Linear Actuator Force Calculator (push force for a load on a slope)

Understanding the linear actuator force calculator — concept and principle

This calculator works out the push force a linear actuator needs to move a load along a straight path tilted at any angle, including gravity, guide friction, acceleration and a safety factor. It also gives the mechanical power at the chosen speed. It helps when choosing electric, pneumatic or hydraulic actuators for lifts, slides, hatches and automation.

Add the slope component of weight, the friction and the force to accelerate, then size with a margin.

How it is calculated

Gravity component = m g sin θ

Friction component = μ m g cos θ

Acceleration component = m a

Required force F = m g sin θ + μ m g cos θ + m a; rated force = F × safety factor

Mechanical power = F × speed (without the safety factor)

m in kg, θ from horizontal in degrees, a in m/s², speed in mm/s; g = 9.80665 m/s².

The principle

On a slope, gravity splits into a part along the path, which the actuator must push against, and a part pressing the load onto its guide. That pressing force creates sliding friction, proportional to the friction coefficient. Getting the load moving also takes force to accelerate it. Adding the three gives the force at the start of the move; the safety factor covers uncertainty, wear and losses in the actuator.

Worked example

Default inputs: 50 kg, 30°, μ = 0.1, a = 0.5 m/s², safety factor 1.5, speed 20 mm/s.

Weight = 50 × 9.80665 = 490.3 N.
Gravity component = 490.3 × sin 30° = 245.2 N; friction = 0.1 × 490.3 × cos 30° = 42.5 N; acceleration = 50 × 0.5 = 25 N.
Force = 245.2 + 42.5 + 25 = 312.6 N, or 47.82 kgf.
With safety factor: 312.6 × 1.5 = 468.9 N.
Power = 312.6 × 0.020 = 6.25 W.

Each point is the calculator re-run with only “Load mass (kg)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Load mass (kg)	Actuator force with safety factor (N)
12.5	117.2
25	234.5
37.5	351.7
50	468.9
62.5	586.2
75	703.4
100	937.9

How to read the result

Choose an actuator whose rated dynamic force exceeds the force with safety factor, at the speed you need. A vertical lift (90°) needs the full weight plus acceleration; a horizontal slide needs only friction and acceleration. Check also the static holding force and the duty cycle.

Common mistakes

Forgetting the acceleration force for fast moves.
Mounting the actuator at an angle to the motion, as on a hinged lid, where the needed force is larger and changes along the stroke.
Ignoring side loads, which most actuators handle poorly.
Using static friction values for moving loads, or the reverse.

Keep in mind: Actuator selection must also consider side loads, duty cycle and safe holding of the load. Follow the manufacturer's data and machinery safety requirements.

Frequently asked questions

Why does the force depend on the angle?

The share of the weight along the path is m g sin θ, which grows from zero when horizontal to the full weight when vertical.

What safety factor should I use?

It depends on the application and standards; 1.5 is a common starting point, not a rule.

Does speed change the required force?

Not directly, but faster moves usually need higher acceleration, which adds force.

Why is power calculated without the safety factor?

It reflects the actual mechanical work rate at the stated force and speed.

Sources: Standard mechanics of forces on an inclined path (m g sin θ, μ m g cos θ, m a) and power P = F v

Checked 9 Nov 2026. Forces on an inclined path (weight component mg sin θ, friction μmg cos θ, inertia ma) and power P = F·v: standard formula. Standard gravity 9.80665 m/s² (exact).

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