Learn: Relative density
Relative density locates a granular soil between its loosest and densest reference states. It compares void ratios, not the soil’s mass density directly.
What the formula is saying
The available change from loosest to densest is emax − emin. The amount already achieved is emax − e. Dividing achieved change by the full interval and multiplying by 100 gives relative density.
Read the symbols in plain language
- emax
- Maximum void ratio
Maximum void ratio. Subtract the current void ratio from the loose-state reference value.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- e
- Current void ratio
Void volume divided by solid volume, not total volume. This ratio may exceed one.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- emin
- Minimum void ratio
Minimum void ratio. The loose-to-dense interval must be positive to define a meaningful relative position.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- Dr
- Result to find
Relative density. Express the achieved fraction of densification as a percentage.
%
Sort out the units first
All three void ratios are dimensionless and the output is percent. Do not substitute porosities or densities into a formula explicitly written in terms of void ratios.
Assumptions before calculating
The limiting void ratios are representative laboratory reference values for the same granular material and test convention. Require emax > emin ≥ 0 and emin ≤ e ≤ emax.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find Dr and explain the result in the stated output unit.
- emax · Maximum void ratio
- 0.9
- e · Current void ratio
- 0.6
- emin · Minimum void ratio
- 0.5
Find reduction from the loosest void ratio
Subtract the current void ratio from the loose-state reference value.
(0.9)-(0.6) = 0.3Find the full reference interval
The loose-to-dense interval must be positive to define a meaningful relative position.
(0.9)-(0.5) = 0.4Locate the sample within the interval
Express the achieved fraction of densification as a percentage.
(0.3) ÷ (0.4) × 100 = 75 %
Does this worked answer make sense?
At e = emax the result is 0%; at e = emin it is 100%. Densifying the sample lowers e and raises the relative-density percentage.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- emax · Maximum void ratio
- 1
- e · Current void ratio
- 0.75
- emin · Minimum void ratio
- 0.5
Find reduction from the loosest void ratio
Subtract the current void ratio from the loose-state reference value.
(1)-(0.75) = 0.25Find the full reference interval
The loose-to-dense interval must be positive to define a meaningful relative position.
(1)-(0.5) = 0.5Locate the sample within the interval
Express the achieved fraction of densification as a percentage.
(0.25) ÷ (0.5) × 100 = 50 %
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- emax · Maximum void ratio
- 0.85
- e · Current void ratio
- 0.65
- emin · Minimum void ratio
- 0.45
Find: Learn: Relative density
A hint, not the answer
The available change from loosest to densest is emax − emin. The amount already achieved is emax − e. Dividing achieved change by the full interval and multiplying by 100 gives relative density.
All three void ratios are dimensionless and the output is percent. Do not substitute porosities or densities into a formula explicitly written in terms of void ratios.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find reduction from the loosest void ratio
Subtract the current void ratio from the loose-state reference value.
(0.85)-(0.65) = 0.2Find the full reference interval
The loose-to-dense interval must be positive to define a meaningful relative position.
(0.85)-(0.45) = 0.4Locate the sample within the interval
Express the achieved fraction of densification as a percentage.
(0.2) ÷ (0.4) × 100 = 50 %
Avoid the common trap
Do not reverse emax and emin. Do not place e − emin in the numerator, which measures the opposite progression, or confuse relative density with relative compaction.
When this method applies — and when it does not
This index is mainly meaningful for applicable granular soils and is not a universal strength or compaction acceptance measure. Different reference procedures or particle crushing can change the limiting states.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Relative density. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.