Filament Extruder Torque Calculator

Input definitions (to avoid common interpretation errors)

• Screw diameter: This calculator treats the diameter as the effective diameter of the pressurized circular cross-section used for area (A). In many builds this is closest to the barrel internal diameter (or the diameter of the melt “piston” you are effectively pressurizing). If you enter the screw OD but the pressurized area is smaller (or larger), the torque estimate will be off.
• Extrusion pressure: Use the best estimate you have for the melt pressure driving flow through the die (often near the die entrance). If you only have a force measurement at a plunger/ram or a pressure gauge at a different location, recognize that pressures can vary along the barrel and through adapters/screens.
• Drivetrain efficiency: Enter the overall mechanical efficiency from motor shaft to screw shaft (losses in gearbox, belt/chain, couplings, bearings). Typical ranges are often 60–95% depending on hardware condition and load.

How the calculation works (formulas)

The model uses a pressure-to-force conversion and then converts force to torque using the screw radius as a lever arm, with an efficiency correction.

Step 1: Cross-sectional area

The pressurized area is modeled as a circle:

Step 2: Force from pressure

Pressure times area gives axial force:

F = P · A

Step 3: Torque at the screw

A simple torque estimate uses T = F · r. The calculator then divides by drivetrain efficiency (η) to estimate required motor torque:

T_motor = (F · r) / η

Unit conversions

• Diameter d in mm → radius in meters: r = (d / 2) / 1000
• Pressure in MPa → Pa: P(Pa) = P(MPa) × 1,000,000
• Efficiency percent → fraction: η = eff% / 100

Important scaling note: because A ∝ r² and torque uses F·r, the estimate scales approximately with r³ (or diameter cubed). Small changes in diameter can change torque a lot.

Interpreting the result

The reported torque is best interpreted as a baseline running torque implied by the pressure you entered. In real extruders, the motor must usually be sized with margin for:

• Start-up and stall conditions (cold material, partially solid plugs, inconsistent feed)
• Transient pressure spikes (screen clogs, die build-up, inconsistent pellet size)
• Speed effects (some losses and required torque increase with RPM)

Practical sizing often uses a safety factor (for example, 1.5× to 3×) depending on how variable the feedstock and process are.

Worked example

Suppose you have:

• Screw (effective) diameter: 20 mm
• Extrusion pressure: 5 MPa
• Drivetrain efficiency: 80% (η = 0.8)

1) Radius: r = (20/2)/1000 = 0.01 m

2) Area: A = π·r² = π·(0.01)² ≈ 3.1416×10⁻4 m²

3) Pressure in Pa: P = 5×10⁶ Pa

4) Force: F = P·A ≈ 5×10⁶ · 3.1416×10⁻4 ≈ 1570.8 N

5) Screw torque: T_screw = F·r ≈ 1570.8 · 0.01 ≈ 15.7 N·m

6) Motor torque with efficiency: T_motor = T_screw/0.8 ≈ 19.6 N·m

So, you’d look for a motor+gearbox combination that can deliver roughly 20 N·m continuous at your target screw RPM, then apply an additional margin for start-up and pressure spikes.

Typical pressure ranges (very approximate)

Extrusion pressure depends strongly on melt temperature, viscosity, die/nozzle geometry (length, taper, screen packs), and throughput. The ranges below are ballpark values people may see in small-scale filament extrusion, not guarantees.

If you can measure force (for example, with a load cell on a plunger test) you can estimate pressure using P = F/A and then feed that pressure into this calculator.

Limitations and assumptions (read before using for motor selection)

• Not a full screw-extrusion model: Real screw torque includes viscous shear on screw flights, drag flow, leakage, mixing elements, and frictional effects. This calculator only uses a pressure-based approximation.
• Pressure definition uncertainty: “Extrusion pressure” can mean die entrance pressure, barrel pressure, or a measured pressure at a gauge port—these may differ significantly.
• Effective area simplification: The model uses a circular area derived from the entered diameter. If your pressurized area is not well represented by that circle, results can be materially wrong.
• Efficiency is load-dependent: Gearbox and belt/chain efficiency changes with torque, speed, lubrication, and alignment. Treat efficiency as an estimate.
• No dynamic effects: Does not include start-up torque, acceleration torque, pressure pulsation, or jamming events.
• No thermal/viscosity coupling: Melt temperature and viscosity can change pressure dramatically. A small temperature drift can change the required torque more than the calculator suggests.
• Safety margin recommended: For DIY recycled feedstock (variable grind size/contamination), consider sizing the drive for higher-than-calculated torque.

References / further reading (optional)

• General polymer processing texts on screw extrusion (pressure generation, die flow, and torque contributors).
• Manufacturer datasheets for gearboxes (efficiency curves) and motors (continuous vs peak torque ratings).

Note: The pressure ranges table is illustrative and should be validated against your specific die geometry, melt temperature, and throughput.