Civil Engineering Formula Sheet
Key formulas for RCC, steel, soil mechanics, hydraulics, surveying, highways and estimation — with links to free calculators.
Concrete & RCC (ACI 318)
| Topic | Formula |
|---|---|
| Modulus of elasticity | Ec = 4700√f′c (MPa) |
| Modulus of rupture | fr = 0.62λ√f′c |
| Stress block | a = As·fy / (0.85·f′c·b); β1 = 0.85 for f′c ≤ 28 MPa |
| Flexure | φMn = φ·As·fy·(d − a/2), φ = 0.9 (tension-controlled) |
| Minimum steel (beams) | As,min = max(0.25√f′c/fy, 1.4/fy)·b·d |
| Shrinkage steel (slabs) | 0.0018·b·h (Grade 60) |
| Concrete shear | Vc = 0.17λ√f′c·b·d |
| Stirrups | s = Av·fy·d / Vs; s ≤ d/2 (≤ d/4 if Vs > 0.33√f′c·bd) |
| Columns (tied) | φPn,max = 0.80·φ·[0.85f′c(Ag − Ast) + fy·Ast], φ = 0.65 |
| Deflection (simply supported UDL) | δ = 5wL⁴ / (384EI) |
Steel (AISC 360)
| Topic | Formula |
|---|---|
| Plastic moment | φMn = 0.9·Fy·Zx (compact, braced) |
| Euler stress | Fe = π²E / (KL/r)² |
| Column (inelastic) | Fcr = 0.658^(Fy/Fe)·Fy when KL/r ≤ 4.71√(E/Fy) |
| Column (elastic) | Fcr = 0.877·Fe |
| Bolt shear | φRn = 0.75·Fnv·Ab per shear plane |
| Bolt bearing | φRn = 0.75·2.4·d·t·Fu |
Soil mechanics
| Topic | Formula |
|---|---|
| Moisture content | w = Ww/Ws × 100 |
| Void ratio & porosity | e = Vv/Vs; n = e/(1 + e) |
| Dry density | γd = γ/(1 + w) |
| Saturation | S·e = w·Gs |
| Zero air voids | γd = Gs·γw / (1 + w·Gs) |
| Plasticity index | PI = LL − PL; A-line PI = 0.73(LL − 20) |
| Shear strength | τ = c + σ′·tanφ |
| Rankine | Ka = (1 − sinφ)/(1 + sinφ) = tan²(45 − φ/2) |
| Consolidation settlement | S = Cc·H/(1 + e0)·log[(σ′0 + Δσ)/σ′0] |
| Terzaghi/Meyerhof | qu = cNc + qNq + ½γBNγ (with shape & depth factors) |
| Darcy | v = k·i; Q = k·i·A |
Hydraulics
| Topic | Formula |
|---|---|
| Continuity | Q = A·V |
| Bernoulli | z + p/γ + V²/2g = constant (+ losses) |
| Manning | V = (1/n)·R^⅔·S^½ (SI) |
| Darcy–Weisbach | hf = f·(L/D)·V²/2g |
| Hazen–Williams | hf = 10.67·L·Q^1.852 / (C^1.852·D^4.87) |
| Froude number | Fr = V/√(g·D_h) |
| Rational method | Q = C·i·A/360 (m³/s, mm/h, ha) |
Surveying
| Topic | Formula |
|---|---|
| Rise & fall check | ΣBS − ΣFS = ΣRise − ΣFall = Last RL − First RL |
| Latitude / departure | L·cosθ / L·sinθ |
| Bowditch correction | e × (line length / perimeter) |
| Curve | T = R·tan(Δ/2); L = πRΔ/180; δ (min) = 1718.87·c/R |
| Tacheometry | D = K·s·cos²θ + C·cosθ |
| Curvature & refraction | c = 0.0673·d² (m, d in km) |
Highways & traffic
| Topic | Formula |
|---|---|
| Stopping sight distance | SSD = 0.278Vt + V²/[254(a/9.81 ± G)] |
| Minimum radius | R = V²/[127(e + f)] |
| Greenshields | q = vf·k·(1 − k/kj); qmax = vf·kj/4 |
| Webster cycle | Co = (1.5L + 5)/(1 − Y) |
| CBR thickness | t = √[P(1/(8.1CBR) − 1/(pπ))] (in, lb, psi) |
Estimation (Pakistani practice)
| Topic | Formula |
|---|---|
| Dry volume of concrete | wet volume × 1.54 |
| Dry volume of mortar | wet volume × 1.33 |
| Cement bag | 50 kg = 1.25 cft (0.0347 m³) |
| Bricks | 13.5 bricks per cft of 9″ masonry (9″×4½″×3″) |
| Steel weight | d²/162.2 kg/m (d in mm) |
| Land | 1 marla = 272.25 sq ft (225 in many societies); 1 kanal = 20 marla; 1 acre = 8 kanal |
Calculators
Every formula above has a free calculator in our engineering tools.
Need an engineer for a real project?
Design, testing, supervision and construction across AJK & Punjab.