Lead Screw Torque Calculator
Torque to raise and to lower a load on a power screw, with the efficiency and the drive power.
Results
What this tool does
Power screws are wonderfully strong and terribly inefficient: a typical trapezoidal screw turns barely a third of the input work into useful lifting, and the rest goes into heat in the thread. That inefficiency is also what makes them self-locking, so the low efficiency is a feature as often as it is a cost. Use the mean thread diameter, not the outside diameter.
Formula
T = F dm ÷ 2 × (L + π µ dm) ÷ (π dm − µ L)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
fx | Force | N |
dm | Mean thread diameter | mm |
ph | Screw lead | mm |
mu | Friction coefficient | — |
rp | Rotational speed | rpm |
TR | Torque | N·m |
TL | Torque | N·m |
EF | Efficiency | % |
PW | Power | W |
SP | Speed | mm/s |
Worked example
- Force5000 N
- Mean thread diameter22 mm
- Screw lead5 mm
- Friction coefficient0.15
- Rotational speed120 rpm
- Torque12.3630 N·m
- Torque4.2253 N·m
- Efficiency32.184 %
- Power155.36 W
- Speed10.000 mm/s
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
What does a negative lowering torque mean?
That the screw is self-locking: friction alone holds the load and no torque is needed to stop it running back. That is what makes a screw jack safe to walk away from. A positive lowering torque means the load will drive the screw backwards on its own, so a brake or a worm reduction is required. Self-locking generally happens when the lead angle is below the friction angle, which for a coefficient of 0.15 is around eight and a half degrees.