Enter the trials of a liquid limit and a plastic limit test. The calculator draws the flow curve, reads the liquid limit at 25 blows and works out the plasticity index, plus the shrinkage limit and the liquidity index if you have their data. It follows ASTM D4318, and it’s free and needs no account.

Calculator · ASTM D4318

Liquid limit

Trials at different water contents. The flow curve is drawn with the blows on a log scale and gives the limit at 25 blows.

Trial	Blows	Container(g)	Container + wet(g)	Container + dry(g)
#1
#2
#3

Plastic limit

The thread crumbles at this water content; the valid trials are averaged.

Trial	Container(g)	Container + wet(g)	Container + dry(g)
#1
#2

Shrinkage limit

Besides the masses, the pat's volume is measured before and after drying: the shrinkage limit is the water content at which the soil stops shrinking.

Container

Container + wet

Container + dry

Wet volume

cm³

Dry volume

cm³

The soil's natural water content (%)

Optional. The soil's water content where it lies, not the test's: with it come the liquidity and consistency indices.

Flow curve

With 3 trials from 19 to 32 blows, the flow curve gives LL = 38.9 % at 25 blows, with a flow index of 0.031. PL = 21.4 %, so the plasticity index is PI = 17.5 %. At 23 % natural water content, the liquidity index is 9 % and the consistency index 91 %

Atterberg limits

Quantity	Value
Liquid limit · LLwater content at 25 blows on the flow curve	38.9%
Plastic limit · PLaverage of the valid trials	21.4%
Plasticity index · PILL − PL	17.5%
Flow index · Ifthe flow curve's slope	0.031
Shrinkage limit · SLw − (V₁ − V₂) / dry mass	10.0%
Liquidity index · LI(wn − PL) / PI	9%
Consistency index · CI(LL − wn) / PI	91%

This calculator is offered for information and technical support. It doesn't replace professional judgment or the reviews due, and its use is the user's responsibility.

How it calculates

Each trial’s water content comes from three weighings of its container: empty ( $M_c$ ), with the wet soil ( $M_{tc}$ ) and with the oven-dried soil ( $M_{dc}$ ).

w = \frac{M_{tc} - M_{dc}}{M_{dc} - M_c}

The liquid limit follows the multipoint method of ASTM D4318. The calculator fits a straight line by least squares to the water content against the logarithm of the number of blows, the flow curve, and reads it at 25 blows:

w = a + b \log_{10} N, \qquad LL = a + b \log_{10} 25

The flow index, $I_F = |b|$ , is how much the water content drops each time the blows grow tenfold. The plastic limit, $PL$ , is the average water content of its trials. The two limits and the soil’s natural water content, $w_n$ , give the indices:

PI = LL - PL, \qquad LI = \frac{w_n - PL}{PI}, \qquad CI = \frac{LL - w_n}{PI}

The shrinkage limit follows ASTM D4943. It starts from the pat’s water content $w$ and takes off the water that left while the pat was still shrinking, with $V$ and $V_d$ the pat’s wet and dry volumes and $M_s$ its dry mass:

SL = w - \frac{(V - V_d)\,\rho_w}{M_s}

The calculator warns about fewer than three liquid limit trials, blows outside the 15 to 35 window the standard asks for, a plasticity index of zero or less, and a shrinkage limit below zero or above the plastic limit.

The full procedure, equipment and report are in the Academy lesson: Atterberg limits test.

How to use it

Under Liquid limit, enter each trial’s blows and the three masses of its container: empty, with the wet soil and with the dry soil.
Under Plastic limit, enter the masses of the two trials the same way.
Under Shrinkage limit, enter the pat’s masses and its volume before and after drying. It’s optional, and its result appears once the data are in.
For the liquidity and consistency indices, add the soil’s natural water content, the one it has in the ground.
Read the flow curve with the liquid limit at 25 blows. The headline figure is the plasticity index, and the table lists LL, PL, PI and the flow index, plus SL, LI and CI when they have their data.

Restore the example brings back the worked example. The liquid limit and the plasticity index place a fine soil on the plasticity chart of the USCS classification calculator.

Frequently asked questions

How do you determine the liquid limit?

With the Casagrande cup. The soil goes into the cup at several water contents, a groove is cut in it, and you count the blows it takes to close the groove over about 13 mm. Plotted against the logarithm of the blows, the water contents fall close to a straight line, the flow curve, and the liquid limit is its water content at 25 blows.

How do you calculate the plasticity index?

Subtract the plastic limit from the liquid limit: $PI = LL - PL$ . It’s the range of water contents over which the soil behaves as a plastic. With the liquid limit, it places a fine soil on the plasticity chart, where the A-line separates clays from silts.

What are the Atterberg limits?

They’re the water contents at which a fine soil changes state. Below the shrinkage limit it stops losing volume as it dries; at the plastic limit it goes from semisolid to plastic; and at the liquid limit it starts to flow like a thick liquid.

What does the liquidity index tell you?

Where the natural water content sits between the two limits. At 0 the soil is at its plastic limit and at 1 at its liquid limit; above 1, it’s wetter in the ground than its liquid limit. The consistency index reads the other way, $CI = 1 - LI$ . The calculator shows both as percentages.

Liquid limit and plasticity index calculator (Atterberg)