How to Calculate CBR (California Bearing Ratio)
The CBR formula, standard loads, curve correction and which value to report
What the test measures
The California Bearing Ratio (CBR) test (commonly run per a standard such as ASTM D1883 for laboratory-compacted samples) measures the resistance of a compacted soil sample to penetration by a standard cylindrical plunger at a controlled rate, typically at penetrations of 0.1 inch and 0.2 inch.
Calculating the ratio
CBR (%) = (corrected stress at a given penetration ÷ standard stress at that penetration) × 100. The standard stresses are 1,000 psi (6.9 MPa) at 0.1 in (2.54 mm) and 1,500 psi (10.3 MPa) at 0.2 in (5.08 mm), representing a high-quality crushed-stone reference material. The CBR at 0.1 in is normally reported. If the CBR at 0.2 in is higher, the test is rerun; if the check test gives similar results, the CBR at 0.2 in is used.
Standard loads at 2.5 and 5.0 mm
The standard loads are what a high-quality crushed stone carries at each penetration — the 100% reference. ASTM D1883 and AASHTO T 193 express them as stresses on a 3 in² (1,935 mm²) piston and read them at 2.54 mm and 5.08 mm. IS 2720 (Part 16), the Indian standard, uses a 50 mm plunger, reads at 2.5 mm and 5.0 mm, and tabulates its own standard loads, which come out slightly higher. The two sets differ by less than 1%, but a result should use the loads of the standard the test followed.
The CBR Calculator works in kN. Example: a specimen carries corrected loads of 2.0 kN at 2.5 mm and 2.7 kN at 5.0 mm. CBR at 2.5 mm = 2.0 ÷ 13.345 × 100 = 15.0%, and CBR at 5.0 mm = 2.7 ÷ 20.017 × 100 = 13.5%. The 2.5 mm value is higher, so the reported CBR is 15%.
| Item | ASTM D1883 / AASHTO T 193 | IS 2720 (Part 16) |
|---|---|---|
| Penetrations read | 2.54 mm and 5.08 mm (0.10 and 0.20 in) | 2.5 mm and 5.0 mm |
| Piston / plunger | 3 in² (1,935 mm²), about 49.6 mm diameter | 50 mm diameter |
| Penetration rate | 0.05 in (1.27 mm) per minute | 1.25 mm per minute |
| Standard load, first reading | 1,000 psi × 3 in² = 3,000 lbf ≈ 13.345 kN | 70 kg/cm² → 1,370 kgf ≈ 13.44 kN |
| Standard load, second reading | 1,500 psi × 3 in² = 4,500 lbf ≈ 20.017 kN | 105 kg/cm² → 2,055 kgf ≈ 20.15 kN |
| Second value higher than first | Rerun; use it if the check test gives similar results | Repeat; use it if identical results follow |
Correcting the load-penetration curve
The loads in the formula are corrected loads, not raw readings. Plot load against penetration first. The curve is normally convex upward, but its first part can bend the other way because of irregularities on the specimen surface. IS 2720 (Part 16) corrects this by drawing a tangent at the point of greatest slope and taking the point where it meets the penetration axis as the new zero; the corrected loads at 2.5 mm and 5.0 mm are then read from that new zero. ASTM D1883 and AASHTO T 193 likewise calculate CBR from corrected load values, and corrected loads are what the calculator expects as inputs.
Soaked vs unsoaked samples
For a soaked CBR, ASTM D1883 and AASHTO T 193 place surcharge weights of at least 4.54 kg (10 lb) on the compacted specimen, immerse it for 96 hours (4 days) and measure its swell. Some clays may need longer than four days, and AASHTO T 193 allows not less than 24 hours for materials that drain readily if tests show the shorter soak doesn't affect the result. The specimen then drains for 15 minutes and is penetrated with the same surcharge in place.
IS 2720 (Part 16) also soaks for 96 hours, and sets the penetration surcharge equal to the weight of the base material and pavement that will sit on the soil. It allows the specimen to be tested without soaking when that isn't required. The calculation — and the calculator — is the same either way; the choice is made before testing.
In practice, a CBR result describes the soil only at the density the specimen was compacted to, so for the design value to hold, the field layer needs to reach that density too — see Understanding In-Situ Dry Density.
Laboratory test vs. the calculator
The laboratory test is the physical part: the specimen is compacted, soaked when a soaked CBR is required, loaded with surcharge weights, and penetrated by the piston while load and penetration are recorded. The load-penetration curve is then corrected where needed, and the corrected values at 0.1 in and 0.2 in are read from it.
The CBR Calculator does not perform any of that testing. It does only the final step: you enter the corrected loads at 2.5 mm (0.1 in) and 5.0 mm (0.2 in), and it divides each by the standard load for that penetration — 3,000 lbf (about 13.345 kN) and 4,500 lbf (about 20.017 kN), which are the standard stresses applied over the 3 in² piston — and multiplies by 100. It reports the 0.1 in value and flags a retest when the 0.2 in value comes out higher.
What the result is used for
CBR is a key input to flexible pavement thickness design methods — a low CBR (a weak subgrade) generally calls for a thicker pavement structure to spread traffic loads adequately, while a high CBR (a strong subgrade, closer to the crushed-stone reference) can support a thinner structure. Specific pavement thickness requirements come from the design method and governing specification being used, not from the CBR value alone.
For when the test is specified, how CBR is measured in the field and what typical values indicate, see What Is a CBR Test and When Is It Used?.
Worked Example
At 0.1 in penetration, the corrected stress on the piston is 620 psi. The standard stress at 0.1 in is 1,000 psi.
CBR at 0.1 in = 620 ÷ 1,000 × 100 = 62%
Assumptions & Limitations
- General ranges sometimes cited for subgrade quality (for example, low CBR for poor subgrades versus high CBR for excellent ones) vary by design method and agency — always check the specific pavement design method being used rather than a single rule of thumb.
FAQ
- Which CBR value is normally reported?
- The CBR at 0.1 in (2.54 mm) penetration. The value at 0.2 in (5.08 mm) is calculated as well, but it only replaces the 0.1 in value under the retest rule.
- What if the 0.2 in CBR is higher than the 0.1 in CBR?
- The test is rerun. If the check test gives similar results, the CBR at 0.2 in is used as the reported value.
- What standard stresses are used for the CBR calculation?
- 1,000 psi (6.9 MPa) at 0.1 in penetration and 1,500 psi (10.3 MPa) at 0.2 in. On the 3 in² piston these equal standard loads of 3,000 lbf and 4,500 lbf.
Related Calculators
Related Guides
From the Blog
Sources
ASTM D1883
Standard Test Method for California Bearing Ratio (CBR) of Laboratory-Compacted Soils.
AASHTO T 193
Standard Method of Test for The California Bearing Ratio.
IS 2720 (Part 16): 1987
Methods of Test for Soils — Laboratory Determination of CBR: load-penetration curve correction (cl. 7.2) and standard loads (cl. 7.3).