ARE 5.0 Key Formulas
This cheat sheet compiles the essential formulas you need for the ARE 5.0 exam across all divisions. Bookmark this page and review regularly. See related study guides for PA, PDD, and PjM.
Occupant Load & Egress
| Formula | Equation | Notes |
|---|
| Occupant load | Floor area ÷ Occupant load factor | Use gross or net per IBC Table 1004.5 |
| Exit width (stairs) | OL × 0.3" per occupant | With sprinklers: OL × 0.2" |
| Exit width (other egress) | OL × 0.2" per occupant | With sprinklers: OL × 0.15" |
| Number of exits | 1–500 OL = 2 exits; 501–1000 = 3; 1001+ = 4 | Some occupancies require 2 exits at lower thresholds |
| Exit separation (2 exits) | 1/2 diagonal distance | 1/3 diagonal with sprinklers |
See the full Egress Requirements topic for detailed examples.
Structural Formulas
| Formula | Equation | Application |
|---|
| Stress | f = P / A | Axial stress (psi) = Force / Area |
| Strain | ε = ΔL / L | Deformation / Original length |
| Modulus of Elasticity | E = f / ε | Stress / Strain (material stiffness) |
| Bending moment (uniform load, simple span) | M = wL² / 8 | Max moment at midspan |
| Bending moment (point load, midspan) | M = PL / 4 | Max moment at load point |
| Deflection (uniform load, simple span) | Δ = 5wL⁴ / 384EI | Max deflection at midspan |
| Shear (uniform load, simple span) | V = wL / 2 | Max shear at supports |
| Section modulus | S = I / c | Moment of inertia / Distance to extreme fiber |
| Bending stress | fb = M / S | Must be ≤ allowable bending stress |
HVAC Formulas
| Formula | Equation | Application |
|---|
| Heat transfer | Q = U × A × ΔT | BTU/hr through building envelope |
| R-value / U-factor | U = 1 / Rtotal | R = thermal resistance; U = thermal transmittance |
| Sensible heat | Qs = 1.08 × CFM × ΔT | Sensible cooling/heating load (BTU/hr) |
| Total heat | Qt = 4.5 × CFM × Δh | Total heat with enthalpy difference (BTU/hr) |
| Ventilation rate | Vbz = Rp × Pz + Ra × Az | ASHRAE 62.1 breathing zone outdoor air |
| COP | COP = Output BTU / Input BTU | Coefficient of Performance (heat pumps) |
| EER | EER = BTU/hr ÷ Watts | Energy Efficiency Ratio (cooling) |
| SEER | Seasonal average EER | Higher = more efficient |
Stormwater & Site
| Formula | Equation | Application |
|---|
| Rational method | Q = C × I × A | Q = peak runoff (cfs); C = runoff coefficient; I = rainfall intensity (in/hr); A = area (acres) |
| Runoff coefficients | Pavement: 0.85–0.95; Roofs: 0.75–0.95; Lawns: 0.10–0.35; Woods: 0.05–0.25 | Higher C = more runoff |
| Slope/gradient | S = rise / run × 100% | Min site drainage: 1–2% away from building |
| Cut & fill balance | Vcut = Vfill (ideally) | Minimize earthwork hauling costs |
Lighting
| Formula | Equation | Application |
|---|
| Foot-candle level | fc = Lumens / Area (sf) | Average illuminance on work plane |
| Zonal cavity method | N = (fc × A) / (Lumens/lamp × CU × LLF) | Number of luminaires needed |
| Daylight factor | DF = (Ein / Eout) × 100% | Interior vs exterior illuminance ratio |
| Watts per SF (LPD) | LPD = Total watts / Area (sf) | Lighting power density per energy code |
Plumbing Fixture Count
| Step | Procedure |
|---|
| 1 | Determine occupancy type and occupant load |
| 2 | Look up IPC Table 403.1 for fixture ratios per occupant |
| 3 | Apply male/female split (typically 50/50 unless specified) |
| 4 | Calculate WC, lavatories, drinking fountains per gender |
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