Linear to Rotational Motion Conversion Calculator

Posted by Robbie Dickson on

← Back to Engineering Library

Linear to Rotational Motion Conversion Calculator + Formula, Examples & Applications

If your motor delivers rotation and your application needs straight-line movement, you’re dealing with a lead screw. The pitch of the screw is what ties rotational inputs (RPM, torque) to linear outputs (speed, force). If you get the math wrong, it either won’t move or you’ll burn something out. This calculator helps you convert speed and force between the motor side and the actuator’s output, taking lead screw pitch (and real-world efficiency) into account. Below are the core equations, hands-on examples, and what you actually need to watch for when selecting or sizing an actuator drivetrain.

What Is Linear to Rotational Motion Conversion?

This is just translating the rotation you get out of a motor — RPM and torque — into how fast and how hard your load actually moves using a lead screw. The screw’s pitch is the main conversion factor.

Friction changes the calculation. The math on paper assumes a perfect screw — the screw on your bench loses 20% or more before the nut moves.

"Catalog torque is not delivered torque. Acme screws lose roughly 20% to friction before any of your motor's effort reaches the load — size the motor for what arrives at the nut, not what leaves the shaft." — Robbie Dickson, FIRGELLI Automations founder and former Rolls-Royce, BMW, and Ford engineer

How does a lead screw convert rotation to linear motion?

Treat a lead screw like a ramp that wraps around a shaft — each full turn moves the nut by the screw’s pitch. A coarse thread (big pitch) gets you speed, but you lose mechanical advantage. Fine threads (small pitch) let you push/pull more, but at lower speed; basically, slow but strong versus fast but weaker. This calculator works both forward and backward, so you can start from either the motor or the linear side.

Motor Shaft RPM Acme Lead Screw P (in/rev) 1 rev = P inches Nut v (in/sec) F (lbs) Speed Conversion RPM = (v × 60) / P Speed Conversion v = (RPM × P) / 60 Force → Torque T = (F × P) / (2π × η) Torque → Force F = (T × 2π × η) / P

Linear to Rotational Motion Conversion Calculator

Linear travel per one full screw revolution. Acme standard is typically 0.1–0.5 in/rev.
80% for Acme thread. 90–95% for ball screw.
Engineering calculation notice

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.

Found a calculation error? Message us

Linear to rotational motion conversion interactive visualizer

Watch how lead screw pitch determines the exchange rate between motor RPM and linear speed, and how torque converts to force through the mechanical advantage of threaded motion.

Conversion Mode
Lead Screw Pitch 0.20 in/rev
Linear Speed 0.5 in/sec

REQUIRED RPM

150

LINEAR SPEED

0.50 in/s

PITCH RATIO

5:1

FIRGELLI Automations — Interactive Engineering Calculators

🎥 Video — Linear to Rotational Motion Conversion Calculator

Linear to Rotational Motion Conversion Calculator

How do you use this calculator?

There are four basic conversion modes here. Pick your direction, fill in your numbers, and get your answer — nothing more complicated than using the correct values and units.

  1. Select your conversion mode. Choose from the dropdown: Linear Speed → RPM, RPM → Linear Speed, Linear Force → Shaft Torque, or Shaft Torque → Linear Force.
  2. Enter your lead screw pitch. Use the actual linear travel per revolution — check the datasheet. Acme screws are usually 0.1 to 0.5 in/rev.
  3. Enter your known value. Depending on the mode, this means either the motion (speed, RPM) or the force/torque, plus efficiency for force/torque conversions.
  4. Click "= Calculate." Results appear immediately in both imperial and metric units as needed.
  5. Try Example shows you a filled-out problem. It’s a shortcut to see typical input values and the kind of answer you should expect, so you know what correct feels like before trying your own specs.

What are the formulas for linear-to-rotational motion conversion?

Speed Conversions

RPM = (Linear Speed × 60) / Pitch
Linear Speed (in/sec) = (RPM × Pitch) / 60

Force / Torque Conversions

Torque (lb-in) = (Linear Force × Pitch) / (2π × Efficiency)
Linear Force (lbs) = (Torque × 2π × Efficiency) / Pitch
Symbol Variable Unit
P Lead Screw Pitch inches/rev
v Linear Speed inches/sec
RPM Rotational Speed revolutions per minute
F Linear Force lbs
T Shaft Torque lb-in
η Lead Screw Efficiency decimal (e.g., 0.80)

What does a simple worked example look like?

Problem: You need 100 lbs of linear push force from an Acme lead screw with a 0.2 in/rev pitch and 80% efficiency. What shaft torque does your motor need to deliver?

Formula: Torque = (Force × Pitch) / (2π × Efficiency)

Calculation:
Torque = (100 × 0.2) / (2 × 3.14159 × 0.80)
Torque = 20 / 5.02655
Torque = 3.979 lb-in (≈ 0.4496 Nm)

What this means: Your gearmotor needs to deliver roughly 4 lb-in of continuous torque at the screw shaft to produce 100 lbs of linear force. That's a very achievable number for a small DC gearmotor — which is exactly why lead screws are so effective at converting modest motor torque into substantial push/pull force.

How is this used in real engineering applications?

Why Pitch Is Everything

Screw pitch is what actually relates rotational motion to linear travel. Pitch is the distance the nut moves for one revolution, and there's always a direct tradeoff: Coarse (large) pitch gives you speed but reduces force. Finer (small) pitch does the opposite. There’s no magic here — you just decide which trade-off fits your job.

The 300 RPM / 0.2 Pitch Reference Point

This is a useful touchstone: 0.2 in/rev pitch at 300 RPM gives you exactly 1 in/sec. That’s in a comfortable range for typical actuators and motors. Want double the speed? Double the pitch or double the RPM, but each has drawbacks — higher pitch means less force, more RPM usually costs more on the motor side.

Where Does 2π Come From?

The 2π in the force-torque equations comes from basic physics: one revolution is 2π radians, and each revolution translates to the amount of linear travel your pitch sets. Rotational work (torque × 2π) equals linear work (force × pitch), so 2π is there to keep everything properly balanced. If your calculation is way off, double-check you included (or didn’t double-count) 2π in the right spot.

Efficiency Losses Are Real

Acme screws typically turn 20% of your input torque into heat and friction. That’s just the nature of the thread geometry and real-world sliding friction. Don’t ignore it when you size a motor — whatever number you get on paper with 100% efficiency is almost never what arrives at the output nut. Use 80% for Acme, 90–95% for ball screw, and lower than that if you can see dirt or lack of grease.

Practical Motor Sizing

Usually you work backward — you know the force and speed you want at the output, so you calculate how much torque your motor actually needs to deliver. With a 0.2 in/rev Acme screw and 100 lbs required, you’ll land around 4 lb-in for the shaft torque, then allow some headroom for startup, wear, and contingencies. This approach takes the guesswork out of selecting a gearmotor and helps avoid under-sizing.

How does an Acme screw compare to a ball screw in a real motor-sizing problem?

Scenario: You're designing a custom positioning stage that needs to deliver 250 lbs of push force at a linear speed of 0.5 in/sec. You're choosing between an Acme screw (80% efficiency) and a ball screw (93% efficiency), both with 0.25 in/rev pitch. What motor specs do you need for each option?

Step 1 — Required RPM (same for both screws)

RPM = (v × 60) / Pitch = (0.5 × 60) / 0.25 = 120 RPM

Step 2 — Required Torque with Acme Screw (η = 0.80)

Torque = (250 × 0.25) / (2π × 0.80)
Torque = 62.5 / 5.0265
Torque = 12.43 lb-in (1.40 Nm)

Step 3 — Required Torque with Ball Screw (η = 0.93)

Torque = (250 × 0.25) / (2π × 0.93)
Torque = 62.5 / 5.843
Torque = 10.70 lb-in (1.21 Nm)

Design Interpretation

The ball screw reduces your torque requirement by about 14% — from 12.43 to 10.70 lb-in. That's meaningful because it might let you use a smaller, lighter, cheaper gearmotor. But ball screws cost 3–5× more than Acme screws and aren't self-locking. For a positioning stage that needs to hold position when the motor stops, the Acme screw's self-locking property might be worth the extra torque. Both options need a motor rated for at least 120 RPM continuous — a fairly gentle speed that most 12V or 24V DC gearmotors handle easily.

What are common mistakes when using this calculator?

  1. Mixing pitch units. Pitch must be entered in inches per revolution. A 5 mm pitch screw is 0.197 in/rev, not 5. Convert before entering.
  2. Confusing pitch with lead on multi-start screws. For single-start screws, pitch and lead are equal. For multi-start screws, lead = pitch × number of starts — and lead is what the calculator wants.
  3. Forgetting efficiency on a force/torque calculation. Leaving efficiency at 100% gives an idealized number that no real screw delivers. Use 80% for Acme, 90–95% for ball screw.
  4. Applying efficiency to the speed conversion. Efficiency only affects force and torque. Linear speed per revolution is purely geometric.
  5. Sizing the motor at exactly the calculated torque. Startup loads, temperature derating, and wear all eat into available torque. Always size with margin on top of the calculated value.

How can you verify the calculator output is reasonable?

  1. Use the 0.2 / 300 / 1 reference point. A 0.2 in/rev pitch at 300 RPM should give exactly 1 in/sec linear speed. If your numbers are in that neighborhood for similar inputs, the math is working.
  2. Check units. Pitch in inches/rev, speed in inches/sec, force in lbs, torque in lb-in. Mixing imperial and metric mid-calculation is the most common source of a wrong answer.
  3. Check the 2π. One revolution = 2π radians of rotation = "pitch" inches of travel. If your torque looks 6.28× too large or too small, you likely forgot 2π.
  4. Compare Acme vs ball screw direction. Ball screws (90–95% efficiency) should always require less torque than Acme (80%) for the same force. If your ball-screw torque comes out higher, you've mixed up the efficiency values.
  5. Cross-check with a coarse hand calculation. For 100 lbs at 0.2 in pitch and 80% efficiency, expect roughly 4 lb-in. If the calculator gives you 40 or 0.4, recheck inputs.

Frequently Asked Questions

What's the difference between pitch and lead on a screw? +

For single-start screws — which is most of what you'll encounter — pitch and lead are the same thing. Pitch is the distance between adjacent threads. Lead is the distance the nut advances per revolution. On a multi-start screw, lead = pitch × number of starts. This calculator uses "pitch" in the lead sense: linear travel per revolution.

Can I use this calculator with metric lead screws? +

Yes — just convert your metric pitch to inches first. Divide your pitch in mm by 25.4 to get inches/rev. For example, a 5 mm pitch screw is 0.197 in/rev. Enter that, and all the formulas work exactly the same way. The RPM-to-linear-speed mode also outputs mm/sec for convenience.

Why doesn't the speed conversion use efficiency? +

Efficiency affects force and torque — it represents energy lost to friction. But the kinematic relationship between RPM and linear speed is purely geometric. One revolution always moves the nut exactly "pitch" inches regardless of friction. Speed doesn't change with efficiency; only the force you can deliver does.

What efficiency should I use if I don't know my screw type? +

Default to 80% — that covers most standard Acme thread screws, which is what you'll find inside the vast majority of linear actuators including ours. If you're using a ball screw, bump it to 90–93%. If your screw is old, dirty, or running without lubrication, drop to 60–70% to be safe. When in doubt, be conservative.

Does this calculator account for backdrive and self-locking? +

No — this calculator handles the forward direction only: motor torque driving the screw to create linear force. Self-locking (whether the load can backdrive the screw) depends on the screw's helix angle and friction coefficient. As a rule of thumb, Acme screws with efficiency below 50% are self-locking. Most standard Acme screws are self-locking; ball screws are not.

Can I use this for rack and pinion or belt drive systems? +

The speed formulas work for any mechanism where you know the linear distance per revolution — for a rack and pinion, that's the pinion circumference (π × diameter). The torque formulas apply too, but the efficiency values will be different. Belt drives typically run 95–98% efficient, and rack-and-pinion systems around 90–95%. Adjust accordingly.

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.

Wikipedia - Full Bio

Need to implement these calculations?

Explore the precision-engineered motion control solutions used by top engineers.

Share This Article
Tags
actuator calculator engineering-calculator lead-screw linear-motion rotational-motion rpm