Linear Actuator Force Calculator
Size a linear actuator: the force a load needs on a vertical, inclined or sliding path, the screw torque behind it, and the motor power to deliver it.
🔧 What is Linear Actuator Force?
Linear actuator force is the push or pull an actuator must deliver along its stroke to move a load. A linear actuator turns another form of energy, usually electrical power through a motor and a screw, into motion in a straight line. To pick one you first need the force the load demands, which is the sum of several parts: the part of the weight that acts along the direction of motion, the friction of guides or sliding surfaces, the force to accelerate the mass, and any extra force pushing back such as a spring, a seal or a process load. A safety factor is then applied on top, because real systems have shock, wear and uncertainty in the friction.
The calculation appears wherever something has to be moved on command: raising a hospital bed or a standing desk, tilting a solar panel or a TV lift, opening a hatch or a damper, pushing a gate, feeding a machine slide or lifting a platform. The geometry decides how much gravity matters. A vertical lift carries the entire weight, a horizontal slide carries only friction, and an incline is in between. The relationship is the familiar inclined plane result F = m g (sin α + μ cos α), with the angle α measured from the horizontal.
Most electric actuators use a lead screw or a ball screw, so the force at the rod is tied to the torque at the screw. The lead is the distance the nut moves in one revolution. A fine lead gives a large force from a small torque but a slow speed, and thread friction wastes part of the torque. Efficiency and self-locking both come from the thread friction compared with the lead angle. The motor then has to supply the torque at a speed that gives the wanted travel rate, so force, speed and power are linked: the output power is the thrust times the speed, and the input power is larger by the efficiency of the motor, gear stage and screw.
This calculator has three modes. Load force finds the required actuator force for a vertical, horizontal or inclined load with friction, acceleration, an extra force and a safety factor. Screw torque converts the screw force to torque, efficiency, lead angle and a self-locking check. Motor power turns the voltage, current, gearing and lead into thrust, speed and output power. The thread model covers the thread only, so collar friction, side loads, buckling of a long screw and duty cycle limits still need a separate check against the actuator data sheet.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Vertical Lift
100 kg lifted vertically, no acceleration, safety factor 1.5
Example 2 — Load on a 30 Degree Incline
50 kg, 30° slope, μ = 0.15, a = 0.5 m/s², 20 N extra opposing force, SF = 1.25
Example 3 — Horizontal Slide
200 kg on a horizontal slide, μ = 0.3, constant speed, SF = 2
Example 4 — Lead Screw Torque (Bronze Nut)
F = 5000 N, lead 5 mm, mean diameter 16 mm, μ = 0.15, 600 rpm
Example 5 — Ball Screw
F = 2 kN, lead 10 mm, mean diameter 20 mm, μ = 0.01, 300 rpm
Example 6 — 24 V Geared Motor and Lead Screw
24 V, 5 A, motor 75 % at 3000 rpm, 20 to 1 gear at 85 %, 5 mm lead screw at 40 %
Example 7 — Higher Power Ball Screw Drive
48 V, 8 A, motor 85 % at 3000 rpm, 10 to 1 gear at 90 %, 10 mm lead ball screw at 90 %
❓ Frequently Asked Questions
🔗 Related Calculators
How do I calculate the force a linear actuator needs?
Add the gravity component along the motion m g sin(alpha), the friction m g mu cos(alpha), the inertia m a and any extra opposing force, then multiply by a safety factor. For 100 kg lifted vertically with a factor of 1.5 that is 980.7 N times 1.5, or 1471 N.
What force is needed to push a load up an incline?
F = m g (sin(alpha) + mu cos(alpha)) plus any acceleration and extra force. A 50 kg load on a 30 degree slope with mu = 0.15 needs 245.2 N for gravity and 63.7 N for friction, so 308.9 N before acceleration and the safety factor.
How much safety factor should I use for an actuator?
A factor of 1.5 to 2 is a common starting point for ordinary loads. Use more for shock loads, long duty cycles, uncertain friction or loads that could injure someone if the actuator stalls. The factor multiplies the whole load force.
What is the torque needed for a lead screw?
For a square thread, T = (F d_m / 2) (l + pi mu d_m) / (pi d_m - mu l), where F is the axial force, d_m the mean thread diameter, l the lead and mu the thread friction. For 5000 N, a 5 mm lead, 16 mm diameter and mu = 0.15 the torque is 10.13 N m.
How do I find lead screw efficiency?
Efficiency is eta = F l / (2 pi T), the ideal torque F l / (2 pi) divided by the actual torque. It equals l (pi d_m - mu l) / (pi d_m (l + pi mu d_m)). The 5 mm lead example above is 39.3 percent efficient, while a ball screw can reach about 94 percent.
When is a lead screw self-locking?
When the thread friction mu is at least tan of the lead angle, which is l / (pi d_m). Then the lowering torque is positive and the screw holds the load by itself. The calculator reports the lowering torque and a yes or no.
How does the lead of the screw change force and speed?
At constant motor power a finer lead gives more thrust and less speed. Thrust is F = 2 pi eta T / l, speed is l n / 60, and their product is the output power. The chart in the motor mode shows this as a hyperbola.
How do I find the linear speed of an actuator?
Linear speed equals the lead times the screw speed in revolutions per second, v = l n / 60. A 5 mm lead at 600 rpm moves 50 mm/s, and the same lead after a 20 to 1 reduction from a 3000 rpm motor (150 rpm) moves 12.5 mm/s.
What motor power does a linear actuator need?
Mechanical output power is thrust times speed, P = F v. Divide by the overall efficiency (motor times gear times screw) to get the electrical input. A 2448 N, 12.5 mm/s actuator delivers 30.6 W but needs 120 W from a 24 V, 5 A supply at 25.5 percent overall efficiency.
Does this include the friction of the thrust bearing or collar?
No. The screw torque formula covers only the thread. A collar or thrust bearing adds a friction torque equal to its friction coefficient times the force times its mean radius, so add it if the load bears on a thrust washer.
Is the actuator force the same for raising and lowering?
No. When lowering, gravity helps and the friction term changes sign, so the force can be small or even negative, which means the load drives the actuator. Size the actuator for the raising case and check that the brake or screw can hold the load while lowering.