Motor Sizing for Linear Motion Calculator + Formula, Examples & Applications
You've picked a 12V linear actuator from a spec sheet — you know the stall force. But will it actually move your load fast enough? That depends on 2 drivetrain parameters most people overlook: gear ratio and lead screw pitch. This calculator takes those 3 inputs and tells you exactly how much force you'll get at the output and how fast it'll move. We also cover the formulas, worked examples, and the engineering tradeoffs between force, speed, and efficiency so you can size your actuator with confidence.
What Is Motor Sizing for Linear Motion?
Motor sizing for linear motion means figuring out whether a DC motor and lead screw drivetrain can deliver enough force and speed for your application — before you build anything.
Simple Explanation
Think of a car's transmission. Low gear gives you pulling power but not much speed. High gear gives you speed but less torque. A linear actuator works the same way — a gearbox and lead screw convert a fast-spinning motor into a slow, powerful push or pull. The gear ratio and screw pitch determine where you land on that force-vs-speed tradeoff, and drivetrain friction always eats some of the energy along the way.
Motor Sizing for Linear Motion
🎥 Video — Motor Sizing for Linear Motion
How to Use This Calculator
This calculator handles 3 solve modes — pick the one that matches what you already know and what you need to find out.
- Choose your solve mode. Select "Output Force and Speed" if you know your drivetrain specs and want to see what the actuator delivers. Select "Required Gear Ratio" or "Required Lead Screw Pitch" if you know your target speed and need to design the drivetrain around it.
- Enter your actuator's stall force. You'll find this on the spec sheet — it's the maximum force the actuator produces at zero speed. Every mode needs this value.
- Fill in the remaining inputs. Depending on your mode, enter gear ratio, lead screw pitch, motor free-run RPM, or your target linear speed. The calculator shows only the fields relevant to your chosen mode.
- Click Calculate. The calculator applies an 80% Acme screw efficiency factor automatically and displays your results instantly.
- Use "Try Example" to see it in action. This fills in realistic default values for whichever mode you've selected — great for understanding the math before plugging in your own numbers.
Motor Sizing for Linear Motion Formula
Three formulas drive this calculator. Each one handles a different piece of the force-speed-drivetrain puzzle.
Available Force (lbs) = Stall Force × ηWhere η = 0.80 for Acme lead screw efficiency.
Linear Speed (in/sec) = (Motor RPM / Gear Ratio) × Pitch / 60
Gear Ratio = (Motor RPM × Pitch) / (Target Speed × 60)
Pitch (in/rev) = (Target Speed × 60 × Gear Ratio) / Motor RPM
| Symbol | Variable | Unit |
|---|---|---|
| Stall Force | Maximum actuator force at zero speed | lbs |
| η (eta) | Drivetrain efficiency (fixed at 0.80 for Acme screw) | — |
| Gear Ratio (N) | Motor revolutions per 1 output shaft revolution | :1 |
| Pitch (P) | Linear travel per 1 lead screw revolution | inches/rev |
| Motor RPM | Motor free-run (no-load) speed at 12V | RPM |
| Linear Speed | Achievable linear travel rate at the output | in/sec |
Simple Example
Given: A 12V actuator with a 200 lb stall force, 20:1 gear ratio, 0.2 in/rev Acme lead screw pitch, and a motor free-run speed of 5,000 RPM.
Step 1 — Available Force:
Available Force = 200 × 0.80 = 160 lbs
Step 2 — Output Shaft RPM:
Output Shaft RPM = 5,000 / 20 = 250 RPM
Step 3 — Linear Speed:
Linear Speed = 250 × 0.2 / 60 = 0.833 in/sec
What this means: This actuator can push 160 lbs at about 0.83 inches per second — roughly 50 inches per minute. That's a solid combination for applications like adjustable workbenches, solar panel tilts, or lightweight gate openers. If you need more speed, you'd reduce the gear ratio or increase the screw pitch — but you'll sacrifice force to get it.
Engineering Applications
Stall Force Is Not Working Force
This is the single biggest misconception we see. Stall force is the maximum force the actuator produces at zero speed — the motor is locked, drawing maximum current, and generating peak torque. You never run there. Once the screw starts turning, friction in the Acme threads and gearbox eats into that peak number. At 80% Acme efficiency, a 200 lb stall force actuator delivers 160 lbs of usable output force. That 20% loss is real, and it's already baked into this calculator. If you skip that correction, you'll undersize your actuator and wonder why it stalls under load.
The Gear Ratio Tradeoff
Gear ratio is your biggest lever for tuning an actuator's behavior. Doubling the gear ratio from 20:1 to 40:1 halves the output shaft RPM — which halves your linear speed. But the motor operates at a more favorable torque point, effectively doubling the force it can transmit through the drivetrain. This is the classic force-vs-speed tradeoff, and there's no way around it with a fixed motor. You're splitting a finite amount of mechanical power between force and speed. Choose based on your application: a heavy hatch needs high force and tolerates slow speed, while a rapid positioning system needs speed and can accept lower force.
Lead Screw Pitch Controls Linear Travel
Pitch determines how far the nut travels per revolution of the screw. A coarser pitch — say 0.5 in/rev instead of 0.2 in/rev — moves the load faster but reduces the mechanical advantage. A finer pitch gives you more force multiplication at the cost of speed. For most FIRGELLI actuators, we use Acme thread pitches between 0.1 and 0.5 in/rev depending on the model and its intended duty.
Why Acme Threads — Not Ball Screws?
Acme threads run at about 80% efficiency, which sounds worse than ball screws at 90–95%. But that "inefficiency" is actually a feature. The friction in an Acme thread prevents back-driving — meaning the load can't push the screw backward and drop. This is critical for vertical lifts, adjustable desks, TV mounts, and any application where you need the actuator to hold position when power is off. Ball screws back-drive freely, so they need a separate brake mechanism for vertical loads. More parts, more cost, more failure modes.
Never Run at 100% Stall Force
Stall force is a peak rating, not a continuous one. Running an actuator at or near stall draws maximum current, generates maximum heat, and will burn out the motor in minutes. We recommend designing your system so the actual working load stays below 60–70% of the stall force rating. That gives you a safety margin for friction variations, temperature changes, and the occasional overload event. If your required force is 150 lbs, choose an actuator rated for at least 200–250 lbs of stall force.
Advanced Example
Scenario: You're building a solar panel tilt system that needs to push 100 lbs at a minimum speed of 0.75 in/sec. You have a 12V DC motor with a free-run speed of 6,000 RPM. You've selected an actuator rated at 300 lbs stall force. What gear ratio and screw pitch combination works?
Step 1 — Verify force capacity:
Available Force = 300 × 0.80 = 240 lbs
Your load is 100 lbs. That's only 42% of the available force — a healthy safety margin. Good.
Step 2 — Solve for gear ratio (assume 0.2 in/rev pitch):
Required Gear Ratio = (6,000 × 0.2) / (0.75 × 60)
Required Gear Ratio = 1,200 / 45 = 26.67 :1
Interpretation: A 26.67:1 gear ratio isn't a standard off-the-shelf value. You'd round to the nearest available — likely 25:1 or 30:1.
Step 3 — Check speed with a 25:1 ratio:
Output Shaft RPM = 6,000 / 25 = 240 RPM
Linear Speed = 240 × 0.2 / 60 = 0.80 in/sec ✓ (exceeds 0.75 target)
Step 4 — Alternatively, solve for pitch with a 30:1 ratio:
Required Pitch = (0.75 × 60 × 30) / 6,000
Required Pitch = 1,350 / 6,000 = 0.225 in/rev
Design decision: The 25:1 gear ratio with 0.2 in/rev pitch delivers 0.80 in/sec at 240 lbs available force — both exceed your requirements. The 30:1 option would need a slightly coarser 0.225 in/rev pitch to hit the speed target, which is less standard. Go with 25:1 and 0.2 in/rev. Clean, available components, and comfortable margins on both force and speed.
Frequently Asked Questions
Why does this calculator use 80% efficiency instead of 100%?
Because Acme lead screws lose about 20% of the input energy to friction between the screw and nut. This is an industry-standard baseline for a well-lubricated Acme thread. The 80% figure gives you a realistic output force rather than a theoretical maximum you'll never achieve in practice. If your system is poorly lubricated or heavily loaded at an angle, real efficiency could drop even lower.
Can I use this calculator for ball screw actuators?
The formulas for speed work identically for ball screws. However, the force calculation uses a fixed 80% efficiency — ball screws typically run at 90–95% efficiency. You'd need to mentally adjust the force result upward by about 12–19% for a ball screw. Keep in mind that ball screws back-drive freely, so you'll need a brake mechanism for any vertical or gravity-loaded application.
What happens if my required load exceeds the available force result?
The actuator will stall — it won't move the load, and the motor will draw maximum current continuously. This generates excessive heat and will damage or destroy the motor. You need to either select an actuator with a higher stall force rating, increase the gear ratio to boost mechanical advantage, or reduce the load on the system.
Is motor free-run RPM the same as the speed under load?
No. Free-run RPM (also called no-load speed) is the maximum speed the motor achieves with nothing attached to the shaft. Under load, the motor slows down — the heavier the load, the slower it runs. This calculator uses free-run RPM as the starting point, which gives you the maximum possible linear speed. Your actual speed under load will be somewhat lower, depending on how close you are to the stall force limit.
How do I find the gear ratio and lead screw pitch for my FIRGELLI actuator?
We publish stall force, speed, and stroke length on every product page. Gear ratio and lead screw pitch aren't always listed separately because we optimize the full drivetrain as a system. If you need those specific parameters for custom integration work, contact our engineering team directly — we're happy to provide detailed drivetrain specs for any model.
What safety margin should I use when sizing a linear actuator?
We recommend keeping your working load at 60–70% of the available output force — not the stall force. So if the calculator shows 160 lbs available force, design your system for a maximum working load of 96–112 lbs. This accounts for friction variations, temperature effects, component wear, and occasional dynamic loads like wind gusts or vibration.
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About the Author
Robbie Dickson — Chief Engineer & Founder, FIRGELLI Automations
Robbie Dickson brings over two decades of engineering expertise to FIRGELLI Automations. With a distinguished career at Rolls-Royce, BMW, and Ford, he has deep expertise in mechanical systems, actuator technology, and precision engineering.
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