Enter the mass of dry soil, the mass of water (moisture) in the specimen, and the total volume of the saturated (wet) soil into the Saturated Unit Weight of Soil Calculator. The calculator computes the saturated bulk density (ρsat) and, when you select kN/m³, it reports the corresponding saturated unit weight (γsat = ρsat·g).

Saturated Unit Weight (γsat) / Saturated Density (ρsat) Calculator

By Masses & Volume
Submerged Unit Weight
From Gs and e/n
From Gs and w (sat.)

Enter any 3 values to calculate the missing variable (mass units give ρsat; select kN/m³ to view γsat = ρsat·g)

Saturated Unit Weight (γsat) / Saturated Bulk Density (ρsat) Formula

The following formulas are used to calculate saturated bulk density and saturated unit weight of soil.

\rho_{sat} = \frac{m_d + m_w}{V}
\qquad
\gamma_{sat} = \rho_{sat}\, g
\qquad
\gamma_{sat} = \gamma_w\frac{G_s + e}{1+e}\; (S=1)

Variables:

  • ρsat is the saturated bulk density (mass/volume), e.g., g/cm³ or kg/m³
  • γsat is the saturated unit weight (force/volume), e.g., kN/m³ (and commonly written as lb/ft³ in US practice)
  • md is the mass of dry soil (e.g., g or kg)
  • mw is the mass of water in the saturated specimen (e.g., g or kg)
  • V is the total volume of the saturated (wet) soil specimen (e.g., cm³ or m³)
  • g is standard gravity (9.80665 m/s²)
  • γw is the unit weight of water, Gs is specific gravity of solids, and e is void ratio (the last equation applies for saturated soil, S = 1)

To calculate saturated bulk density, sum the mass of dry soil and the mass of water in the saturated specimen, then divide by the specimen volume. To convert bulk density to saturated unit weight, multiply by g (or select kN/m³ in the calculator).

How to Calculate Saturated Unit Weight of Soil?

The following steps outline how to calculate saturated bulk density (ρsat) and saturated unit weight (γsat).

  1. First, measure the mass of dry soil, md.
  2. Next, measure the mass of water in the saturated specimen, mw. 
  3. Next, determine the total volume of the saturated (wet) soil specimen, V. 
  4. Next, use ρsat = (md + mw) / V.
  5. If you need unit weight, compute γsat = ρsat·g (or use the Gs–e relationship shown above for saturated soils).
  6. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

mass of dry soil (g) = 1500

mass of water (moisture) (g) = 300

total volume of saturated (wet) soil (cm^3) = 1000

ρsat = (md + mw) / V = (1500 + 300) / 1000 = 1.8 g/cm³ (γsat ≈ 1.8 × 9.80665 = 17.65 kN/m³)