Atterberg Limits Calculator: LL, PL, PI and Casagrande Chart
Atterberg limits are the backbone of fine-grained soil classification. This calculator takes the (N, w) pairs from the Casagrande cup test to obtain the liquid limit (LL) by logarithmic interpolation, calculates the plastic limit (PL) from the average of threads, derives the plasticity index (PI), and plots the point (LL, PI) on the Casagrande chart according to ASTM D4318 and AASHTO T 90. Essential for classifying CL, CH, ML, MH and MH-OH in USCS and AASHTO.
What are they and when to use them?
Atterberg limits define the moisture content at which a fine-grained soil changes state: from liquid to plastic (LL) and from plastic to solid (PL). The difference PI = LL − PL measures the moisture range over which the soil behaves plastically. They apply to the fraction passing the No. 40 sieve and are indispensable for classifying any soil with more than 5% fines, evaluating expansiveness, estimating compressibility, controlling clay fills, and defining stabilization treatments with lime or cement.
Applied formulas
LL by multipoint method: plot (log N, w) and interpolate the moisture content at N = 25 blows.
LL = w₁ + (w₂ − w₁) × (log 25 − log N₁) / (log N₂ − log N₁)
LL by one-point method: LL = w × (N/25)^0.121
PL: average moisture content of 2-3 threads that crack at 3.2 mm.
PI: PI = LL − PL
A-Line (Casagrande): PI = 0.73 × (LL − 20)
U-Line (Casagrande): PI = 0.9 × (LL − 8) — theoretical upper limit
Calculation example
| Can | Blows (N) | Moisture content (w %) |
|---|---|---|
| LL-1 | 35 | 43.2 |
| LL-2 | 26 | 45.8 |
| LL-3 | 18 | 48.4 |
| PL-1 | — | 22.6 |
| PL-2 | — | 23.2 |
Interpolating on a semi-logarithmic scale between the two points closest to 25 blows (N=26 and N=35): LL = 45.8 + (43.2 − 45.8) × (log 25 − log 26) / (log 35 − log 26) = 45.8 + (−2.6) × (−0.017 / 0.128) = 45.8 + 0.35 = 46.2%. Rounding to the nearest integer, LL = 46. The average PL is (22.6 + 23.2) / 2 = 22.9%, rounded PL = 23. Therefore PI = 46 − 23 = 23. With LL = 46 and PI = 23, the point lies above the A-Line (0.73 × (46 − 20) = 19), so it is a CL clay of medium plasticity.
Result: LL = 46 · PL = 23 · PI = 23 — CL clay (medium plasticity).
Interpretation of results
CL with PI = 23 is a medium plasticity clay: susceptible to moderate expansion, medium compressibility, and low permeability. Requires strict moisture control during compaction (near the Proctor optimum). If LL had exceeded 50 it would be classified as CH (high plasticity) and would require more aggressive treatments. PI below the A-Line shifts the classification to ML/MH (silts).
Reference standards
- ASTM D4318 — Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils
- AASHTO T 90 — Soil Mechanics Laboratory — Determination of liquid limit
- AASHTO T 90 — Determination of plastic limit
- AASHTO T 90 — Determination of plasticity index
- AASHTO T 89 / T 90
Frequently asked questions
Can the Casagrande cup be replaced by the fall cone?
Yes, the penetration cone (British / European method) has been accepted by ASTM D4318 since 2017 as an alternative. It gives very similar LL values but with less inter-laboratory scatter. AASHTO T 90 still favors the Casagrande cup in common regional practice.
What do I do if the soil cannot be rolled to 3.2 mm for the PL?
It is reported as NP (non-plastic) and, by definition, PI is not calculable. This typically occurs in non-plastic silts (ML) and silty sands with inert fine fraction. In the USCS classification it remains with PI < 4 or not obtainable.
Why does a U-Line exist on the Casagrande chart?
It defines the practical upper limit: no natural soil should plot above the U-Line (PI = 0.9 × (LL − 8)). If your point crosses it, there is a test error, contamination, or artificial alteration (e.g., added bentonite).
How many points do I need for the multipoint LL method?
ASTM D4318 recommends three or four points with N between 15 and 35. It is preferable to have at least one point above and one below 25 blows to interpolate, not extrapolate. The one-point method is accepted for quick work but has greater scatter.