Concrete Compressive Strength Calculator
Estimate the compressive strength of concrete based on the water-to-cement ratio and curing age using Abrams' Law combined with a maturity (age) factor.
Formulas Used
1. Abrams' Law – 28-Day Compressive Strength
f'c₂₈ = A / B(w/c)
Where A and B are empirical constants that depend on cement type, and w/c is the water-to-cement ratio by mass.
2. Age (Maturity) Factor – ACI 209R-92
f'c(t) = f'c₂₈ × [t / (a + b·t)] / [28 / (a + b·28)]
Where t is the curing age in days, and a, b are cement-type constants.
3. Modulus of Rupture – ACI 318-19 §19.2.3.1
fr = 0.62 · λ · √f'c(t) [MPa] (λ = 1.0 for normal-weight concrete)
4. Elastic Modulus – ACI 318-19 §19.2.2.1
Ec = 4700 · √f'c(t) [MPa] (normal-weight concrete, wc ≈ 2300 kg/m³)
Cement Type Constants
| Cement Type | A (MPa) | B | a | b |
|---|---|---|---|---|
| Type I (OPC) | 96.5 | 8.2 | 4.0 | 0.85 |
| Type III (High Early) | 110.0 | 8.2 | 2.3 | 0.92 |
| Type II (Mod. SR) | 90.0 | 8.2 | 5.0 | 0.83 |
| Type IV (Low Heat) | 80.0 | 8.2 | 6.5 | 0.80 |
Assumptions & References
- Abrams' Law is valid for water-to-cement ratios between 0.30 and 0.80; results outside this range are unreliable.
- The age factor model follows ACI 209R-92 (Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures) assuming standard moist curing at 23 °C (73 °F).
- Elastic modulus formula is from ACI 318-19 §19.2.2.1, valid for normal-weight concrete (unit weight ≈ 2300 kg/m³ / 145 lb/ft³).
- Modulus of rupture formula is from ACI 318-19 §19.2.3.1 with λ = 1.0 (normal-weight concrete).
- Empirical constants A and B are calibrated from: Neville, A.M. (2011). Properties of Concrete, 5th Edition. Pearson.
- Results assume adequate compaction, proper curing conditions, and no admixtures (SCMs, plasticisers, etc.).
- This calculator provides estimates only. Actual strength must be verified by laboratory cylinder/cube testing per ASTM C39 or BS EN 12390-3.
- Supplementary cementitious materials (fly ash, slag, silica fume) are not accounted for and will alter results.