Motor Sizing for Linear Motion Calculator + Formula, Examples & Applications
If you’re looking at a spec sheet, you might see “stall force” for a 12V linear actuator and think you’re set. But unless you pay attention to gear ratio and lead screw pitch, you’re not seeing the whole picture. These two details, often missed, directly affect how much real force and speed you get at the output. This calculator uses all three: stall force, gear ratio, and lead screw pitch, to show you output force and speed—what actually matters in practice. Below, you’ll find straight-shooting formulas, real worked examples, and the real-world tradeoffs you’ll deal with when engineering force, speed, and efficiency.
What Is Motor Sizing for Linear Motion?
Motor sizing for linear motion means working out whether your DC motor and lead screw setup will actually provide enough force and speed for the job, before you buy parts or cut metal.
Simple Explanation
It’s like a car transmission: use a low gear to pull heavy loads, but you won’t go fast. High gear gets you speed, not pulling power. Linear actuators work the same way—gearbox and lead screw convert a fast-spinning motor into a slower, stronger push or pull. Gear ratio and screw pitch dictate how much force and speed you get. Friction in the mechanism always eats some of your input, so you never get 100% out.
Motor Sizing for Linear Motion
This calculator is intended for education, concept evaluation, and preliminary design. Results are based on the equations and assumptions described on this page, but cannot account for every real-world load case, tolerance, material property, environmental condition, installation detail, safety factor, code, or regulatory requirement. Verify all inputs, assumptions, units, and results independently before selecting components or using the result in a real application. Safety-critical, structural, medical, lifting, transportation, or regulated applications must be reviewed by a qualified engineer.
Motor sizing for linear motion interactive visualizer
Tweak gear ratio and lead screw pitch—watch how force and speed interact in real time. The animation shows what the drivetrain is doing mechanically, so you see the impact of each setting right away.
OUTPUT FORCE
160 lbs
LINEAR SPEED
0.83 in/s
EFFICIENCY
80%
FIRGELLI Automations — Interactive Engineering Calculators
🎥 Video — Motor Sizing for Linear Motion
How to Use This Calculator
The calculator offers three solve modes. Pick the one that matches what you know vs. what you need.
- Select solve mode. “Output Force and Speed” is for when you have drivetrain specs and want to know what the actuator actually delivers. “Required Gear Ratio” or “Required Lead Screw Pitch” is for when you know targets and want to design backwards to a solution.
- Input actuator stall force. Get this from the datasheet. It’s the force at zero speed. Every solve mode requires it.
- Enter the rest. Depending on mode, enter gear ratio, screw pitch, motor free-run RPM, or target linear speed. Calculator only shows the fields needed for your mode.
- Click Calculate. The calculator factors in 80% efficiency for Acme screws by default. Results update instantly.
- Try Example fills in values to demo the math. Good for seeing the real output before you use your own specs.
Motor Sizing for Linear Motion Formula
There are three main formulas here—each covers a key part of how force, speed, and drivetrain interact.
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—about 50 inches a minute. That’s a decent fit for things like adjustable benches, solar panel tilts, or light-duty gates. If you want more speed, look at reducing gear ratio or bumping up screw pitch—but expect your available force to drop as a result.
Engineering Applications
Stall Force Is Not Working Force
Don’t confuse stall force for what is available during actual operation. Stall force is the max possible force at zero speed—motor fully loaded, drawing peak amps, and not rotating. As soon as you move, friction in the Acme lead and geartrain cuts into that number. For an 80% efficiency Acme screw, a 200 lb stall actuator only gives you 160 lbs usable. Ignore this and you’ll pick too small an actuator and get stuck with stalls under normal load.
The Gear Ratio Tradeoff
Gear ratio is how you decide between speed and force. Double the gear ratio (e.g., 20:1 to 40:1) and your output RPM and linear speed both drop by half, but force doubles (ignoring losses). You’re always trading between speed and load capacity. If your application requires moving something heavy but you don’t care about speed, gear higher. If it’s a rapid move of a light load, lower gear ratio is fine. With a fixed input power, you can’t increase both speed and force.
Lead Screw Pitch Controls Linear Travel
Lead screw pitch tells you how far the nut will travel per turn. Coarser threads (higher pitch) move the carriage faster, but you lose out on force. A finer pitch gives better force for a given motor but moves slower. Most FIRGELLI actuators use pitches in the 0.1–0.5 in/rev range, depending on what they’re built for.
Why Acme Threads — Not Ball Screws?
Acme screws aren’t as efficient as ball screws (about 80% vs. 90–95%), but that inefficiency is what keeps loads from back-driving. For vertical lifts, desk actuators, and anything that needs to stay put even if power’s off, Acme is useful. Ball screws easily back-drive, so if you’re lifting, you also need a brake—extra hardware, more maintenance, and more parts to fail.
Never Run at 100% Stall Force
Stall force is the limit, not a working target. If you run close to stall, the motor pulls max current and gets hot fast—that’s when you burn up windings and trip breakers. Proper engineering practice: keep working loads under 60–70% of stall force. This gives margin for dirt, heat, and unexpected surges. For example, if you need 150 lbs, size your parts for 200–250 lbs 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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