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) as the average of threads, derives the plasticity index (PI), and plots the point (LL, PI) on the Casagrande chart in accordance with BS 1377-2 (+ BS EN ISO 17892-12) and BS 5930. Essential for classifying CL, CH, ML, MH and MH-OH in BS 5930 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 425 µm sieve and are indispensable for classifying any soil with more than 5% fines, assessing expansiveness, estimating compressibility, controlling clay fills, and defining stabilisation treatments with lime or cement.
Formulas applied
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
| Container | 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 clay of medium plasticity: susceptible to moderate expansion, medium compressibility and low permeability. Requires strict moisture control during compaction (close to 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
- BS 1377-2 (+ BS EN ISO 17892-12) — Methods of test for soils for civil engineering purposes — Determination of liquid limit, plastic limit and plasticity index
- BS 5930 — Code of practice for ground investigations
- BS EN ISO 17892-12 — Geotechnical investigation and testing — Laboratory testing of soil — Determination of liquid and plastic limits
- 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) is accepted by BS 1377-2 (+ BS EN ISO 17892-12) as an alternative. It gives very similar LL values but with lower inter-laboratory scatter. BS 5930 still favours 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 BS 5930 classification it remains with PI < 4 or unobtainable.
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?
BS 1377-2 (+ BS EN ISO 17892-12) 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.