Alloy Density Calculator
The density of an alloy can be estimated from the densities and mass fractions of its constituent elements using the inverse rule of mixtures: 1/rho_alloy = w1/rho1 + w2/rho2, where w1 and w2 are mass fractions summing to 1.0. This calculator handles up to three components. For a steel alloy (Fe 97%, Cr 2%, Mo 1%): 1/rho = 0.97/7874 + 0.02/7190 + 0.01/10280. Solving: rho = 1 / (0.0001232 + 0.0000028 + 0.0000010) = 7,809 kg/m^3. Enter element densities and mass fractions (as decimals summing to 1.0) to compute alloy density.
Alloy density formula
1 / rho_alloy = w1/rho1 + w2/rho2 + w3/rho3
rho_alloy = 1 / (w1/rho1 + w2/rho2 + w3/rho3)
Where rho_i is the density of component i (kg/m^3) and w_i is its mass fraction (dimensionless, all fractions summing to 1.0). This is the volumetric inverse rule of mixtures, which correctly weights density contributions by volume.
Common element reference densities
Aluminum (Al): 2,700 kg/m^3. Iron (Fe): 7,874 kg/m^3. Nickel (Ni): 8,908 kg/m^3. Chromium (Cr): 7,190 kg/m^3. Cobalt (Co): 8,900 kg/m^3. Titanium (Ti): 4,506 kg/m^3. Copper (Cu): 8,960 kg/m^3. Molybdenum (Mo): 10,280 kg/m^3. Tungsten (W): 19,300 kg/m^3. Carbon (C): 2,267 kg/m^3. Source: NIST and ASM International materials databases.
Alloy density: frequently asked questions
How is alloy density estimated from constituent densities?
The rule of mixtures for density uses mass fractions: 1/rho_alloy = sum(w_i / rho_i), where w_i is the mass fraction of component i and rho_i is its density. This is the volumetric (inverse) rule of mixtures, which is more accurate than the simple linear rule for density because volume fractions control density.
Why use the inverse rule instead of simple weighted average?
Density depends on volume, not mass. The inverse rule 1/rho = w1/rho1 + w2/rho2 correctly converts mass fractions to volume-weighted contributions. The simple weighted average (rho = w1*rho1 + w2*rho2) gives an overestimate when components have similar density, but can be significantly wrong for dissimilar elements.
What are the densities of common alloying elements?
Iron: 7,874 kg/m^3. Nickel: 8,908 kg/m^3. Chromium: 7,190 kg/m^3. Molybdenum: 10,280 kg/m^3. Aluminum: 2,700 kg/m^3. Titanium: 4,506 kg/m^3. Carbon: 2,267 kg/m^3. These are room-temperature values from NIST and ASM databases.
Does the rule of mixtures account for volume change on mixing?
No. The rule of mixtures assumes ideal mixing with no volume change. In reality, alloy formation causes small volume changes (excess volume of mixing). For most engineering alloys, the deviation is less than 1 to 2 percent and is acceptable for most design purposes.
How accurate is this density estimate?
The inverse rule of mixtures typically gives density estimates within 1 to 3 percent of measured values for metal alloys. For greater accuracy, use measured density data from materials handbooks or standards, especially for compositions outside normal commercial ranges.
Official sources
- NIST, "NIST Standard Reference Database 64 - Element Densities": nist.gov.
- ASM International, "ASM Handbook Vol. 2: Properties and Selection: Nonferrous Alloys": asminternational.org.
- ASTM B311, "Standard Test Method for Density of Powder Metallurgy Products": astm.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.