Calculate volume-weighted mixture density or the mean and sample standard deviation of repeated density measurements.

Assumes component volumes are additive. Actual mixing can change volume.

Third component

Average Density Formula

The following formula is used to calculate the average density of a collection of objects.

D = (D1 × V1 + D2 × V2 + DX × VX) / (V1 + V2 + VX)
  • Where D is the average density of the mixture
  • D1,D2,DX are the densities of the individual substances
  • V1,V2,VX are the volumes of each substance in the mixture.

Average Density Definition

An average density is defined as the total mass per unit of volume of a mixture of 2 or more substances. In the case of the formula above, this is for a mixture with different quantities of each compound.

Mean Density from Repeated Trials

Select Mean of density trials for 2–20 positive measurements of the same material under comparable conditions. Enter one unit for the whole list. Every trial has equal weight; the result also reports sample standard deviation, count, minimum and maximum.

Mean density = Σdᵢ / n. Sample standard deviation s = √[Σ(dᵢ − mean)² / (n − 1)]. Here dᵢ is a measured density and n is the number of trials. The NIST definition of the mean and sample standard deviation describe these calculations. Standard deviation uses the same unit as density and describes trial-to-trial scatter, not the uncertainty of the mean.

For measurements of 0.998, 1.002 and 1.000 g/mL, the mean is 1.000 g/mL and the sample standard deviation is 0.002 g/mL. This is different from combining materials: a mixture uses total mass divided by final volume. The component formula above is volume-weighted and assumes additive volumes. An arithmetic average of component densities is generally not the mixture density.

Example Problem

How to calculate the average density of a mixture?

  1. First, determine the densities of each compound.

    For this example, there are 3 compounds with densities of 10 g/L, 5 g/L, and 2 g/L respectively.

  2. Next, determine the volumes of each substance.

    In this problem, the volumes are measured to be 2 L, 5 L, and 1 L respectively.

  3. Finally, calculate the average density of the mixture.

    Using the formula above, the average density is calculated as (10*2+5*5+2*1) / (2+5+1) = 5.875 g/L.

FAQ

How do you calculate an average density of a mixture?

Calculating the average density of a mixture is done by multiplying the densities of each compound by the volume of the respective compound, then dividing the result by the sum of all of the volumes.

What is the SI unit of density?

The SI unit of density is kg/m³. Another common unit is g/cm³; 1 cm³ equals 1 mL. The weighted-mixture formula assumes additive component volumes.