Bulk Density Formula: ρ_b = m/V_total, Porosity, Examples

The bulk density formula is $\rho_b = \frac{m_{dry}}{V_{total}}$ : the dry mass of a loose or porous material divided by the whole volume it fills, air gaps and all. It is the density of a heap, a bag or a block of soil, not of the individual grains inside it.

Ordinary density uses only the volume of solid matter. Bulk density spreads the same mass over a bigger volume, so it is always lower for anything with pores. Soil scientists, civil engineers, farmers and powder chemists all rely on it, and it is listed with the other matter results on our fluids and matter sheet.

Quick facts

Formula
$\rho_b = \frac{m_{dry}}{V_{total}}$
SI unit
kg/m³; soil reports use g/cm³ (1 g/cm³ = 1000 kg/m³)
Dimensional formula
[M¹ L⁻³ T⁰]
Porosity link
$n = 1 - \frac{\rho_b}{\rho_s}$
Typical soil
about 1.1 to 1.7 g/cm³
Compare
always less than or equal to the particle density

Parts of the formula of bulk density

Terms in ρ_b = m_dry / V_total
Symbol	What it means	SI unit
$\rho_b$	Bulk density of the sample	kg/m³
$m_{dry}$	Mass after drying, so water in the pores is not counted	kg
$V_{total}$	Volume of the container or core the sample fills	m³

Drying matters for soil. A wet sample carries extra mass from water, which would make the figure look higher than the soil really is. The usual method is to oven dry the core at about 105 °C until its mass stops changing. For grain, cement or sand in a bin, the material is already dry and the mass can be weighed directly.

How to use the bulk density formula in practice

Fill a known volume. Drive a metal ring of known size into the soil, or fill a measuring container level with the powder or grain without pressing it down.
Dry and weigh the contents to get m_dry.
Divide mass by the container volume.
State the unit. Soil and powder reports usually give g/cm³; physics answers use kg/m³.

The calculator above takes SI values. If you work in grams and cubic centimetres, the number you get in g/cm³ is one thousandth of the kg/m³ value.

Worked examples

Example 1: a soil core

A steel ring of volume 300 cm³ is filled with soil. After oven drying the soil has a mass of 400 g. Find the bulk density.

$\rho_b = \frac{400\ \text{g}}{300\ \text{cm}^3} = 1.33\ \text{g/cm}^3 = 1330\ \text{kg/m}^3$

Example 2: porosity from bulk density

The mineral grains in the same soil have a particle density of 2.65 g/cm³. What fraction of the soil volume is pore space?

$n = 1 - \frac{\rho_b}{\rho_s} = 1 - \frac{1.333}{2.65} = 1 - 0.503 = 0.497$

Almost half the volume, about 50 percent, is air and water space between the grains.

Example 3: mass of a sand load

Dry sand has a bulk density of 1600 kg/m³. What mass of sand fills a 5.0 m³ truck bed?

$m = \rho_b V = 1600 \times 5.0 = 8.0 \times 10^3\ \text{kg}$

That is 8.0 tonnes. Using the density of quartz grains (about 2650 kg/m³) instead would overestimate the load by two thirds.

For loose solids, the total volume includes every gap. A container filled level is the volume to use.

Bulk density versus particle density and tapped density

Three densities of a granular material
Quantity	Volume used	Typical use
Particle (true) density	solid grains only	mineral identification
Bulk density	grains plus loose gaps	soil health, storage bins
Tapped density	grains plus gaps after tapping	powder flow in pharmacy

Tapping or vibrating a powder settles the grains, shrinks the volume and raises the density. That settled value is covered on the tapped density formula page. Comparing a bulk value with water gives a relative density, useful for judging whether a material will float.

Mistakes with bulk density

Using wet mass. Always dry soil first unless the question says otherwise.
Using the grain volume. That gives particle density, not bulk density.
Packing the sample. Pressing powder into a cylinder changes the result; fill it loosely.
Unit slips. 1 g/cm³ is 1000 kg/m³, not 100.

High bulk density in farm soil often signals compaction, which makes it harder for roots and water to move through.

Frequently asked questions

What is the formula of bulk density?

Bulk density = dry mass ÷ total volume, ρ_b = m_dry / V_total. The total volume includes the spaces between particles.

Which unit is used for bulk density?

The SI unit is kg/m³. Soil and powder data usually appear in g/cm³; multiply by 1000 to get kg/m³.

Why is bulk density lower than particle density?

The same mass is divided by a larger volume, because bulk volume includes air and water filled pores while particle volume counts only solid grains.

How do you find porosity from bulk density?

Porosity n = 1 − ρ_b / ρ_s, where ρ_s is the particle density. A soil with ρ_b = 1.33 g/cm³ and ρ_s = 2.65 g/cm³ has a porosity close to 0.50.