Free Lead Screw Pitch & Linear Speed Calculator

Calculate linear carriage feed rate, mechanical thread lead, microstep resolution in microns, and verify anti-backdrive self-locking.

🔩 Lead Screw Pitch & Motor RPM

Standard Lead Screw Preset

Thread Pitch (mm) Distance between adjacent crests

Number of Starts

Rotational Speed (RPM)

Stepper Full Steps

📊 Linear Speed & Positional Resolution

Linear Carriage Travel Speed

80.0 mm / s

189.0 in/min (4.80 meters / min)

Screw Lead

8.0 mm / rev

Linear travel per 360° turn

Full-Step Resolution

40.0 μm (0.04 mm)

2.5 μm @ 1/16 microstep

Back-Drive / Gantry Drop: Back-drives easily (Bed may drop when power cut)

Pulse Frequency (1/16 step): 32.0 kHz

Marlin steps_per_mm: 400 steps / mm

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Pitch vs. Lead: The Crucial Distinction

In mechanical thread design, Pitch is the distance between adjacent thread peaks. Lead is the actual linear axial distance the nut travels in one complete 360-degree rotation.

Linear Speed & Step Resolution Equations

\text{Lead} = \text{Pitch} \times \text{Starts} \quad (\text{e.g., } 2\text{mm pitch} \times 4\text{ starts} = 8\text{mm lead})

V_{\text{linear}} = \frac{\text{Lead} \times RPM}{60} \quad (\text{in mm/s})

\text{Resolution} = \frac{\text{Lead}}{\text{Steps per Rev}} \quad (\text{in mm per step})

\text{steps\_per\_mm} = \frac{\text{Steps per Rev} \times \text{Microsteps}}{\text{Lead}}

Why T8x8 Screws Cause 3D Printer Gantry Sag

A steep helix angle (such as a 4-start T8x8 lead screw with an 8mm lead) has low friction efficiency ($>50\%$) that allows back-driving. When stepper motor holding current turns off at the end of a 3D print, the weight of the heavy X-gantry or bed easily spins the screw backwards and crashes down into the build plate. Switching to a single-start T8x2 (2mm lead) provides self-locking friction that holds the bed securely in place without power.

Frequently Asked Questions

Why do ballscrews always backdrive?

Ballscrews replace sliding friction with circulating ball bearings, raising mechanical efficiency to over 90%. Because rolling friction is virtually zero, ballscrews can never be self-locking and will always freewheel back-drive under vertical gravity loads without a motor brake.

What is the Marlin firmware steps_per_mm for T8x8?

For a standard 1.8° stepper (200 steps/rev) at 1/16 microstepping: (200 * 16) / 8mm lead = 400 steps/mm. For a T8x2 screw, it is 1,600 steps/mm.

How does lead screw whip occur?

Long, slender screws spinning at high RPM reach a "critical speed" where centrifugal resonance causes the rod to bow outward and whip violently, shaking the machine frame. Thicker screw diameters (e.g. 12mm or 16mm) and tensioned end bearings prevent whip.