chemistry · tool
Bogue Calculator
Compute potential clinker phases (C3S, C2S, C3A, C4AF) from an oxide analysis.
Executive summary
Enter CaO, SiO2, Al2O3, Fe2O3 (and optionally SO3 and free lime) to estimate the four potential Bogue phases. The tool selects the standard or low-alumina formula based on the alumina/ferric ratio and flags implausible results. Output is potential (not measured) phase composition.
Calculator
| Phase | % |
|---|---|
| C₃S (alite) | 64.4 |
| C₂S (belite) | 13 |
| C₃A | 8.7 |
| C₄AF | 9.1 |
Method: standard (A/F >= 0.64) · A/F = 1.73
Potential phase composition (equilibrium, pure-phase assumption). Not measured phases. Verify against your lab and applicable standards before any quality or process decision.
Method
Classical Bogue equations (ASTM C150 form). Standard branch when Al2O3/Fe2O3 >= 0.64; low-alumina branch (no C3A; ferrite as C4AF+C2F solid solution) when < 0.64. Total CaO is corrected for free lime when provided.
Formulas (so an agent can compute without the UI)
Let CaO* = CaO − freeLime (free lime subtracted when provided). Compute A/F = Al₂O₃ / Fe₂O₃.
Standard branch — when A/F ≥ 0.64:
C3S = 4.071·CaO* − 7.600·SiO2 − 6.718·Al2O3 − 1.430·Fe2O3 − 2.852·SO3
C3A = 2.650·Al2O3 − 1.692·Fe2O3
C4AF = 3.043·Fe2O3
C2S = 2.867·SiO2 − 0.7544·C3S
Low-alumina branch — when A/F < 0.64 (no separate C₃A):
C3S = 4.071·CaO* − 7.600·SiO2 − 4.479·Al2O3 − 2.859·Fe2O3 − 2.852·SO3
C3A = 0
C4AF (ss) = 2.100·Al2O3 + 1.702·Fe2O3 (C4AF + C2F solid solution)
C2S = 2.867·SiO2 − 0.7544·C3S
Worked example
Inputs: CaO 66.6, SiO₂ 21.5, Al₂O₃ 5.2, Fe₂O₃ 3.0, SO₃ 0, free lime 1.0. A/F = 5.2 / 3.0 = 1.73 → standard branch.
Approximate result: C₃S ≈ 64.4, C₂S ≈ 13.0, C₃A ≈ 8.7, C₄AF ≈ 9.1.
Copyable JSON input/output contract
{
"CaO": 66.6,
"SiO2": 21.5,
"Al2O3": 5.2,
"Fe2O3": 3,
"SO3": 0,
"freeLime": 1
}{
"C3S": 64.4,
"C2S": 13,
"C3A": 8.7,
"C4AF": 9.1,
"aluminaFerricRatio": 1.73,
"method": "standard (A/F >= 0.64)",
"warnings": []
}Output values above illustrate the contract shape; run the calculator for exact figures.
Inputs needed
| Input | Unit | Required | Notes |
|---|---|---|---|
| CaO | % | Yes | — |
| SiO2 | % | Yes | — |
| Al2O3 | % | Yes | — |
| Fe2O3 | % | Yes | — |
| SO3 | % | No | used in the CaO correction term |
| freeLime | % | No | subtracted from total CaO if provided |
Outputs expected
| Output | Unit | Notes |
|---|---|---|
| C3S | % | alite |
| C2S | % | belite |
| C3A | % | 0 when A/F < 0.64 |
| C4AF | % | ferrite (solid solution when A/F < 0.64) |
Limitations & cautions
- Potential phase calculation only — assumes chemical equilibrium and pure phases. Not the same as actual mineralogy.
- Oxide basis matters: mixing ignited and as-received analyses shifts results. Keep a consistent basis.
- Accuracy degrades with high minor-oxide content (alkalis, MgO, P2O5) not accounted for in the classical equations.
- The low-alumina branch reports ferrite as a solid solution, not pure C4AF.
- Not a substitute for XRD/QXRD or plant-specific QC review.
- Verify against your plant's lab methods and standards before any quality or process decision.
⚠️ Safety & compliance
- Potential phases are an estimate, not a measurement. Do not release, reject, or re-blend product based on Bogue values alone.
Authority: Quality release and process decisions require QC authority, your plant's test methods, and applicable standards. This tool is advisory.
AI agent use cases
- Convert an XRF oxide analysis into potential phase composition for reasoning about strength and setting.
- Replicate the calculation from the stated formulas when the UI cannot be run.
- Flag when an oxide analysis yields implausible (e.g., negative) phase values.
Human use cases
- Quick lab/control-room estimate of clinker phases from routine oxides.
- Teaching aid for the relationship between oxides and phases.
Related
Tools:lsf sm am calculator
Prompts:raw mix correction
Pages:lsf sm am, clinker phases, raw mix design, low c3s
Sources & assumptions
Assumption: Oxides entered on an ignited, normalized basis.
Bogue, R. H. — The Chemistry of Portland Cement — origin of the phase equations
ASTM C150 — standard form of the Bogue calculation