Power Number & Impeller Torque Calculator
How to use: Select an impeller type and fluid, enter dimensions and RPM. The calculator shows power number (Np), shaft power, torque, P/V and a motor sizing recommendation. Enable gassing to see the power drop under aeration.
Impeller Type
Fluid Preset
Impeller Diameter (m) ?
RPM (rev/min)
Fluid Density (kg/m³) ?
Dynamic Viscosity (Pa·s) ?
Vessel Diameter (m) ?
Number of Impellers ?
Aeration (gassed power correction)
Motor Sizing Parameters
Gearbox Efficiency (%)
Safety Factor ?
0.00
W
Ungassed Shaft Power (P0 = Np ρ N³ D&sup5;)
—
Power Number (Np)
—
Reynolds Number
—
Torque (N·m)
—
Tip Speed (m/s)
—
P/V (W/m³)
—
P/V (kW/m³)

Motor Sizing Recommendation

Shaft power (ungassed)—
After gearbox losses—
With safety factor—
Recommended motor (IEC) —

Power Number Chart (Np vs Re)

Power & Torque vs RPM

Impeller Comparison at Current Conditions

ImpellerNpPower (W)Torque (N·m)P/V (W/m³)Motor (kW)

Scale-Up at Constant P/V

ScaleT (m)D (m)RPMRePower (W)Torque (N·m)Tip Speed (m/s)

Full Results

ParameterValueUnit

Turbulent Power Numbers Reference

Impeller TypeNp (turbulent)NQ (flow)Typical D/TApplication
Rushton Turbine (6-blade)5.00.720.33Gas dispersion, high shear
Pitched-Blade Turbine (45°)1.270.790.33–0.50Blending, solids suspension
Marine Propeller (3-blade)0.350.500.25–0.40Low shear, axial flow
Hydrofoil (Lightnin A315)0.750.560.35–0.50Cell culture, shear-sensitive
Lightnin A3200.640.600.35–0.50Down-pumping axial
Ekato Intermig0.350.800.60–0.70Large-scale blending
Elephant Ear (up-pumping)1.600.850.33–0.50Gas dispersion + blending

Standard IEC Motor Sizes (kW)

0.12 · 0.18 · 0.25 · 0.37 · 0.55 · 0.75 · 1.1 · 1.5 · 2.2 · 3.0 · 4.0 · 5.5 · 7.5 · 11 · 15 · 22 · 30 · 37 · 45 · 55 · 75 · 90 · 110 · 132 · 160 · 200

About Power Number and Impeller Power Calculations

The power number (Np) is the central dimensionless group for impeller power calculations in stirred-tank bioreactors. Defined as Np = P/(ρN³D&sup5;), it relates shaft power draw to fluid density, impeller speed and diameter. In the turbulent regime (Re > 10,000), Np is constant for a given impeller geometry, making it the key lookup value for motor sizing. This calculator uses published Np vs Re correlations from Hemrajani & Tatterson and the classic Rushton et al. dataset to compute power from first principles, then sizes the drive motor using IEC standard ratings with gearbox efficiency and safety-factor corrections.

Gassed power is always lower than ungassed power because gas cavities form behind impeller blades, reducing effective drag. The gassed-to-ungassed power ratio (Pg/P0) depends on the aeration number Na = Qg/(ND³) and the Froude number. Rushton turbines show the largest power drop (Pg/P0 ≈ 0.4 at 1 vvm), while down-pumping hydrofoils retain 70–90% of ungassed power. This tool estimates Pg/P0 from the aeration number and impeller type, or accepts a manual override when you have measured data. For the full Reynolds number analysis, use the companion calculator.

Power per unit volume (P/V) is the most widely used scale-up criterion for microbial fermentations. Typical ranges: 0.01–0.05 kW/m³ for mammalian cell culture, 1–5 kW/m³ for microbial fermentation, and up to 10 kW/m³ for high-viscosity mycelial processes. The scale-up table in this calculator shows how RPM, torque, tip speed and motor size change when P/V is held constant from bench to production scale. Combined with the Scale-Up Calculator and OTR & kLa Estimator, this tool completes the agitation and mixing design suite for bioreactor engineers.

Related Articles

Impeller Power Numbers
Np reference table for all impeller geometries
Reynolds Number in Bioreactors
Calculation, flow regimes and worked examples
Scale-Up Criteria Compared
Constant P/V vs tip speed vs Re vs kLa
Bioreactor Sizing Guide
How to calculate the volume you need

Frequently Asked Questions

What is the power number (Np) of an impeller?

The power number (Np) is a dimensionless group defined as Np = P/(ρN³D&sup5;). In the turbulent regime (Re > 10,000), Np is constant for a given impeller geometry: Rushton turbine ≈ 5.0, pitched-blade 45° ≈ 1.27, marine propeller ≈ 0.35, hydrofoil ≈ 0.75. It determines how much power an impeller draws at a given speed and is the key parameter for motor sizing.

How do you calculate impeller shaft power?

Shaft power P = Np × ρ × N³ × D&sup5;, where Np is the power number, ρ is density (kg/m³), N is speed in revolutions per second (RPM/60), and D is diameter (m). For multiple impellers, multiply by the count. This gives ungassed power in watts. Under aeration, multiply by the Pg/P0 ratio (typically 0.3–0.7).

How does gassing reduce impeller power?

Gas cavities form behind impeller blades during sparging, reducing the effective drag area and lowering power consumption. The Pg/P0 ratio depends on the aeration number (Na = Qg/ND³) and impeller type. Rushton turbines show the largest power drop (Pg/P0 ≈ 0.4 at 1 vvm). Hydrofoils retain 70–90% of ungassed power because their blade geometry minimizes cavity formation.

How do you size a motor for a bioreactor?

Calculate ungassed shaft power, divide by gearbox efficiency (typically 0.90–0.95), then multiply by a safety factor (1.2–1.5) to account for viscosity increases and startup torque. Select the next IEC standard motor size above this value. The motor must deliver sufficient torque at the operating speed, not just match the average power requirement.

What P/V is typical for different bioprocesses?

Mammalian cell culture: 0.01–0.05 kW/m³ (very low shear). Insect cell culture: 0.05–0.2 kW/m³. Microbial fermentation (E. coli, yeast): 1–5 kW/m³. High-viscosity mycelial fermentation: 3–10 kW/m³. P/V is the most common scale-up criterion for microbial fermentations, while tip speed is preferred for shear-sensitive mammalian cultures.

What is the relationship between Np and Re?

In the laminar regime (Re < 10), Np is inversely proportional to Re: Np = KL/Re. In the transitional regime (10 < Re < 10,000), Np decreases gradually. In the turbulent regime (Re > 10,000), Np is constant and independent of Re. The Np vs Re chart is the fundamental design tool for sizing impeller drives.

Further reading