Void Ratio, Porosity, and Unit Weight Converter: Making Sense of Soil Phase Relationships

Geotechnical reports throw a lot of overlapping terms at you. One table lists void ratio, the next talks about porosity, a soil boring log gives moisture content, and a bearing capacity calculation somewhere down the page wants dry unit weight and saturated unit weight both. They’re all describing the same handful of physical facts about a soil sample, just through different lenses, and converting between them by hand means juggling several formulas that are easy to mix up under deadline pressure.

I built this calculator to do that conversion properly. Give it a specific gravity and one void parameter, either void ratio or porosity, add a water content or degree of saturation if you have one, and it solves the full phase relationship at once: void ratio, porosity, saturation, water content, and all four common unit weights. It also draws a phase diagram and a unit weight comparison chart right in the results, and you can download the whole thing as a PDF report to keep with your project files.

The Three-Phase Model, in Plain Terms

Soil is never just solid particles. Every real sample is some mix of solid grains, water filling part of the space between them, and air filling whatever’s left. Geotechnical engineers call this the three-phase model, and pretty much every formula on this page comes from carefully bookkeeping the volumes and weights of those three phases.

Void ratio (e) is the volume of voids divided by the volume of solids. It’s a ratio of empty space to solid material, and it can technically run higher than 1 for very loose or organic soils, where there’s more void space than actual solid grain.

Porosity (n) is the volume of voids divided by the total volume, solids and voids combined. It’s always less than 1 (or under 100%), since it’s a fraction of the whole sample rather than a ratio against just the solids.

These two describe the same underlying fact, how much empty space is in the soil, just normalized differently, and they convert into each other cleanly: porosity equals void ratio divided by (1 plus void ratio), and void ratio equals porosity divided by (1 minus porosity).

Bringing Water Into the Picture

Once you know void ratio, adding water content or degree of saturation completes the picture.

Water content (w) is the weight of water in the sample divided by the weight of the dry solids, usually expressed as a percentage. It’s the most commonly reported moisture value in a lab report, since it comes directly from a simple oven drying test.

Degree of saturation (S) is the volume of water divided by the total volume of voids, also as a percentage. A degree of saturation of 100% means every void is completely full of water, no air pockets remain, which is exactly the condition assumed for saturated unit weight calculations.

These two connect through a genuinely elegant little formula: degree of saturation times void ratio equals water content times specific gravity of solids. Know any three of those four values, Gs, e, w, or S, and the fourth follows immediately. This is the exact relationship the calculator uses to fill in whichever moisture parameter you didn’t directly provide.

The Four Unit Weights, and Why You Need All of Them

This is where a lot of confusion happens in practice, since a soil doesn’t have just one unit weight, it has several, depending on the moisture condition you’re evaluating.

Dry unit weight (gamma d) describes the soil with all the water removed, just solids and air. It’s the reference value used constantly in compaction specifications and proctor testing, since compaction requirements are almost always expressed as a percentage of maximum dry unit weight.

Moist unit weight (gamma), sometimes called bulk unit weight, reflects the soil at whatever water content it actually has in the field, somewhere between fully dry and fully saturated. This is often the most realistic value for everyday load calculations, since soil in the ground is rarely perfectly dry.

Saturated unit weight (gamma sat) assumes every void is filled with water, the maximum possible water content for that void ratio. This matters most for soils below the water table, or for worst case scenarios in slope stability and settlement analysis.

Submerged, or buoyant, unit weight (gamma prime) is the effective weight of the soil when it’s sitting underwater, accounting for the buoyant uplift of the surrounding water. It’s simply saturated unit weight minus the unit weight of water, and it’s essential for any calculation involving soil below a water table, since ignoring buoyancy there significantly overstates the effective stress.

A Worked Example

Say you’ve got a sand sample with a specific gravity of 2.65 and a void ratio of 0.60, and lab testing shows a water content of 15%.

Porosity: 0.60 divided by (1 plus 0.60), which comes out to 0.375, or 37.5%.

Degree of saturation: using S times e equals w times Gs, rearranged to S equals (w times Gs) divided by e. That’s (0.15 times 2.65) divided by 0.60, which works out to about 0.6625, or 66.25%, meaning roughly two thirds of the void space is filled with water.

Dry unit weight: Gs times unit weight of water, divided by (1 plus e). Using 9.81 kN/m3 for water, that’s (2.65 times 9.81) divided by 1.60, giving about 16.25 kN/m3.

Moist unit weight: dry unit weight times (1 plus w), so 16.25 times 1.15, giving about 18.69 kN/m3.

Saturated unit weight: (Gs plus e) times unit weight of water, divided by (1 plus e), which is (2.65 plus 0.60) times 9.81, divided by 1.60, giving about 19.93 kN/m3.

Submerged unit weight: saturated unit weight minus the unit weight of water, 19.93 minus 9.81, giving about 10.12 kN/m3.

Notice how much lower the submerged value is compared to the others. That difference is exactly why forgetting buoyancy in a below water table calculation leads to a meaningfully wrong answer.

Common Mistakes

Using saturated unit weight for a soil that clearly isn’t saturated in the field, inflating the effective load or settlement estimate.

Forgetting to subtract buoyant uplift for soil sitting below the water table, which overstates effective stress and can throw off a slope stability or bearing capacity calculation significantly.

Mixing up void ratio and porosity in a formula, since they look similar but aren’t interchangeable without the conversion step.

Assuming a textbook Gs value without checking whether the soil in question is organic or unusually mineral rich, both of which shift specific gravity meaningfully away from the common 2.65 to 2.70 range.

Who Uses This

Geotechnical engineers and lab technicians converting between phase relationship values reported in different formats across a project.

Students working through soil mechanics problem sets and wanting to check their formula application against a known method.

Construction quality control staff comparing field density test results against specified dry unit weight targets.

Anyone reviewing a geotechnical report who wants to sanity check that the reported saturated and submerged unit weights are internally consistent with the stated void ratio and specific gravity.

Try It Above

Enter your specific gravity and whichever void parameter you know, add a water content or saturation value if you have one, and get the complete phase relationship at once, along with a visual phase diagram and unit weight comparison chart. Use the PDF download to keep a clean record of the calculation with your project files.

Related Calculators and Reference

• Porosity and Void Ratio Relations, for the relations behind the conversion rather than the arithmetic.
• USCS Soil Classification Tool, to classify the soil these values describe.
• Terzaghi Bearing Capacity Calculator for Shallow Foundations, once the unit weight is settled and bearing capacity is next.
• Sieve Analysis and Gradation Test, for the gradation test that produces the input data.
• ASTM D2487, the standard practice for classifying the soils these values belong to.