Relative Density Calculator: From Void Ratio to Dr

Void ratio alone does not say much about how dense a granular soil is, since the same void ratio can be loose for one sand and dense for another depending on grain shape and gradation. Relative density fixes this by comparing the in-situ void ratio against the loosest and densest states the same soil can reach in standard laboratory tests, giving a packing description that is comparable across different sands and gravels.

The relative density formula

Dr = [(emax minus e) / (emax minus emin)] x 100%

Here emax is the void ratio at the loosest state achievable in a standard test (ASTM D4254), emin is the void ratio at the densest state achievable (ASTM D4253), and e is the actual in-situ void ratio. Dr = 0% represents the loosest possible packing and Dr = 100% represents the densest.

Finding void ratio from unit weight

When void ratio is not measured directly, it can be back-calculated from a field dry unit weight test and the specific gravity of the soil solids:

e = (Gs x gamma_water / gamma_dry) minus 1

Porosity, the more commonly reported quantity in some fields, converts directly from void ratio: n = e / (1 + e).

Density classification

• Dr under 15%: very loose
• 15 to 35%: loose
• 35 to 65%: medium dense
• 65 to 85%: dense
• 85 to 100%: very dense

Worked example

A sand has emax = 0.90 and emin = 0.40 from lab testing, and an in-situ void ratio of 0.65.

1. Dr = [(0.90 minus 0.65) / (0.90 minus 0.40)] x 100 = (0.25 / 0.50) x 100 = 50%
2. Porosity, n = 0.65 / 1.65 = 0.394
3. Dr = 50% classifies as medium dense

These are the exact numbers the calculator returns when you click Load Example, confirming the tool matches a hand calculation before applying it to real lab or field data.

Why this matters

Relative density is a key input to correlations for friction angle, liquefaction susceptibility, and settlement behavior of sands and gravels, all of which depend far more on how densely the grains are packed than on void ratio alone. It is also a common compaction specification target for engineered fill, where contractors are required to achieve a minimum relative density rather than a specific void ratio, since the target adjusts automatically for the particular material being placed.

Something to watch for: emax and emin are notoriously sensitive to how carefully the lab test was run, and two labs testing the same sand can report noticeably different values depending on compaction and pouring technique. Because relative density is a ratio between those two numbers, a small lab inconsistency can shift the calculated Dr by more than it would shift either void ratio on its own. When the classification sits close to a boundary, like the line between medium dense and dense, it is worth treating the result as an estimate rather than an exact figure.

Related Calculator and Reference

For correcting field SPT blow counts, which are commonly correlated to relative density, see the SPT N-Value Corrections Calculator. For the standard test methods behind emax and emin, see the ASTM D4254 reference on minimum index density.