How this instrument works
A lead screw turns rotation into thrust by trading angle for distance. Every full turn, the motor's shaft sweeps through 2π radians while doing work equal to 2πT; that same turn advances the nut riding the screw by one pitch length, so the nut does work F × pitch against whatever it is pushing. Setting output work against input work, scaled by how much friction in the threads and bearings steals along the way, gives F = 2πT·η ⁄ pitch. Notice what is absent: rotational speed. Because both work terms are counted per revolution rather than per second, the RPM that produced them cancels out — a motor spinning at 30 rpm and one at 3,000 rpm deliver identical thrust for the same torque, pitch and efficiency, differing only in how fast the actuator travels.
Automation and mechatronics engineers reach for this relation constantly, usually while picking a stepper or servo motor to pair with a screw for a specific job — raising a camera slider, closing a valve gate, ejecting a part from an injection mould, driving a lab jack under a fixed load. The torque figure comes off the motor's datasheet; the pitch comes off the screw's part number; efficiency is the one number that has to be estimated or measured, because it folds together thread friction, preload drag and bearing losses that no simple geometry predicts.
The efficiency term hides real engineering history. Acme and trapezoidal lead screws, cut with a shallow thread angle, typically run 30 to 50 percent efficient — wasteful, but that same friction makes them self-locking, holding a raised load with the motor off and no brake fitted. Ball screws swap sliding thread contact for recirculating ball bearings and routinely clear 90 percent, moving the same load with a far smaller motor, but they back-drive freely and need a brake or a worm stage to hold position unpowered. Picking the wrong family for the job is a common and expensive mistake, not a rounding error.
- Enter the motor's rated torque into Motor torque, choosing Nm, inlb or ftlb to match the figure on its datasheet.
- Enter Lead screw pitch, mm ⁄ rev — the distance the nut travels in one full turn, not the crest-to-crest thread spacing on a multi-start screw.
- Enter Mechanical efficiency, % — around 30–50 for an Acme or trapezoidal screw, 85–95 for a ball screw, or a value measured on your own hardware.
- Read Linear force output, switching between N, kN and lbf to match how the actuator's load is rated.
- To check a trade-off, halve the pitch and watch force exactly double — the same motor now pushes harder but the actuator crawls at half the linear speed.
Worked example — 2 N·m through an 85%-efficient, 2 mm screw
A stepper motor rated at 2 N·m of holding torque drives a ball screw with a 2 mm pitch and a manufacturer-quoted 85% mechanical efficiency. Convert the pitch to metres first: 2 mm becomes 0.002 m. Then apply the formula: F = 2π × 2 × 0.85 ⁄ 0.002 = 10.681415 ⁄ 0.002 = 5,340.71 N. That is roughly 5.34 kN of thrust, or about 545 kilograms-force, from a motor small enough to hold in one hand — the pitch is doing the heavy lifting, quite literally, by packing a large mechanical reduction into one turn of the screw.
Swap that 2 mm pitch for a 4 mm one, keeping torque and efficiency unchanged, and thrust is cut exactly in half: F = 2π × 2 × 0.85 ⁄ 0.004 = 2,670.35 N. The coarser thread lets the nut travel twice as far per turn, so it moves the actuator twice as fast for the same shaft speed, but each newton now has to be earned with half as much mechanical advantage. Force and speed trade against each other through the pitch, one for one, every time.
Questions
Why doesn't the motor's RPM appear anywhere in this formula?
Because the formula balances work per revolution, not power per second, and the revolution count cancels from both sides of that balance. Torque, pitch and efficiency alone fix how much force the screw delivers; RPM only decides how quickly the actuator covers ground once it's moving. A slow-turning motor and a fast one sharing the same torque, pitch and efficiency push with identical force.
What efficiency figure should I use if the datasheet doesn't list one?
As a starting estimate, use 30–50% for a plain Acme or trapezoidal lead screw and 85–95% for a ball screw — the two families differ mainly in whether the nut slides or rolls against the thread. Treat either figure as provisional; measured efficiency on real hardware runs lower with age, dirt or dry lubrication, so retest under load whenever the answer matters.
Is the pitch field asking for thread pitch or lead?
It wants lead — the axial distance the nut moves in one complete turn, which is what the mm ⁄ rev label means. On an ordinary single-start screw, lead and thread pitch are the same number, but a multi-start screw's lead equals pitch multiplied by the number of starts. Entering the smaller thread-pitch figure by mistake on a multi-start screw understates the force and overstates the actuator's travel speed.
What does entering zero for Motor torque give me?
Exactly zero force output, whatever the pitch or efficiency — a stalled or unpowered motor cannot push through the screw at all. It's a useful sanity check: if the result field ever reads a nonzero force with zero torque entered, something in the input has been mistyped rather than the physics behaving oddly.
Does a higher force reading mean the screw can hold that load once the motor stops?
Not necessarily. This formula gives the force the motor can actively push with while running; whether the screw holds that load unpowered depends on self-locking, a separate property set by thread angle and friction. Low-efficiency Acme screws typically self-lock and hold; efficient ball screws typically back-drive and need a brake, no matter how large a force this calculator returns.