About the Linear Actuator Force Calculator
A linear actuator must overcome the forces resisting the motion of whatever it pushes, pulls, or lifts. For a load moving along a straight path tilted at an angle θ from horizontal, gravity contributes a component along the direction of travel (m·g·sin θ) and a component pressing the load into its guide or track (m·g·cos θ), which sliding friction resists with a force of μ·m·g·cos θ. Adding these gives the general force equation F = m·g·(sin θ + μ·cos θ), which covers horizontal sliding (θ = 0°), vertical lifting (θ = 90°), and any ramp or hinge angle in between. This calculator applies that equation and adds a safety margin so you can size an actuator with confidence.
Deriving the force equation
Newton's second law states that a net force accelerates a mass: F = ma. For an actuator moving a load at a slow, roughly constant speed, acceleration is negligible, so the actuator force only needs to balance gravity's pull and friction's resistance along the direction of travel. Splitting the load's weight (m·g) into components parallel and perpendicular to the travel direction gives a parallel component of m·g·sin θ — the part directly opposing motion up an incline — and a perpendicular (normal) component of m·g·cos θ, the part pressing the load against its rails or track. Kinetic friction opposes motion with a force equal to the coefficient of friction (μ) times that normal force: μ·m·g·cos θ. Adding the two resisting components gives the total force an actuator must produce: F = m·g·(sin θ + μ·cos θ).
Choosing angle, friction, and safety factor
The angle θ is measured from horizontal along the actuator's direction of travel — use 0° for a purely horizontal push or pull, such as sliding a drawer or gate, 90° for a straight vertical lift, and the ramp or hinge angle for anything in between, such as tilting a solar panel or opening a hatch. The friction coefficient μ depends on the materials and bearings involved: well-lubricated linear rails or ball screws are often in the 0.05-0.15 range, while dry sliding contact between metal and plastic can run 0.3-0.6 or higher. Because real installations add unmodeled effects — acceleration at the start and end of the stroke, static friction (stiction) that can exceed kinetic friction, temperature effects, and load variation over the actuator's lifetime — manufacturers commonly recommend sizing the actuator to 20-30% above the calculated ideal force, entered here as the safety factor.
Real-world applications
This model applies directly to common actuator jobs: raising a vertical gate or barrier (θ = 90°, minimal friction), sliding a horizontal drawer or platform (θ = 0°, friction-dominated), and opening a tilted hatch, awning, or solar tracker (θ between 0° and 90°). For loads that pivot on a hinge rather than sliding in a straight line, the actuator force also depends on the mounting geometry — the lever arm length and attachment angle — which this straight-line model does not capture; for hinged loads, a torque-based calculation is more accurate.