What is stepper motor torque
Stepper motor torque is the rotational force a stepper motor produces at its output shaft, measured in Newton-centimeters (N-cm) or ounce-inches (oz-in). It determines whether a motor can move a given load without stalling, which is the point where the motor loses synchronization with its drive pulses and stops moving reliably. Choosing the right motor torque is one of the most important decisions when designing a linear motion system such as a CNC router, 3D printer, laser cutter, or robotic actuator.
Stepper motors are permanent magnet motors that divide a full rotation into a fixed number of discrete steps, typically 200 per revolution (1.8 degrees per step). Unlike DC motors that spin freely, steppers hold position precisely and move in controlled increments, making them ideal for applications that require accurate positioning without feedback sensors. However, this precision comes with a tradeoff: stepper motors must be sized correctly for the load, or they will skip steps, lose position, and produce poor results.
The total torque a stepper motor needs depends on three main factors. First is the load torque, which is the force required to overcome gravity (for vertical motion) or friction (for horizontal motion) and translate that force through a lead screw mechanism. Second is the acceleration torque, which is the additional force needed to change the speed of the load and all rotating components. Third is a safety margin, typically 1.5 to 2 times the calculated torque, to account for real-world conditions like wear, misalignment, and momentary load spikes.
The relationship between the motor and the load is governed by the lead screw, which converts rotary motion into linear travel. A lead screw with a larger pitch moves the load faster per revolution but requires more torque, while a finer pitch reduces the torque requirement but also reduces maximum speed. Screw efficiency also plays a major role: ball screws achieve around 90% mechanical efficiency, while acme or trapezoidal screws operate at roughly 40% efficiency due to sliding friction, meaning the motor must produce significantly more torque to move the same load.
Understanding these relationships allows you to select from standard NEMA motor sizes with confidence, avoiding the common mistake of either oversizing the motor (adding unnecessary cost and weight) or undersizing it (causing stalling and lost steps during operation).
How torque is calculated
This calculator uses standard mechanical engineering formulas to determine total required torque.
**Load Torque** represents the steady-state force needed to keep the load moving:
\`\`\` Load Torque = (Force x Lead) / (2 x pi x Efficiency) \`\`\`
Where Force depends on the direction of travel: - **Vertical motion:** Force = Mass x g (full gravitational force, 9.81 m/s squared) - **Horizontal motion:** Force = Mass x g x Friction Coefficient (only friction needs to be overcome)
**Acceleration Torque** is the additional torque needed to change speed:
\`\`\` Angular Acceleration = Linear Acceleration x (2 x pi / Lead) Reflected Inertia = Mass x (Lead / (2 x pi))^2 Acceleration Torque = Total Inertia x Angular Acceleration \`\`\`
The load inertia is "reflected" back to the motor shaft through the lead screw ratio. A fine-pitch screw reduces reflected inertia (making it easier to accelerate) but also reduces speed.
**Total Required Torque** combines both components with a safety margin:
\`\`\` Total Torque = (Load Torque + Acceleration Torque) x Safety Factor \`\`\`
A safety factor of 1.5x is standard for most applications. Use 2.0x or higher for systems that experience shock loads, must operate reliably for extended periods, or are safety-critical.
NEMA motor sizes reference
NEMA (National Electrical Manufacturers Association) defines standard frame sizes for stepper motors. The NEMA number refers to the faceplate dimension in tenths of an inch.
- **NEMA 17** (42mm frame): Holding torque up to approximately 40 N-cm (56 oz-in). The most common motor in desktop 3D printers (such as the Ender 3 and Prusa i3), small CNC routers, and lightweight pick-and-place machines. Compact and affordable. - **NEMA 23** (57mm frame): Holding torque up to approximately 200 N-cm (283 oz-in). Used in mid-range CNC machines, larger laser cutters, plasma tables, and medium-duty automation systems. Offers significantly more power while remaining reasonably compact. - **NEMA 34** (86mm frame): Holding torque up to approximately 1200 N-cm (1699 oz-in). Required for full-size CNC mills and routers, large format machines, and industrial automation. These motors are heavy and require more powerful drivers. - **NEMA 42** (110mm frame) and larger: For extreme torque requirements exceeding NEMA 34 capacity. At this level, servo motors are often a better choice as they maintain torque at higher speeds.
Keep in mind that a stepper motor's rated holding torque is measured at zero speed. Actual available torque drops as RPM increases, following the motor's torque-speed curve. Always check that your motor can deliver sufficient torque at your operating speed, not just at standstill.
How to use this calculator
1. Enter the total load mass in kilograms, including the weight of the carriage, workpiece, and any mounted tooling. 2. Select whether the axis moves horizontally or vertically. Vertical axes must overcome full gravitational force, while horizontal axes only need to overcome friction. 3. For horizontal motion, set the friction coefficient. Use 0.1 for linear guide rails, 0.15 to 0.2 for V-slot wheels, or 0.3 or more for slide bearings. 4. Enter your lead screw pitch in millimeters. This is the linear distance traveled per full revolution. Common values are 2mm, 4mm, and 8mm for T8 lead screws. 5. Select your screw type. Ball screws are more efficient but cost more. Acme and trapezoidal screws are affordable but require more motor torque. 6. Enter your desired maximum travel speed in millimeters per second and the acceleration rate in millimeters per second squared. 7. Adjust the safety factor slider. Start at 1.5x for typical use and increase to 2.0x or higher for demanding applications. 8. Review the total required torque and the recommended NEMA motor size. Check the torque breakdown to understand where the demand comes from.
Common applications
- **CNC routers and mills**: Sizing X, Y, and Z axis motors for cutting wood, aluminum, or plastics. The Z axis typically needs the most torque because it fights gravity. - **3D printers**: Selecting motors for the print head carriage and bed platform. Most FDM printers use NEMA 17 motors, but large-format printers may need NEMA 23. - **Laser cutters and engravers**: Lightweight gantry systems that prioritize speed over force. Low mass and ball screws keep torque requirements minimal. - **Pick-and-place machines**: Precise, repeatable positioning with moderate loads. Acceleration performance matters more than sustained load torque. - **Laboratory automation**: Sample handling, microscope stages, and fluid dispensing systems where accuracy and smooth motion are paramount. - **Robotics and actuators**: Linear actuators for robotic arms, grippers, and positioning systems that require calculated torque margins for reliable operation.
FAQs
Q: What happens if I choose a motor that is too small? A: An undersized motor will stall under load, meaning it loses synchronization with the drive pulses and skips steps. This causes positioning errors that accumulate over time. In a CNC machine, this results in ruined workpieces. In a 3D printer, it causes layer shifts. The motor may also overheat and potentially damage itself or its driver.
Q: Why does an acme screw need so much more motor torque than a ball screw? A: Acme screws use sliding contact between the screw threads and the nut, which creates substantial friction. Only about 40% of the motor's torque actually moves the load, while 60% is lost to friction and heat. Ball screws use recirculating ball bearings between the threads, achieving roughly 90% efficiency. For the same load, an acme screw requires more than twice the motor torque compared to a ball screw.
Q: Should I always choose the largest motor available for maximum safety margin? A: No. Oversized motors add unnecessary weight, cost, and power consumption. A heavier motor also increases the inertia of the system, which can actually reduce acceleration performance. The goal is to match the motor to the application with an appropriate safety factor, typically 1.5 to 2 times the calculated requirement.
Q: How does microstepping affect torque? A: Microstepping divides each full step into smaller increments for smoother motion, but it reduces the available torque per microstep. At 16x microstepping, the incremental torque per microstep is only about 10% of the full-step torque. This calculator estimates full-step holding torque requirements. If you plan to use high microstepping ratios, consider adding extra safety margin.
Q: What is the difference between holding torque and running torque? A: Holding torque is the maximum torque the motor can produce at zero speed (standstill). Running torque, also called dynamic torque, is the torque available while the motor is spinning. Running torque decreases as speed increases, following the motor's torque-speed curve. This calculator uses holding torque as the reference because motor datasheets specify this value. Always verify that your motor's torque-speed curve provides sufficient torque at your operating RPM.
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