Compute the motor torque required to drive a linear axis (belt/pulley or lead screw) from load mass, effective radius, and target acceleration.
This calculator estimates the motor torque needed to drive a linear axis — a belt-and-pulley stage, a lead-screw stage, or similar — from the load mass, the effective radius converting linear force to rotational torque, and the target acceleration.
The tool computes three force components: the force needed to accelerate the mass (F = m × a), an estimated friction force (a simple coefficient × weight approximation), and, if the axis lifts vertically, the gravity force needed just to hold the load up. These are summed into a total force, converted to torque by multiplying by the effective radius (pulley radius, or lead screw radius derived from lead ÷ 2π), and then multiplied by a safety factor to account for real-world losses (gearbox efficiency, unmodeled friction, inertia of the drivetrain itself) that a simple hand calculation does not fully capture.
A safety factor of 1.5-2.0× is a reasonable starting point for a first-pass estimate. Higher-precision designs should refine this with the actual drivetrain's efficiency rating, the reflected inertia of belts/screws/couplings, and a proper motion profile (trapezoidal or S-curve velocity profile) rather than a single acceleration figure — this calculator is a sizing starting point, not a substitute for the manufacturer's selection software once you've narrowed down candidate motors.
A computed torque requirement doesn't by itself tell you whether to choose a stepper or a servo motor — that decision depends more on load predictability and required fault detection than on the torque number alone. See our companion article on servo vs. stepper motion control for the full decision framework: steppers for predictable, well-characterized loads where occasional undetected step loss is tolerable; servos for variable loads or where guaranteed, fault-detected positioning is required.
No — this calculator computes the torque required directly at the load-facing pulley or lead screw shaft. If your design uses a gearbox or belt reduction between the motor and that shaft, divide the result by the gear ratio (and account for gearbox efficiency, typically 85-95% for a quality planetary gearbox) to get the torque required at the motor shaft itself.
An estimated friction coefficient (0.1-0.2 is a reasonable starting range for linear guides and bearings) is far better than ignoring friction entirely, since friction is a real, continuous load the motor must overcome even at constant velocity, not just during acceleration. Refine this value with manufacturer bearing/rail friction specifications once you have a specific hardware selection.
For a rotational joint, replace the linear force calculation with the joint's actual load torque directly: the torque needed to support and accelerate the arm and its payload at that specific joint, which depends on the arm's length and mass distribution (its moment of inertia) rather than a simple radius conversion. This calculator's force-and-radius model is built for linear axes; a full robot joint sizing calculation requires the arm's specific inertia properties.