How to use this calculator
- Enter the working load. Use the axial force the screw must move before service factor.
- Enter lead and efficiency. Use screw lead per revolution and a realistic mechanical efficiency from catalog data or test data.
- Apply service factor. Set a load multiplier for startup friction, uncertainty, duty and shock.
- Enter motor and speed. Use usable torque at the screw and the planned screw RPM, not only motor nameplate holding torque.
- Check screw geometry. Enter pitch diameter for lead angle, root diameter and unsupported length for critical speed.
- Read the margins. Keep torque utilization below 1.0 and operating speed below the recommended maximum speed.
How it works
A lead screw converts rotary work into linear work. One screw revolution moves the
nut by the screw lead L, so the ideal work balance is torque through
one revolution against axial force through one lead. With mechanical efficiency
included, the design torque is:
T_req = F_design · L / (2 · pi · eta)
The available thrust reverses the same relation:
F_available = 2 · pi · T_motor · eta / L
The calculator applies the service factor to the entered working load before sizing torque, but also shows the working-load torque without that multiplier. Linear speed comes directly from screw lead and screw RPM:
v = L · n / 60
Lead angle is a geometry check from lead and pitch diameter:
lambda = atan(L / (pi · d_p))
For speed screening, the page estimates the first bending critical speed of a uniform round screw shaft from the entered root diameter, unsupported length, material properties and end support condition:
n_cr = beta^2 · sqrt(EI / (rho A)) · 60 / (2 · pi · L_s^2)
Use this as an early sizing check before selecting catalog hardware. Pair it with the torque power RPM calculator for motor power and the shaft deflection calculator when the screw span also carries transverse load.
Worked example
Verified against the live calculator
Suppose a screw must move a 1000 N axial load. It has a
5 mm/rev lead, estimated efficiency of 35%, service factor
1.25, and 4 N*m usable torque at the screw. The screw runs
at 600 rpm, with a 12 mm pitch diameter,
10 mm root diameter, 500 mm unsupported length and
simple-simple steel supports.
The design load is 1000 x 1.25 = 1250 N. Required torque is
1250 x 0.005 / (2 x pi x 0.35) = 2.842 N*m, so the torque utilization is
2.842 / 4 = 0.711. Available thrust is
2 x pi x 4 x 0.35 / 0.005 = 1759 N, giving about
509 N thrust margin.
Linear speed is 5 x 600 / 60 = 50 mm/s. Lead angle is about
7.55 deg. The critical-speed estimate is about 4757 rpm,
so the 80% recommended limit is 3806 rpm; operating at
600 rpm uses only about 0.158 of that limit.
Frequently asked questions
How do you calculate lead screw torque?
Use T = F_design * L / (2*pi*eta), where F_design is the axial load after service factor, L is screw lead per revolution, and eta is mechanical efficiency. The calculator uses metres for lead internally, so a 5 mm lead is 0.005 m.
How do you calculate thrust from motor torque?
Rearrange the same power relation: F_available = 2*pi*T_motor*eta / L. Use usable running torque at the screw after couplings, gearing and speed derating. Stepper holding torque is usually too optimistic at speed.
What efficiency should I use for an Acme or trapezoidal lead screw?
Use the screw or nut manufacturer value when available. Plain sliding lead screws can be much lower than ball screws, and efficiency changes with lead angle, nut material, lubrication, preload and wear. A first-pass Acme estimate often lands in the 20% to 50% range, but catalog data should control the final number.
What is lead screw critical speed?
Critical speed is the first bending resonance of the rotating screw shaft. The calculator estimates it from root diameter, unsupported length, material stiffness, density and end support. It then uses 80% of that value as the recommended maximum operating speed.
Should I use pitch diameter or root diameter?
Pitch diameter is used only for lead angle. Root diameter is used for critical speed because the screw is weakest and least stiff at the thread root. If a catalog gives a minor or root diameter, use that for the speed check.
Does this check screw buckling, nut pressure or backdriving?
No. It checks torque, thrust margin, linear speed and critical speed. Vertical or compressive screws also need column buckling, nut PV/load rating, bearing load, braking/backdrive and acceleration checks.
Does this work for ball screws?
The torque, thrust and critical-speed screening logic also applies to ball screws if you enter the correct lead, efficiency, root diameter and support condition. For final selection, use the ball-screw catalog dynamic load, DN, life and support-bearing limits.
Method & assumptions
- Torque and thrust use the practical screw power relation with entered efficiency. It does not separately model thread friction, collar friction, preload drag or seal drag.
- Service factor is applied only to the entered working axial load for torque sizing. Add acceleration, vertical gravity load and process force into the load before applying service factor.
- Critical speed uses a uniform circular shaft model based on root diameter. Real nuts, bearing cartridges, unsupported overhangs, runout and mounting stiffness can change the limit.
- The recommended speed limit is 80% of calculated critical speed. Manufacturer charts and catalog limits should control final screw selection.
- Column buckling, nut pressure/PV limits, screw life, lubrication, brake sizing and backdriving are outside this first-pass calculator.