Density Calculator

About the Density Calculator

Density is how much mass fits in a given volume: ρ = m ÷ V. This calculator solves for any one of density, mass or volume and converts between kg/m³, g/cm³ (the same as g/mL and kg/L), g/L, lb/ft³, lb/in³ and pounds per gallon. If you do not know the volume, it works it out from the shape and its measurements (box, cylinder, tube, sphere, cone, pyramid and more) or from the rise of the water level in a measuring cylinder.

With the density it gives the specific gravity against water at 4 °C or another reference temperature, the closest materials in a table of about 140 sourced densities, and a float or sink check in fresh water, seawater, air, any listed liquid or your own fluid — with the share of the object that would sit under the surface. A separate panel gives the density of water at any temperature from 0 °C to boiling.

Common uses

• School and college lab work: finding the density of a sample and identifying the material.
• Working out the weight of a part, a tank of liquid or a load from its volume and material.
• Checking whether a boat, buoy, float or packaging foam will float, and how deep it sits.
• Correcting volumetric measurements for the density of water at the lab temperature.
• Converting densities between metric and US units for specifications and data sheets.

The formulas

• Density: ρ = m ÷ V; so m = ρ × V and V = m ÷ ρ. 1 g/cm³ = 1 g/mL = 1 kg/L = 1,000 kg/m³ = 62.43 lb/ft³.
• Volumes: box l × w × h; cylinder π r² h; tube π (R² − r²) h; sphere 4/3 π r³; hemisphere 2/3 π r³; cone 1/3 π r² h; pyramid 1/3 l × w × h; triangular prism ½ b t L. A diameter is halved to get the radius.
• Displacement: a sunken object pushes aside its own volume of water, so V = level after − level before.
• Specific gravity: SG = ρ ÷ ρ_water. Against water at 4 °C (999.975 kg/m³) it equals the density in g/cm³ to within 0.003 %.
• Floating: an object floats when its average density is less than the fluid’s; the fraction below the surface is ρ_object ÷ ρ_fluid (Archimedes’ principle). A sinking object weighs less in the fluid by the factor 1 − ρ_fluid ÷ ρ_object.

Density of water by temperature

Water is densest at 3.98 °C (999.975 kg/m³) and gets lighter both above and below: 999.843 kg/m³ at 0 °C, 998.207 at 20 °C, 993.33 at 37 °C, 983.21 at 60 °C and 958.37 at the boiling point (99.97 °C at 101.325 kPa). From 0 to 40 °C the values come from the formula recommended by Tanaka et al. (2001) for pure, air-free water at standard atmospheric pressure; from 40 °C to boiling from the IAPWS-IF97 formulation (the two agree to 0.01 kg/m³ at 40 °C). Seawater uses the one-atmosphere international equation of state EOS-80: at salinity 35 it is 1,028.1 kg/m³ at 0 °C and 1,023.3 kg/m³ at 25 °C. Air is treated as an ideal gas at 101.325 kPa.

Where the material densities come from

Every value in the table names its source and its conditions:

• OpenStax, University Physics Vol. 1, Tables 14.1 and 14.2 — everyday solids and liquids at 0 °C (brass, cork, glass, granite, oak, pine, petrol, ethanol, glycerin, olive oil, ice) and gases at 0 °C and 101.3 kPa.
• NIST Standard Reference Database 126 (X-ray attenuation), Table 2 — plastics (PE, PET, acrylic, polystyrene, PTFE, PVC), concretes, glasses, crystals and body tissues.
• PubChem Periodic Table (NCBI) — 96 elements, solids and liquids near room temperature and gases at 0 °C and 1 atm.
• Water, seawater and steam are calculated with the formulas above.

Real samples vary: alloys, woods, rocks, soils and foods can differ by several per cent (or much more) from a table value, so treat the closest match as a hint, not an identification.

Sources

• OpenStax, University Physics Volume 1 (CC BY 4.0): §14.1 Fluids, Density, and Pressure (Eq. 14.1, Tables 14.1–14.2, specific gravity) and §14.4 Archimedes’ Principle and Buoyancy (fraction submerged, Example 14.4).
• M. Tanaka, G. Girard, R. Davis, A. Peuto and N. Bignell, “Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports”, Metrologia 38 (2001) 301–309, doi:10.1088/0026-1394/38/4/3.
• IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97).
• UNESCO (1981), one-atmosphere international equation of state of seawater (EOS-80; Millero and Poisson 1981), with UNESCO (1983) check values.
• NIST, X-Ray Mass Attenuation Coefficients, Table 2 (SRD 126).
• PubChem Periodic Table (NCBI, public domain).
• NIST, SP 811 Appendix B.8 conversion factors.

Limitations

• The result is the average density of the whole object: a hollow ball or a boat can float even if it is made of a dense material.
• Displacement needs the object to sink fully and not soak up water; read the meniscus at eye level.
• Water values are for pure water at standard atmospheric pressure; tap water, salt solutions and water under pressure differ slightly.
• Densities of gases depend strongly on temperature and pressure; the table gives each value’s conditions.
• Shapes are ideal (sharp edges, exact circles); measure real objects carefully, since a small error in a diameter is doubled in the volume.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.