Lead Screw Calculator
Calculate lead screw linear speed, travel per revolution, and time to travel a distance from RPM and lead.
Introduction
On any screw-driven axis — a lathe leadscrew, a CNC ball screw, a 3D-printer Z-axis — the conversion between rotation and linear motion runs through one number: the lead. The Lead Screw Calculator computes lead from thread pitch and the number of starts, then derives linear speed from RPM and, optionally, the time to traverse a given distance. It exists because pitch and lead are routinely confused on multi-start screws: a popular Tr8×8 printer screw has a 2 mm pitch but four starts, so each revolution advances 8 mm — a 4× error if you mistake one for the other when configuring steps-per-millimeter.
How it Works
Three sequential relations: lead = pitch × starts, the axial travel per revolution; linear speed = RPM × lead, in mm/min or in/min to match your input units; and travel time (s) = distance ÷ linear speed × 60. For example, a two-start screw with 3 mm pitch turning at 300 RPM has a 6 mm lead, advances at 1800 mm/min, and covers a 450 mm stroke in 15 s. Travel-per-revolution is reported separately because it is the figure motion-controller and steps-per-unit configuration actually consumes.
Usage Scenarios
- Configuring firmware for a printer or router conversion: lead, not pitch, sets steps-per-millimeter, and the calculator makes the multi-start distinction explicit.
- Estimating rapid-traverse rate for a screw-driven slide from motor RPM, then checking it against the cycle-time budget for a pick-and-place axis.
- Sizing a stepper for a Z-axis: working backward from required mm/min to the RPM the motor must sustain at usable torque.
- Verifying an unknown salvaged screw: measure pitch with calipers, count thread starts on the end face, and confirm computed lead against measured carriage travel per turn.
- Comparing single-start versus four-start options for a manual fixture, trading positioning resolution against travel speed.
FAQ
What is the difference between pitch and lead?
Pitch is the axial spacing of adjacent thread crests; lead is travel per revolution. They are equal only on single-start screws — on an n-start screw, lead = pitch × starts.
How do I count starts on a screw?
Look at the end face and count the separate thread ridges beginning there, or divide measured travel per revolution by the caliper-measured pitch.
Why do multi-start screws exist?
They deliver fast travel with a fine thread form: large lead for speed while each thread stays shallow, preserving core diameter and stiffness. The trade-off is reduced mechanical advantage and back-drivability.
Does the calculator account for backlash or efficiency?
No — the kinematics are exact, but real drives add backlash in the nut and friction losses. Ball screws run near 90% efficiency; ACME screws often below 50%, which affects required torque, not speed.