Raising torque
-thread + collarEfficiency
-F l / (2π T)Self-locking
-Lowering torque
-Safety factor on yield
-von Mises, screw bodyAll results
| Lead l | - |
| Mean thread diameter dm | - |
| Root diameter dr | - |
| Thread torque to raise | - |
| Collar torque | - |
| Thread efficiency (no collar) | - |
| Torsional shear stress in screw body | - |
| Axial stress in screw body | - |
| Von Mises stress | - |
| Thread bearing pressure | - |
| Thread root shear, screw | - |
| Thread root shear, nut | - |
| Travel speed | - |
| Input power to raise | - |
Method and formulas
These are the standard power screw relations found in machine design texts (for example Shigley, Budynas and Nisbett), so you can check every result by hand. The load is assumed to be axial and steady.
| Quantity | Formula |
|---|---|
| Lead | l = starts × p |
| Mean and root diameter | dm = d − p/2, dr = d − p |
| Thread torque to raise | TR = (F dm/2) (l + π μ dm sec α) / (π dm − μ l sec α) |
| Thread torque to lower | TL = (F dm/2) (π μ dm sec α − l) / (π dm + μ l sec α) |
| Collar torque | Tc = F μc dc / 2 |
| Self-locking (thread only) | π μ dm sec α > l |
| Efficiency | e = F l / (2π T) |
| Half-angle in the axial plane | sec α = 1 / cos α; α = 0° square, 14.5° Acme, 15° Tr |
| Body stresses | τ = 16 T / (π dr3), σ = 4 F / (π dr2), σvM = √(σ² + 3τ²) |
| Thread bearing pressure | pB = 2 F / (π dm nt p), nt = nut length / p |
| Thread root shear | screw: 3 F / (π dr nt p); nut: 3 F / (π d nt p) |
For Acme and trapezoidal threads the friction term is multiplied by sec α because the flank is inclined, which raises the effective friction. The body stress uses the full raising torque (thread plus collar), the torque the screw must carry. Yield strengths are typical values for the materials listed: choose Custom and enter certified values for critical work. The collar torque is ignored in the self-locking check, which is the conservative reading; collar friction also opposes lowering, so the lowering torque is the thread value plus the collar torque, and a screw that is not self-locking can still be held by a high enough collar friction.
Worked example: 1 in Acme screw, 5 TPI, 1 000 lbf
d = 1 in, p = 0.2 in single start, so l = 0.2 in, dm = 0.9 in, dr = 0.8 in. Acme α = 14.5°, sec α = 1.0329. With μ = 0.15, TR (thread) = (1000 × 0.9/2) × (0.2 + π × 0.15 × 0.9 × 1.0329) / (π × 0.9 − 0.15 × 0.2 × 1.0329) = 450 × 0.6381 / 2.7964 ≈ 102.7 lbf·in. Efficiency without collar friction e = 1000 × 0.2 / (2π × 102.7) = 31%. Because π μ dm sec α = 0.438 > 0.2, the screw is self-locking.
Questions
How do you calculate the torque to raise a load with a power screw?
The thread torque to raise a load F is T = F dm/2 × (l + π μ dm sec α) / (π dm − μ l sec α), where dm is the mean thread diameter, l the lead, μ the thread friction coefficient and α the thread half-angle measured in the plane normal to the axis (0° for square threads, 14.5° for Acme, 15° for metric trapezoidal). If the load rests on a thrust collar, add the collar torque F μc dc/2. Example: a 1 in Acme screw with 0.2 in lead (dm 0.9 in), μ = 0.15 and F = 1000 lbf needs about 103 lbf·in of thread torque to raise the load.
When is a power screw self-locking?
A screw is self-locking, so the load cannot back-drive it, when π μ dm sec α is greater than the lead l, which is the same as saying the lowering torque is positive. Collar friction helps hold the load but is not reliable on its own: vibration can reduce the friction coefficient, so safety-critical lifts normally add a brake or a second nut.
What is the efficiency of a lead screw?
Efficiency is the ideal torque (no friction) divided by the actual torque: e = F l / (2π T). Square and Acme screws with a plain nut typically run between 20% and 50%. Efficiency rises with lead and falls with friction, so a high-lead, low-friction screw (bronze nut, lubricated) is efficient but not self-locking, while a self-locking screw is always below 50% efficient.
What is the difference between lead and pitch?
Pitch is the distance between adjacent threads. Lead is the axial distance the nut travels in one revolution: lead = pitch × number of starts. A single-start screw has lead equal to pitch; a 4-start screw travels four times as far per turn. Enter the pitch and the number of starts here and the calculator works out the lead.
What friction coefficient should I use?
Typical values for a steel screw with a bronze nut are 0.08 to 0.15 when lubricated and 0.15 to 0.25 dry. Steel on steel is higher. Collar friction on a plain thrust washer is similar; with a thrust ball bearing it falls to roughly 0.01 to 0.02. Static (breakaway) friction can be 30% higher than running friction, so check the starting torque with a larger coefficient.
Which stresses does the calculator check?
It checks the torsional shear and axial stress in the screw body at the root diameter and combines them as a von Mises stress against yield, the thread bearing pressure on the flank, and the thread root shear of the screw and nut for the nut length you enter. Column buckling of a long, slender screw under compression is not checked here; use the column buckling calculator for that.
What does this calculator not cover?
It covers a single power screw under a steady axial load. It ignores dynamic loads, wear life and PV (pressure-velocity) limits of the nut material, critical speed of the screw, backlash, temperature rise, and ball screws, which have much lower friction and different load ratings. It is an engineering aid; verify critical designs.
Engineering aid for guidance. It assumes a single power screw under steady axial load and does not cover dynamic loading, wear life, PV limits, critical speed, buckling of slender screws, backlash, temperature or ball screws. Friction coefficients and strengths are typical values: use certified data and test the real assembly. Verify critical designs; you remain responsible for the design. Nothing you enter leaves your browser except through a share link you copy yourself.