🔢 IS 10262:2019 · IS 456:2000 · FIVE WORKED EXAMPLES · 2026

Mix Design Example Calculations

Five complete IS 10262:2019 worked examples with every step shown — M20 Mild, M30 Severe, M40 Extreme with SP, M50 HSC with silica fume, and M25 with fly ash. All arithmetic, all IS 456 checks.

🔢 M20 — Mild
🔢 M30 — Severe
⚡ M40 — SP
🔥 M50 — HSC + SF
🌿 M25 — Fly Ash

📋Examples Index

Click any example to jump to the full worked solution
1M20 · OPC 43 · Mild · No SP
2M30 · OPC 53 · Severe · No SP
3M40 · OPC 53 · Extreme · PCE SP
4M50 · OPC 53 · HSC · SF + SP
5M25 · OPC 53 · Moderate · Fly Ash



1
M20 Concrete — Mild Exposure
OPC 43 Grade · IS 10262:2019 · 20mm MSA · 75mm Slump · No SP · Zone II Sand · Crushed Aggregate
fck = 20 MPa
IS 456 Mild
Max w/c = 0.55
Min cement = 300 kg/m³
1Target Mean Strength IS 10262:2019 Cl. 5.3.2
Grade M20: fck = 20 MPa
Standard Deviation (IS 10262 Table 1, M20–M25): S = 4.0 MPa
Margin = 1.65 × S = 1.65 × 4.0 = 6.60 MPa
fcr = fck + 1.65 × S = 20 + 6.60 = 26.60 MPa
2Water-Cement Ratio IS 10262 Fig. 1 + IS 456 Table 5
Strength-derived (IS 10262 Figure 1, OPC 43):
w/c = (90 − fcr) / 110 = (90 − 26.60) / 110 = 63.40 / 110 = 0.576
IS 456 Table 5 (Mild exposure): max w/c = 0.55
Compare: 0.576 > 0.55 → IS 456 durability governs
ADOPTED w/c = 0.55
3Water Content IS 10262:2019 Table 2
IS 10262 Table 2 (20mm MSA, 75mm slump, crushed): W = 186 L/m³
No SP, no rounded aggregate adjustment.
DESIGN WATER W = 186 L/m³
4Cement Content IS 10262:2019 Cl. 5.5 + IS 456 Cl. 8.2.4
C = W / (w/c) = 186 / 0.55 = 338.18 ≈ 338 kg/m³
IS 456 Table 5 checks (Mild exposure):
Minimum cement = 300 kg/m³ → 338 ≥ 300 ✓ PASS
Maximum cement = 450 kg/m³ → 338 ≤ 450 ✓ PASS
DESIGN CEMENT C = 338 kg/m³
5Aggregate Proportioning IS 10262:2019 Table 3 + Absolute Volume
jc (IS 10262 Table 3, 20mm MSA, Zone II, crushed): jc = 0.64
CA = jc × DRBD = 0.64 × 1450 = 928 kg/m³
ABSOLUTE VOLUME BALANCE:
V_cement = 338 / (3.14 × 1000) = 0.1076 m³
V_water = 186 / 1000 = 0.1860 m³
V_CA = 928 / (2.68 × 1000) = 0.3463 m³
V_air = 1.5 / 100 = 0.0150 m³
─────────────────────────────────────────
Sum so far = 0.6549 m³
V_FA_sand = 1.0000 − 0.6549 = 0.3451 m³
FA_sand = 0.3451 × 2.65 × 1000 = 914 kg/m³
Volume check: 0.1076+0.1860+0.3463+0.0150+0.3451 = 1.0000 m³ ✓
✅ M20 Mix Proportions — per m³ (SSD basis)
TMS (fcr)26.6MPa
w/c Adopted0.55IS 456 governs
Cement (OPC 43)338kg/m³
Water186L/m³
Fine Aggregate914kg/m³
Coarse Aggregate928kg/m³
Unit Weight2366kg/m³
Mix Ratio (C:FA:CA)1:2.7:2.7by mass
Key Note: At M20 Mild exposure, IS 456 durability governs over strength (w/c 0.55 vs strength-derived 0.576). The mix is economical — cement 338 kg/m³ vs IS 456 Table 9 nominal mix of ~390 kg/m³, saving 52 kg/m³ = ₹286/m³ at 2026 prices. Design mix always more economical than nominal for M20.



2
M30 Concrete — Severe Exposure
OPC 53 Grade · IS 10262:2019 · 20mm MSA · 75mm Slump · No SP · Zone II · Crushed · DRBD 1450 kg/m³
fck = 30 MPa
IS 456 Severe
Max w/c = 0.45
Min cement = 320 kg/m³
1Target Mean Strength IS 10262:2019 Cl. 5.3.2
Grade M30: fck = 30 MPa
S = 5.0 MPa (IS 10262 Table 1, M30–M55)
Margin = 1.65 × 5.0 = 8.25 MPa
fcr = 30 + 8.25 = 38.25 MPa
2Water-Cement Ratio IS 10262 Fig. 1 + IS 456 Table 5
Strength-derived (IS 10262 Figure 1, OPC 53):
w/c = (102 − fcr) / 116 = (102 − 38.25) / 116 = 63.75 / 116 = 0.549
IS 456 Table 5 (Severe exposure): max w/c = 0.45
Compare: 0.549 > 0.45 → IS 456 durability governs
ADOPTED w/c = 0.45
3Water Content IS 10262:2019 Table 2
IS 10262 Table 2 (20mm MSA, 75mm slump, crushed): W = 186 L/m³
No adjustments.
DESIGN WATER W = 186 L/m³
4Cement Content IS 10262:2019 Cl. 5.5 + IS 456 Cl. 8.2.4
C = W / (w/c) = 186 / 0.45 = 413.33 ≈ 413 kg/m³
IS 456 Table 5 checks (Severe):
Minimum = 320 kg/m³ → 413 ≥ 320 ✓
Maximum = 450 kg/m³ → 413 ≤ 450 ✓
Note: Without SP, C = 413 kg/m³ — approaching IS 456 maximum of 450.
For M30 without SP, this is the typical outcome at Severe exposure.
Adding PCE 20% WR reduces C to 331 kg/m³ (see Example 3 pattern).
DESIGN CEMENT C = 413 kg/m³
5Aggregate Proportioning IS 10262:2019 Table 3 + Absolute Volume
jc = 0.64 (20mm, Zone II, crushed)
CA = 0.64 × 1450 = 928 kg/m³
ABSOLUTE VOLUME BALANCE:
V_cement = 413 / (3.15 × 1000) = 0.1311 m³
V_water = 186 / 1000 = 0.1860 m³
V_CA = 928 / (2.68 × 1000) = 0.3463 m³
V_air = 1.5 / 100 = 0.0150 m³
─────────────────────────────────────────
Sum = 0.6784 m³
V_FA = 1.0000 − 0.6784 = 0.3216 m³
FA_sand = 0.3216 × 2.65 × 1000 = 852 kg/m³
Volume check: 0.1311+0.1860+0.3463+0.0150+0.3216 = 1.0000 m³ ✓
✅ M30 Mix Proportions — per m³ (SSD basis)
TMS (fcr)38.25MPa
w/c Adopted0.45IS 456 governs
Cement (OPC 53)413kg/m³
Water186L/m³
Fine Aggregate852kg/m³
Coarse Aggregate928kg/m³
Unit Weight2379kg/m³
Mix Ratio (C:FA:CA)1:2.06:2.25by mass

📌 M30 Without SP — Note on Economy

Cement = 413 kg/m³ is technically compliant (≤450) but expensive. Adding PCE SP at 20% WR: W reduces to 149 L/m³ → C = 149/0.45 = 331 kg/m³ — saving 82 kg/m³ cement = ₹451/m³, at SP cost of ~₹109/m³, net saving ₹342/m³. SP is strongly recommended for M30 Severe even though not mandatory.



3
M40 Concrete — Extreme Exposure with PCE SP
OPC 53 Grade · IS 10262:2019 · 20mm MSA · 100mm Slump · PCE SP 20% WR · Zone II · Crushed · SG_C=3.15, SG_CA=2.68, SG_FA=2.65, DRBD=1450
fck = 40 MPa
IS 456 Extreme
Max w/c = 0.40
SP Mandatory
Min cement = 360 kg/m³
1Target Mean Strength
fck = 40 MPa | S = 5.0 MPa (IS 10262 Table 1, M30–M55)
fcr = 40 + 1.65 × 5.0 = 40 + 8.25 = 48.25 MPa
2Water-Cement Ratio
Strength-derived (OPC 53, IS 10262 Figure 1):
w/c = (102 − 48.25) / 116 = 53.75 / 116 = 0.463
IS 456 Table 5 (Extreme): max w/c = 0.40
Compare: 0.463 > 0.40 → IS 456 durability governs (significantly)
ADOPTED w/c = 0.40
3Water Content — SP Adjusted
IS 10262 Table 2 (20mm MSA, 100mm slump, crushed): W_base = 194 L/m³
PCE SP water reduction = 20%
W_design = 194 × (1 − 20/100) = 194 × 0.80 = 155.2 ≈ 155 L/m³
DESIGN WATER W = 155 L/m³
4Cement Content
C = W / (w/c) = 155 / 0.40 = 387.5 ≈ 388 kg/m³
Without SP: C = 194 / 0.40 = 485 kg/m³ ← EXCEEDS IS 456 max 450 kg/m³
→ SP is MANDATORY for IS 456 compliance at M40 Extreme.
IS 456 Table 5 checks (Extreme exposure):
Minimum = 360 kg/m³ → 388 ≥ 360 ✓ PASS
Maximum = 450 kg/m³ → 388 ≤ 450 ✓ PASS (SP achieves compliance)
DESIGN CEMENT C = 388 kg/m³
5Aggregate Proportioning
jc = 0.64 (20mm, Zone II, crushed)
CA = 0.64 × 1450 = 928 kg/m³
ABSOLUTE VOLUME BALANCE:
V_cement = 388 / (3.15 × 1000) = 0.1232 m³
V_water = 155 / 1000 = 0.1550 m³
V_CA = 928 / (2.68 × 1000) = 0.3463 m³
V_air = 1.5 / 100 = 0.0150 m³
─────────────────────────────────────────
Sum = 0.6395 m³
V_FA = 1.0000 − 0.6395 = 0.3605 m³
FA_sand = 0.3605 × 2.65 × 1000 = 955 kg/m³
Volume check: 0.1232+0.1550+0.3463+0.0150+0.3605 = 1.0000 m³ ✓
SP Volume: C × 0.005 / 1.06 = 388 × 0.005 / 1.06 = 1.83 L/m³
(0.5% of cement mass; density 1.06 kg/L)
✅ M40 Mix Proportions — per m³ (SSD basis)
TMS (fcr)48.25MPa
w/c Adopted0.40IS 456 governs
Cement (OPC 53)388kg/m³
Water155L/m³
Fine Aggregate955kg/m³
Coarse Aggregate928kg/m³
PCE SP1.83L/m³
Unit Weight2426kg/m³
Critical Point: Without SP, C = 485 kg/m³ — 35 kg/m³ over IS 456 maximum. This proves SP is not optional at M40 Extreme — it is a code compliance requirement. With SP at 20% WR, cement falls to 388 kg/m³ (IS 456 compliant) and net saving vs no-SP = (485−388)×₹5.5 − 1.83×₹70 = ₹534 − ₹128 = ₹406/m³ saving per m³.



4
M50 High-Strength Concrete — Silica Fume + PCE SP
OPC 53 + 10% Silica Fume · IS 10262:2019 Annex C · 20mm MSA · 125mm Slump · PCE SP 25% WR · Extreme Exposure
fck = 50 MPa
HSC
Silica Fume k=2.50
SP Mandatory
Eff. w/c critical
1Target Mean Strength
fck = 50 MPa | S = 5.0 MPa (IS 10262 Table 1; use actual σ once trials available)
fcr = 50 + 1.65 × 5.0 = 50 + 8.25 = 58.25 MPa
2Water-Cement Ratio
Strength-derived (OPC 53, IS 10262 Figure 1):
w/c = (102 − 58.25) / 116 = 43.75 / 116 = 0.377
IS 456 Table 5 (Extreme): max w/c = 0.40
Compare: 0.377 < 0.40 → STRENGTH GOVERNS (typical for HSC) Note: At M50+, strength criterion usually governs IS 456 durability. ADOPTED w/c = 0.377 ≈ 0.38 (rounded to 2 d.p.) 3Water Content — SF Water Demand + PCE SP IS 10262 Table 2 (20mm MSA, 125mm slump, crushed): W_base = 200 L/m³ Silica Fume water demand increase: SF = 10% of OPC → need to know C first (iterative) Assume SF ≈ 45 kg/m³ initially → SF water demand = 45 × 0.02 = 0.9 L/kg × ... Simpler rule: +2 L/m³ per 1% SF of OPC Initial SF% = 10% → Additional water = 10 × 2 = 20 L/m³ Subtotal before SP = 200 + 20 = 220 L/m³ PCE SP water reduction (25% of subtotal): W_design = 220 × (1 − 0.25) = 220 × 0.75 = 165 L/m³ DESIGN WATER W = 165 L/m³ 4Cement + Silica Fume Content OPC Cement: C = W / (w/c) = 165 / 0.38 = 434.2 ≈ 434 kg/m³ Silica Fume (10% of OPC): SF = 434 × 0.10 = 43.4 ≈ 43 kg/m³ IS 456 Table 5 checks (Extreme): Min OPC = 360 kg/m³ → 434 ≥ 360 ✓ PASS Max OPC = 450 kg/m³ → 434 ≤ 450 ✓ PASS EFFECTIVE w/c CHECK (IS 10262 Cl. 5.7): (w/c)_eff = W / (C + k_SF × SF) = 165 / (434 + 2.50 × 43) = 165 / (434 + 107.5) = 165 / 541.5 = 0.305 IS 456 Extreme max = 0.40 → 0.305 ≤ 0.40 ✓ PASS (excellent durability) SP volume: 434 × 0.007 / 1.06 = 2.86 L/m³ (0.7% of cement, PCE) 5Aggregate Proportioning jc = 0.64 (20mm, Zone II, crushed); SG_SF = 2.20 CA = 0.64 × 1450 = 928 kg/m³ ABSOLUTE VOLUME BALANCE: V_OPC = 434 / (3.15 × 1000) = 0.1378 m³ V_SF = 43 / (2.20 × 1000) = 0.0195 m³ V_water = 165 / 1000 = 0.1650 m³ V_CA = 928 / (2.68 × 1000) = 0.3463 m³ V_air = 1.5 / 100 = 0.0150 m³ ────────────────────────────────────────── Sum = 0.6836 m³ V_FA = 1.0000 − 0.6836 = 0.3164 m³ FA_sand = 0.3164 × 2.65 × 1000 = 838 kg/m³ Volume check: 0.1378+0.0195+0.1650+0.3463+0.0150+0.3164 = 1.0000 m³ ✓ ✅ M50 HSC Mix Proportions — per m³ (SSD basis) TMS (fcr)58.25MPa w/c Adopted0.38Strength governs Effective w/c0.305IS 10262 Cl. 5.7 OPC Cement434kg/m³ Silica Fume43kg/m³ Water165L/m³ Fine Aggregate838kg/m³ Coarse Aggregate928kg/m³ PCE SP2.86L/m³ Unit Weight2408kg/m³ HSC Key Points: At M50, strength governs w/c (0.38 < 0.40 IS 456 limit) — the opposite of M20/M30 where durability governed. Silica fume (k=2.50) reduces effective w/c to 0.305 — excellent IS 456 durability. The SF water demand (+20 L/m³) is fully overcome by PCE SP (−55 L/m³). Always use actual σ from production trials once ≥30 results available — the IS 10262 Table 1 assumed 5.0 MPa may be conservative for HSC.



5
M25 Concrete — Moderate Exposure with Fly Ash
OPC 53 + 25% Fly Ash (IS 3812) · IS 10262:2019 Cl. 5.7 · 20mm MSA · 75mm Slump · No SP · Zone II · SG_FA_SCM=2.20
fck = 25 MPa
IS 456 Moderate
Max w/c = 0.50
Fly Ash k=0.25
Min cement = 300 kg/m³
1Target Mean Strength
fck = 25 MPa | S = 4.0 MPa (IS 10262 Table 1, M20–M25)
fcr = 25 + 1.65 × 4.0 = 25 + 6.60 = 31.60 MPa
2Water-Cement Ratio
Strength-derived (OPC 53, IS 10262 Figure 1):
w/c = (102 − 31.60) / 116 = 70.40 / 116 = 0.607
IS 456 Table 5 (Moderate): max w/c = 0.50
Compare: 0.607 > 0.50 → IS 456 durability governs
ADOPTED w/c = 0.50
3Water Content
IS 10262 Table 2 (20mm MSA, 75mm slump, crushed): W = 186 L/m³
No adjustments.
DESIGN WATER W = 186 L/m³
4Cement + Fly Ash Content
OPC Cement: C = W / (w/c) = 186 / 0.50 = 372 kg/m³
Fly Ash (25% of OPC): FA_SCM = 372 × 0.25 = 93 kg/m³
IS 456 Table 5 checks (Moderate):
Min OPC = 300 kg/m³ → 372 ≥ 300 ✓ PASS
Max OPC = 450 kg/m³ → 372 ≤ 450 ✓ PASS
EFFECTIVE w/c CHECK (IS 10262 Cl. 5.7, k_FA = 0.25):
(w/c)_eff = W / (C + k_FA × FA_SCM)
= 186 / (372 + 0.25 × 93)
= 186 / (372 + 23.25)
= 186 / 395.25
= 0.471
IS 456 Moderate max = 0.50 → 0.471 ≤ 0.50 ✓ PASS
The fly ash addition improves effective w/c from 0.50 to 0.471
→ Superior durability to equivalent OPC-only mix.
5Aggregate Proportioning
jc = 0.64 (20mm, Zone II, crushed); SG_FA_SCM = 2.20
CA = 0.64 × 1450 = 928 kg/m³
ABSOLUTE VOLUME BALANCE:
V_OPC = 372 / (3.15 × 1000) = 0.1181 m³
V_FA_SCM = 93 / (2.20 × 1000) = 0.0423 m³
V_water = 186 / 1000 = 0.1860 m³
V_CA = 928 / (2.68 × 1000) = 0.3463 m³
V_air = 1.5 / 100 = 0.0150 m³
──────────────────────────────────────────
Sum = 0.7077 m³
V_FA_sand = 1.0000 − 0.7077 = 0.2923 m³
FA_sand = 0.2923 × 2.65 × 1000 = 775 kg/m³
Volume check: 0.1181+0.0423+0.1860+0.3463+0.0150+0.2923 = 1.0000 m³ ✓
6IS 456 Full Compliance Summary

✅ M25 + Fly Ash Mix Proportions — per m³ (SSD basis)
TMS (fcr)31.60MPa
w/c (simple)0.50IS 456 governs
Effective w/c0.471k=0.25 FA
OPC Cement372kg/m³
Fly Ash (SCM)93kg/m³
Water186L/m³
Fine Aggregate775kg/m³
Coarse Aggregate928kg/m³
Total Binder465kg/m³
Unit Weight2354kg/m³

📌 Benefits of 25% Fly Ash Addition at M25

Effective w/c: 0.471 vs 0.50 (OPC only) → 6% improvement in durability indicator. Heat of hydration: reduced by ~18% (FA heat ≈ 0.014 kgCO₂/kg vs OPC 53 = 0.890 kgCO₂/kg). Carbon footprint: 372×0.890 + 93×0.0135 = 331.3 + 1.3 = 332.6 kgCO₂/m³ vs 372×0.890 = 331 (minimal CO₂ benefit from FA addition alone — OPC content unchanged). Economy: FA at ₹800/t = ₹74 cost for 93 kg vs 0 — marginal addition but worthwhile for durability and heat benefits. Long-term strength at 90d: typically 8–15% higher than 28d for FA mixes vs 5% for OPC.