density [kg/m³], ρ = m/V. The panel also shows g/cm³.
- m
- Mass [kg]. Zero and a negative value are rejected. Pounds from the US header are converted to kilograms before the division.
- V
- Volume [m³]. 1 L = 0.001 m³. Zero and a negative value are rejected, because the calculator divides by V.
- g/cm³
- ρ / 1,000. In these units that same number is kilograms per liter and the specific gravity relative to water at 1,000 kg/m³.
- 1/ρ
- Volume of one kilogram [m³]. At 1,000 kg/m³ it is 0.001 m³.
- γ
- Specific weight ρ·g [N/m³]. This calculator does not compute it. Buoyancy and column pressure are on separate pages.
Material examples
Oil
Lighter than the school value for water: 0.9 kg in 0.001 m³. The quotient is 900 kg/m³. That is the order of many oils, not a certificate for a particular bottle.
ρ = 900 kg/m³
Air
Dry air at room temperature: 1.2 kg in 1 m³. The quotient is 1.2 kg/m³. Moisture and pressure change a real sample.
ρ = 1.2 kg/m³
Steel
School order for steel: 7.8 kg in 0.001 m³. The quotient is 7,800 kg/m³, or 7.8 g/cm³. The grade of steel moves that number.
ρ = 7,800 kg/m³
Wood
Order of dry wood, for example pine: 0.6 kg in 0.001 m³. The quotient is 600 kg/m³. Wet wood is heavier at the same volume.
ρ = 600 kg/m³
Ice
Lighter than water: 0.92 kg in 0.001 m³. The quotient is 920 kg/m³. That is why ice floats, but buoyancy is a different page.
ρ = 920 kg/m³
Concrete
School order for ordinary concrete: 2.4 kg in 0.001 m³. The quotient is 2,400 kg/m³, or 2.4 times water at 1,000 kg/m³. This is not a mix certificate.
ρ = 2,400 kg/m³
Copper
School order for copper: 8.9 kg in 0.001 m³. The quotient is 8,900 kg/m³. Pure copper in tables is often closer to 8,960 kg/m³.
ρ = 8,900 kg/m³
Aluminum
School order for aluminum: 2.7 kg in 0.001 m³. The quotient is 2,700 kg/m³. Aluminum alloys have a different density.
ρ = 2,700 kg/m³
One gram of water in 1 cm³
The same water as the first example, from one cubic centimeter: 0.001 kg in 0.000001 m³. The quotient is 1,000 kg/m³ again. A 1 in the volume field is not 1 cm³.
ρ = 1,000 kg/m³
Common questions
What does this calculator compute, and from which formula?
The calculator finds density from ρ = m/V. It divides mass in kilograms by volume in cubic meters. For 1 kg and 0.001 m³ the result is 1,000 kg/m³.
Which units should I enter for mass and volume?
Enter mass in kilograms and volume in cubic meters. The result is in kg/m³. After the header switches to US units, mass is in pounds and the calculator converts a number you already entered. Volume stays in m³, and density stays in kg/m³. A comma and a period are the same decimal separator.
How do liters and cubic centimeters convert to cubic meters?
1 L = 0.001 m³. One hundred liters is 0.1 m³. 250 ml is 0.00025 m³. 1 cm³ = 0.000001 m³. Enter cubic meters in the volume field. There is no separate field for liters or milliliters.
Does density depend on the acceleration g?
No. Density is the quotient m/V. The acceleration g enters hydrostatic pressure and buoyant force, not this quotient. Specific weight is ρ·g, a different quantity, in N/m³.
How is the result different from specific weight and from buoyancy?
Density is in kg/m³. Specific weight ρ·g is force per volume. Buoyant force F = ρ·V·g is on a separate page, and column pressure p = ρ·g·h is on the hydrostatic-pressure page. This calculator stays with m/V.
What do zero and a negative number mean?
Zero volume and a negative volume are rejected, because the calculator divides by V. Zero mass and a negative mass are rejected too. Both fields need a number greater than zero before the panel appears.
Can the calculator find mass from density and volume?
No. This form computes ρ from m and V. Mass from a known density is recovered with m = ρ·V, but there is no field for a ready-made density. The calculator does not look up a materials table.
What do the panel and the chart show?
The panel reports density in kg/m³, the same value in g/cm³, the volume of one kilogram 1/ρ, mass in kilograms, and volume in cubic meters. The g/cm³ number equals kilograms per liter. The chart draws ρ against V at constant mass. The button “Fill this example” enters the example numbers and refreshes the panel and the chart. The fields start empty.
Does 1,000 kg/m³ mean the sample is water?
No. That is what the numbers 1 kg and 0.001 m³ produce. Water in school problems is on the order of 1,000 kg/m³, and near 20 °C it is closer to 998 kg/m³. The calculator does not correct for temperature, salt, or porosity. The concrete example, 2.4 kg in 0.001 m³, gives 2,400 kg/m³ as an order for ordinary concrete, not as a mix certificate.
Are the material examples laboratory measurements?
No. They are school orders of magnitude entered as mass and volume: water 1,000, oil 900, air 1.2, steel 7,800, wood 600, ice 920, concrete 2,400, copper 8,900, and aluminum 2,700, all in kg/m³. One gram of water in 1 cm³ is 1,000 again. A real sample depends on composition, moisture, and temperature.
How do I calculate density with ρ = m/V?
Divide mass by volume in coherent SI units. For 1 kg and 0.001 m³: 1/0.001 = 1,000 kg/m³.
What is ρ for 1 kg in a volume of 0.001 m³?
1,000 kg/m³, or 1 g/cm³. That is the order of a liter of water under typical school conditions.
How do I convert g/cm³ to kg/m³?
Multiply by 1,000: 1 g/cm³ = 1,000 kg/m³. The panel shows both units next to the kg/m³ result.
Does oil at ρ = 900 kg/m³ float on water?
Comparing the numbers alone, 900 < 1,000, so the average density is lower than water. This calculator does not compute buoyancy F = ρVg or floating stability.
Does the result include gas temperature and pressure?
No. ρ = m/V is the quotient of the numbers you enter. For gases density depends strongly on T and p; there is no equation of state or temperature correction here.
Sources
The definition, the unit, and the historical note come from physics and metrology. This page does not invent publication identifiers.
- Wikipedia — Density
- BIPM — The International System of Units (SI), 9th edition
- NIST SP 330 — The International System of Units
- Halliday D., Resnick R., Walker J., Fundamentals of Physics, chapter on density.
- Young H. D., Freedman R. A., University Physics, chapter on fluids.
- Vitruvius, De architectura, the story of Archimedes and the crown.
Page updated November 3, 2026.