What is relative density of soil?

Relative density (Dr) expresses how compact a granular soil is relative to its loosest and densest possible states. A value of 0% means the soil is at its loosest (maximum void ratio), and 100% means it is at its densest (minimum void ratio). It is defined as Dr = (e_max − e) / (e_max − e_min) × 100%.

When can I use dry unit weight instead of void ratio?

You can use dry unit weight (γ_d) directly when void ratios are not available. The formula becomes Dr = [(1/γ_d_min − 1/γ_d) / (1/γ_d_min − 1/γ_d_max)] × 100%, which is mathematically equivalent to the void ratio formula since void ratio and dry unit weight are inversely related through specific gravity.

What Dr value is considered dense?

The standard Lambe & Whitman classification is: Dr 85% very dense. Dense and very dense soils have low compressibility and low liquefaction risk.

Why must e_max be greater than e_min?

By definition, e_max is the void ratio in the loosest (poured) state and e_min is the void ratio in the densest (vibrated) state. If the in-situ void ratio falls outside this range, the measurement or test data may be in error.

Does this apply to cohesive soils?

No. Relative density is only meaningful for cohesionless granular soils such as sands and gravels. For cohesive soils (clays, silts), use consistency index or liquidity index instead.

Relative Density of Soil Calculator

Name: Relative Density of Soil Calculator
Availability: InStock
Author: Nham Vu

Enter maximum, minimum, and in-situ void ratios (or dry unit weights) to compute the relative density and compaction state of granular soil.

Input Parameters

e_max — Maximum void ratio (loosest state)

e_min — Minimum void ratio (densest state)

e — In-situ void ratio (field sample)

Formulas

D_r = (e_max − e) / (e_max − e_min) × 100%

D_r = [(1/γ_d,min − 1/γ_d) / (1/γ_d,min − 1/γ_d,max)] × 100%

Enter values on the left and click Calculate

Relative Density

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D_r

0% 15% 35% 65% 85% 100%

Input Summary

Compaction Classification

D_r Range	State

Summary

Enter maximum, minimum, and in-situ void ratios (or dry unit weights) to compute the relative density and compaction state of granular soil.

How it works

Choose whether to input void ratios or dry unit weights using the mode toggle.
Enter the maximum (loosest state) and minimum (densest state) values for the soil.
Enter the in-situ (field) value measured from the soil sample.
Click Calculate to get the relative density percentage and compaction classification.
Switch modes to cross-check results using the alternate input method.

Use cases

Classify granular soil as loose, medium, or dense for foundation design.
Assess compaction quality of sandy fill during construction QC.
Estimate liquefaction susceptibility from in-situ void ratio data.
Convert between void ratio and dry unit weight forms of Dr for lab reports.
Check whether a granular layer meets the compaction spec for a project.
Verify SPT-N correlation inputs by computing Dr independently.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu