Relative density Dr and density index Id are not the same number

Updated: September 15, 2026 · ISKRIT

Dr and Id are routinely treated as synonyms. They are not. One is defined on void ratios, the other on densities, and Dr is always the larger of the two.

The two definitions

Relative density works on void ratios:

Dr = (e max − e) / (e max − e min)

Density index works linearly on dry densities:

Id = (ρd − ρd min) / (ρd max − ρd min)

Substituting e = ρs/ρd − 1 into the first expression collapses the particle density out of it and leaves:

Dr = Id · ρd max / ρd

Since ρd max is by construction at least ρd, the ratio is at least one and Dr ≥ Id always holds. Equality only occurs when the soil is already at its maximum index density.

Calculator

Both definitions side by side from the same three densities.

How large is the gap

The multiplier is ρd max/ρd, so the difference grows as the soil gets looser. At Id = 0.30 with ρd max/ρd = 1.15 the relative density is 0.345, four and a half points higher. In the medium-dense band a five-point shift can move a result across the 65 % line that separates “medium dense” from “dense”, and that line is what acceptance criteria are written against.

Which one does the specification mean

ASTM D4254 defines both terms explicitly and separately: relative density in clause 3.2.9, density index in 3.2.8. EN ISO 14688-2 uses “density index ID” for what ASTM calls relative density, on void ratios. Russian GOST 25100 uses the symbol ID for the same void-ratio quantity. So the symbol travels between standards attached to different formulas, and reading the symbol alone is not enough.

The practical rule: if the document defines the quantity through e max and e min, it wants the void-ratio form regardless of which letter it prints.

Questions

Why does the linear form exist at all? It needs only three densities and no particle density measurement, which makes it cheap for field control.

Can I convert an old Id report to Dr? Yes, if the report also gives the in-place dry density and the maximum index density, since the conversion factor is just their ratio.

Both quantities are reported side by side, from the same input, in the relative density calculator.