Fan static pressure calculator (duct pressure and fan power)
The step after duct sizing. Enter airflow, size, length and ΣK for each section from the fan to the farthest outlet, add filter and coil losses and a margin, and get fan static and total pressure, shaft power and a motor size.
Calculation basis
Each section adds friction and fitting losses; equipment losses are added and the margin applied to get fan total pressure. Static pressure is total minus outlet velocity pressure.
| Item | Equation | Notes · basis |
|---|---|---|
| Air density | ρ = p / (R_da · T) | Dry air ideal gas, R_da = 287.042 J/(kg·K). Moisture ignored (about 1 % effect) |
| Friction loss | Δp_f = R · L, R = (f / D) · ρV²/2 | f from Colebrook (laminar 64/Re), the same function as the duct size calculator; roughness from ASHRAE material categories |
| Rectangular equivalent diameter | D_e = 1.30 (a·b)^0.625 / (a + b)^0.25 | Huebscher equation, used for friction only; velocity pressure uses the actual velocity Q/(ab) |
| Fitting loss | Δp_K = ΣK · ρV²/2 | ΣK in multiples of velocity pressure, from the table below or the ASHRAE Duct Fitting Database |
| Fan total and static pressure | P_t = (Σ Δp + Σ Δp_e) × (1 + m), P_s = P_t − Pv₁ | m = margin, Pv₁ = velocity pressure of section 1 (fan outlet duct) |
| Power | P_a = Q · P, P_shaft = P_a / η, P_motor ≥ P_shaft × (1 + α) | Q in m³/s; P is P_t or P_s to match the efficiency basis. The motor is rounded up to a standard rating |
Fitting loss coefficients (reference values)
Typical reference values only. Real K depends strongly on geometry, aspect ratio and flow ratio, so design with the ASHRAE Duct Fitting Database, SMACNA data or maker values. Branch tees vary from about 0 to above 1 with flow ratio and are left out.
| Fitting | K (reference) | Basis and notes |
|---|---|---|
| Duct exit to a large space | 1.0 | Momentum balance: the whole outlet velocity pressure is lost. High confidence |
| Sharp-edged entry, flush with a wall | 0.5 | Typical value in Idelchik and ASHRAE entry fittings. High confidence |
| Sudden expansion (A₁ to A₂) | (1 − A₁/A₂)² | Borda-Carnot, based on upstream (A₁) velocity pressure. High confidence |
| Smooth round 90° elbow, r/D 1.5 | 0.15 | Typical ASHRAE round elbow value (about 0.2 at r/D 1.0). Medium confidence |
| Rectangular mitred 90° elbow, no vanes, H/W 1 | 1.2 | Typical ASHRAE rectangular elbow value; turning vanes reduce it a lot. Medium confidence |
| Butterfly damper, fully open | 0.2 | Typical ASHRAE damper value; varies with blade thickness and design. Medium confidence |
Example
Air at 20 °C and 101.325 kPa, galvanized steel (ε 0.09 mm). The three sections below (calculator defaults) plus a medium filter 150 Pa, chilled water coil 200 Pa and diffuser 30 Pa (Fill example values), margin 10 %, total efficiency 60 %, motor efficiency 90 % and margin 15 %.
| Seg. | Size mm | Flow CMH | Velocity m/s | Velocity pressure Pv Pa | Friction R Pa/m | Sum of fitting loss coefficients ΣK | Section loss Pa |
|---|---|---|---|---|---|---|---|
| 1 | 800 × 400 | 12,000 · L 20 m | 10.42 | 65.3 | 1.94 | 0.5 | 71.5 |
| 2 | 600 × 400 | 8,000 · L 15 m | 9.26 | 51.6 | 1.76 | 1.2 | 88.4 |
| 3 | Ø400 | 3,000 · L 10 m | 6.63 | 26.5 | 1.16 | 1.5 | 51.3 |
| Item | Pa | mmAq |
|---|---|---|
| Duct loss (friction + fittings) | 211.3 | 21.5 |
| Medium filter | 150.0 | 15.3 |
| Chilled water coil | 200.0 | 20.4 |
| Supply diffuser | 30.0 | 3.1 |
| Subtotal | 591.3 | 60.3 |
| Margin 10 % | 59.1 | 6.0 |
| Fan total pressure P_t | 650.4 | 66.3 |
| Outlet velocity pressure Pv₁ (subtract) | −65.3 | −6.7 |
| Fan static pressure P_s | 585.1 | 59.7 |
Fan total pressure 650.4 Pa, static pressure 585.1 Pa, shaft power 3.61 kW, suggested motor 5.5 kW.
Limits
This calculator only sums the entered sections as one series path. It does not search the index run of a branched system, select fan types or curves (operating point), or calculate noise. Enter system effects (fan inlet and outlet connections) as ΣK or equipment losses.
Sources
- ASHRAE Handbook Fundamentals (SI), Duct Design: Darcy-Weisbach, Colebrook, Huebscher, duct material roughness, fitting loss coefficients
- ASHRAE Duct Fitting Database; SMACNA HVAC Systems Duct Design
- I. E. Idelchik, Handbook of Hydraulic Resistance: entry and sudden expansion (Borda-Carnot)
- IEC 60072-1: rated output series of rotating electrical machines
Frequently asked questions
What is the difference between fan static and total pressure?
Total pressure is static plus velocity pressure. The sum of all duct losses is the fan total pressure; subtracting the fan outlet velocity pressure (ρV²/2) gives the fan static pressure. Efficiency also comes as total or static, so compute power on the same basis as the maker data.
How do I calculate duct pressure loss?
Add friction R·L and fitting loss ΣK·ρV²/2 for each section. R comes from Darcy-Weisbach with the Colebrook friction factor; rectangular ducts use the Huebscher equivalent diameter. The section losses along the path to the farthest outlet plus filter and coil losses are what the fan must overcome.
How is fan power calculated?
Air power P_a = Q × P (Q in m³/s, P in Pa, result in W), and shaft power is P_a ÷ fan efficiency. Example: 3.33 m³/s × 650 Pa = 2.17 kW; at 60 % efficiency the shaft power is 3.61 kW. The motor adds a margin (for example 15 %) and rounds up to a standard rating (5.5 kW here).
Last updated 2026-10-19.