Calculate saturated unit weight of soil from specific gravity and void ratio, with dry and submerged unit weight, or solve for void ratio, Gs or porosity.

Typical value 2.65 for sands; clays are often 2.7โ€“2.8. Replace with your measured value.

Voids volume รท solids volume. Typical values: dense sand โ‰ˆ 0.4โ€“0.6, loose sand โ‰ˆ 0.7โ€“0.9, soft clay โ‰ˆ 1 or more.

Standard value 9.81 kN/mยณ (62.4 lbf/ftยณ). Results use this field’s unit.

Optional saturated layer
Blank omits it. A depth gives this uniform layer’s total stress, not effective stress.

Saturated Unit Weight (ฮณsat) / Saturated Bulk Density (ฯsat) Formula

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

ฯsat = (md+mw) / (V)
ฮณsat = ฯsat g
ฮณsat = ฮณw(Gs+e) / (1+e)

The last relationship assumes full saturation (water-filled voids). It is the phase relationship used by this calculator; the mass/volume relationship is separate reference context.

Variables:

  • ฯsat is the saturated bulk density (mass/volume), e.g., g/cmยณ or kg/mยณ
  • ฮณsat is saturated unit weight (force/volume), in kN/mยณ, N/mยณ or lbf/ftยณ. The customary force unit is pound-force; it is not the mass-density unit lb/ftยณ.
  • 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., cmยณ or mยณ)
  • g is standard gravity (9.80665 m/sยฒ)
  • ฮณw 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)

For the separate mass/volume relationship, add dry-soil and water masses and divide by total specimen volume. Multiply mass density by g to obtain unit weight in consistent units. The calculator above takes Gs, e and unit weights; it has no mass/volume input mode. Selecting a unit converts a force-per-volume quantity, not a mass density. The starting Gs = 2.65 and water weight = 9.81 kN/mยณ are typical values, not universal soil properties; enter your soil's void ratio.

How to Calculate Saturated Unit Weight of Soil?

The following steps outline how to calculate saturated bulk density (ฯsat) and saturated unit weight (ฮณsat).

  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 ฯsat = (md + mw) / V.
  5. If you need unit weight, compute ฮณsat = ฯsatยทg (or use the Gsโ€“e relationship shown above for saturated soils).
  6. These steps describe the mass/volume method. To use the calculator, supply the matching saturated phase values instead. For inverse void ratio or porosity, equal saturated and water unit weights give no finite solution when Gs differs from 1, and no unique solution when Gs = 1. Near-equal valid values are not rejected merely for being close. Nonnegative e implies 0 โ‰ค n < 1; a rounded percentage near 100% is identified as approximate. Gs below 1 retains a negative buoyant unit weight, while saturated water content e/Gs may exceed 100%. Optional layer stress is ฮณsat times depth, excluding other layers and pore-pressure subtraction. These relationships follow the FHWA saturated phase relations.

Example Problem:

This separate mass/volume example illustrates density and unit weight; its masses and volume are not direct input fields in the calculator above. The gravity value below is standard gravity, while the calculator uses your entered water unit weight. Force conversions use 1 ft = 0.3048 m and 1 lbf = 4.4482216152605 N; repeating native unit conversions are rounded to 30 significant digits and calculations then use the shown number.

mass of dry soil (g) = 1500

mass of water (moisture) (g) = 300

total volume of saturated (wet) soil (cm3) = 1000

ฯsat = (md + mw) / V = (1500 + 300) / 1000 = 1.8 g/cmยณ (ฮณsat โ‰ˆ 1.8 ร— 9.80665 = 17.65 kN/mยณ)