Lead Screw Torque & Efficiency Calculator — Power Screw Force & Self-Locking
Calculate raising and lowering torque, lead screw efficiency, lifting force from available torque, self-locking and backdrive behavior, travel speed and steady-state power for sliding power screws with optional thrust-collar friction.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Operating direction
Screw geometry
Thread form
Thread friction
Axial force and available drive torque
Thrust collar / plain thrust face (optional)
Steady-state drive speed (optional)
Results
Calculation tools Save, export and manage your results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Lead screw and power screw torque equations
This calculator models a sliding power screw or lead screw carrying an axial load. It calculates both raising and signed lowering torque, raising efficiency, lead angle, self-locking tendency and, when the optional inputs are supplied, lifting force from available torque, torque utilization, travel speed and steady-state power.
Lead, mean diameter and lead angle
Lead per revolution:
L = p Ns
where p is thread pitch and Ns is the number of thread starts. For a single-start screw, lead equals pitch. For a multi-start lead screw, lead is pitch multiplied by the number of starts.
Effective mean thread diameter:
dm = d − p / 2
This estimate is used only when a mean or pitch diameter is not entered directly. When a published or measured pitch diameter is available, it should be entered as the override.
Lead-angle ratio and lead angle:
q = tan(λ) = L / (π dm)
λ = atan(q)
Thread-angle correction and effective friction
The entered thread half-angle is corrected to the normal plane so that the friction model remains applicable to multi-start screws:
αn = atan[cos(λ) tan(α)]
μe = μ / cos(αn)
where α is the axial thread half-angle, αn is the normal-plane half-angle, μ is the sliding thread-friction coefficient and μe is the effective friction factor used by the torque equations.
Raising torque
The required torque to raise the axial load is:
T↑ = F [ dm / 2 · (q + μe) / (1 − μeq) + μcdc / 2 ]
The last term represents optional sliding friction at a plain thrust collar or thrust face. If collar friction is omitted, that term is zero.
Lowering torque and backdriving
The calculator uses a signed lowering torque:
T↓ = F [ dm / 2 · (μe − q) / (1 + μeq) + μcdc / 2 ]
- T↓ > 0: positive drive torque is required to lower the load.
- T↓ = 0: the modeled system is at the holding boundary.
- T↓ < 0: the load can drive the screw in the lowering direction and braking torque is required.
Required braking torque for modeled backdrive:
Tbrake = max(0, −T↓)
Raising efficiency
Ideal frictionless raising torque:
Tideal = F L / (2π)
Raising mechanical efficiency:
η↑ = Tideal / T↑
The reported efficiency is the raising efficiency. It is not replaced by a separate lowering efficiency when lowering mode is selected. If a thrust-collar model is active, its friction is included in T↑ and therefore reduces the calculated overall raising efficiency.
Thread self-locking condition
The thread-alone self-locking tendency is determined from:
μe > q
Because q = tan(λ), this compares effective thread friction with the screw lead angle. Equality represents the modeled thread self-locking boundary.
The calculator also evaluates the signed total lowering torque. A plain thrust collar can resist lowering even when the thread by itself is not self-locking, so the thread self-locking result and the overall modeled backdrive state are reported separately.
Axial force from available raising torque
When available raising torque is entered, the calculator determines the corresponding axial-force capacity from the same raising-torque equation:
Fcapacity = Tavailable / [ dm / 2 · (q + μe) / (1 − μeq) + μcdc / 2 ]
If both axial force and available torque are entered, the calculator also checks:
UT = T↑ / Tavailable
A torque utilization above 100% means the entered available raising torque is insufficient for the analyzed axial force under the modeled friction conditions.
Travel speed and steady-state power
When screw speed n is entered:
ω = 2πn / 60
v = Ln / 60
P↑ = T↑ω
Pbrake = max(0, −T↓)ω
where ω is angular speed, v is axial travel speed, P↑ is steady-state raising input power and Pbrake is the modeled braking power during load-driven backdrive.
Symbols
| Symbol | Meaning | Typical SI unit |
|---|---|---|
| F | Axial design force | N |
| d | Nominal screw diameter | m |
| dm | Mean / pitch diameter | m |
| p | Thread pitch | m |
| L | Lead per revolution | m/rev |
| Ns | Number of thread starts | — |
| λ | Lead angle | deg |
| α | Axial thread half-angle | deg |
| μ | Thread sliding-friction coefficient | — |
| μc | Sliding thrust-collar friction coefficient | — |
| dc | Mean collar friction diameter | m |
| T↑ | Raising torque | N·m |
| T↓ | Signed lowering torque | N·m |
| η↑ | Raising efficiency | % |
| n | Screw rotational speed | rev/min |
When to use this calculator
When to use this lead screw torque calculator
Use this calculator for preliminary analysis of sliding power screws and lead screws that convert rotary torque into axial force. It is intended for screw jacks, presses, vises, clamping mechanisms, lifting axes, manually or motor-driven linear actuators and similar screw-driven mechanisms.
The calculator is particularly useful when you need to:
- calculate the torque required to raise an axial load;
- calculate signed lowering torque and determine whether braking torque is required;
- estimate lead screw efficiency from screw geometry and sliding friction;
- check the thread self-locking tendency from effective friction and lead angle;
- compare single-start and multi-start power screw geometry;
- estimate the axial force available from a known drive torque;
- check how much of the available raising torque is used by a specified load;
- include sliding losses from an optional plain thrust collar;
- calculate axial travel speed from lead and screw RPM;
- estimate steady-state raising power and backdrive braking power.
Choosing the geometry inputs
Enter nominal diameter, thread pitch and number of starts. The calculator forms the screw lead as pitch multiplied by the number of starts. For multi-start screws, do not enter the total lead as the pitch unless it is actually the distance between adjacent threads.
A published or measured pitch diameter should be entered as the mean-diameter override when available. If it is left blank, the calculator estimates dm = d − p/2.
Choosing thread friction
Select an available thread-friction preset or enter a custom sliding-friction coefficient. The friction coefficient should represent the actual screw/nut material pair, lubrication state, surface condition and operating regime as closely as practical.
Square, Acme, trapezoidal and custom thread geometries can be represented through the thread half-angle used by the model.
Force-driven and torque-driven calculations
Enter an axial design force when the objective is to calculate required raising and lowering torque. Enter available raising torque when the objective is to estimate the axial force that the screw can generate. Enter both to compare required raising torque with the available drive torque.
When not to use this calculator alone
This is not a complete power-screw design verification. It does not calculate screw-column buckling, thread-root stress, combined axial and torsional stress, nut bearing pressure, wear life, critical screw speed, backlash, screw deflection, thermal limits, lubrication life, motor acceleration torque or structural safety factors.
It is also not a bolt or nut tightening torque calculator. Fastener preload and tightening torque use a different mechanical model.
Ball screws use rolling-contact behavior and manufacturer-specific efficiency, preload and drag characteristics. Do not treat a sliding-friction power-screw calculation as a substitute for a ball-screw manufacturer's performance data.
How to interpret the result
How to interpret the results
Selected operating torque
The primary torque result follows the selected operating direction. In raising mode it is the calculated raising torque. In lowering mode it is the signed lowering torque.
A negative selected torque in lowering mode is intentional: it means the load tends to backdrive the screw and the magnitude of the negative result represents torque that must be resisted rather than supplied in the lowering direction.
Raising torque
Raising torque is the steady torque required at the screw to move the analyzed axial force upward or against the load. It includes modeled thread friction and, when entered, sliding thrust-collar friction.
Raising efficiency
Efficiency compares ideal axial work with the actual modeled raising input work. Higher friction generally increases required torque and reduces efficiency. Increasing screw lead increases the lead angle and can improve raising efficiency, but it can also reduce or eliminate self-locking.
The efficiency result always refers to raising operation, even when lowering torque is selected as the primary result.
Thread self-locking tendency
The thread-alone result compares effective thread friction with the tangent of the lead angle. A self-locking indication means the modeled thread friction exceeds that geometric threshold. A result near the boundary should not be treated as a robust holding margin because small friction changes can change the behavior.
Lowering and backdrive assessment
- Positive lowering torque: the modeled mechanism requires driving torque to lower the load.
- Holding boundary: calculated lowering torque is effectively zero.
- Negative lowering torque: the load overhauls the modeled screw and braking torque is required.
Thread self-locking and total modeled lowering behavior are not identical when collar friction is included. The calculator therefore reports both the thread self-locking tendency and the signed total lowering torque.
Available torque and force capacity
When available raising torque is supplied, the calculated force capacity is the axial force corresponding to that torque under the entered geometry and friction assumptions. It is not a structural load rating for the screw, nut, bearing or mechanism.
When both axial force and available torque are entered, torque utilization below or equal to 100% means the entered available torque meets the modeled steady-state raising requirement. Utilization above 100% produces an insufficient-torque warning.
Speed and power
Travel speed is screw lead multiplied by rotational speed. Raising power is calculated from raising torque and angular speed. Backdrive braking power is reported only when the modeled lowering torque is negative.
These are steady-state values. They do not include motor acceleration, reflected inertia, gearbox acceleration losses, impact, shock or transient friction.
Safe, warning and invalid states
A warning is generated when the available raising torque is insufficient, modeled lowering requires braking, the mechanism lies at a holding or self-locking boundary, or the thread alone is not self-locking.
A safe status means none of those modeled warning conditions is active for the entered case. It does not establish structural integrity, regulatory compliance or safety of the complete mechanism.
Invalid results indicate that required inputs, geometry or numerical conditions fall outside the implemented calculation domain.
Calculation example
Worked example — trapezoidal-style lifting screw
A screw-driven lifting mechanism must raise an axial load of 10 kN. The screw has a 20 mm nominal diameter, 4 mm pitch and one thread start. The thread half-angle is 15°, the sliding thread-friction coefficient is 0.10, and a plain thrust face is modeled with μc = 0.05 at a 30 mm mean friction diameter.
The drive can supply 30 N·m of raising torque and the screw operates at 120 rev/min. The mean thread diameter is left blank, so the calculator uses its internal estimate.
Inputs
- Operating mode = raising
- d = 20 mm = 0.020 m
- p = 4 mm = 0.004 m
- Ns = 1
- α = 15°
- μ = 0.10
- F = 10,000 N
- Tavailable = 30 N·m
- μc = 0.05
- dc = 30 mm = 0.030 m
- n = 120 rev/min
1. Mean diameter and lead
dm = 0.020 − 0.004/2 = 0.018 m
L = 0.004 · 1 = 0.004 m/rev
2. Lead angle
q = 0.004 / (π · 0.018) = 0.0707355
λ = atan(0.0707355) = 4.046°
3. Effective thread friction
αn = atan[cos(4.046°) tan(15°)] = 14.964°
μe = 0.10 / cos(14.964°) = 0.10351
4. Raising torque
T↑ = 10,000 [ 0.018/2 · (0.0707355 + 0.10351) / (1 − 0.10351 · 0.0707355) + 0.05 · 0.030/2 ]
T↑ = 23.298 N·m
The plain thrust collar contributes:
Tcollar = 10,000 · 0.05 · 0.030/2 = 7.500 N·m
5. Lowering torque and self-locking
T↓ = 10,000 [ 0.018/2 · (0.10351 − 0.0707355) / (1 + 0.10351 · 0.0707355) + 0.05 · 0.030/2 ]
T↓ = +10.428 N·m
Because the lowering torque is positive, the modeled load does not overhaul the screw. Positive input torque is still required to lower it.
The thread-alone self-locking condition is also satisfied because:
0.10351 > 0.0707355
6. Raising efficiency
Tideal = 10,000 · 0.004 / (2π) = 6.366 N·m
η↑ = 6.366 / 23.298 = 0.2733
Raising efficiency = 27.33%
7. Available torque and lifting force
The required raising torque uses:
23.298 / 30.000 × 100 = 77.7% of the available torque.
Using the same screw geometry and friction model, 30 N·m corresponds to an estimated lifting-force capacity of:
Fcapacity = 12.88 kN
8. Travel speed and power
v = 0.004 · 120 / 60 = 0.008 m/s = 8 mm/s
ω = 2π · 120 / 60 = 12.566 rad/s
P↑ = 23.298 · 12.566 = 292.8 W
The calculated backdrive braking power is 0 W because the signed lowering torque is positive in this case.
Engineering interpretation
Under the assumed steady sliding-friction conditions, the 30 N·m drive has sufficient raising torque for the 10 kN load, and the thread shows a self-locking tendency. This does not prove that the complete lifting mechanism is safe to hold a suspended load. Structural strength, buckling, wear, actual friction, braking requirements and applicable safety provisions must be checked separately.
Assumptions and limitations
Assumptions and limitations
- The calculation uses a steady-state sliding-friction model for the screw/nut interface.
- A single thread-friction coefficient is used for the analyzed condition. Starting friction, running friction, lubrication changes and friction variation with speed, temperature or wear are not modeled separately.
- Lead is calculated as pitch multiplied by the integer number of thread starts.
- The thread half-angle is corrected to the normal plane using the calculated lead angle before the effective friction factor is determined.
- If mean thread diameter is not supplied, the calculator estimates it as nominal diameter minus half the pitch. Published or measured pitch diameter should be preferred for a specific screw.
- Optional collar losses use a simple sliding thrust-face model Tc = Fμcdc/2.
- The collar model does not represent rolling-element thrust-bearing drag, seal losses or manufacturer-specific bearing behavior.
- Raising efficiency is based on useful axial work divided by modeled raising input work.
- The self-locking result is based on modeled friction and geometry. It is not a safety-rated holding assessment.
- No service factor is added automatically. The entered axial force should already represent the load case the engineer intends to analyze.
- The calculation does not verify screw buckling, axial stress, torsional stress, combined stress, thread-root stress concentration, nut bearing pressure or thread stripping.
- The calculation does not predict nut wear, lubrication life, PV limits, thermal buildup or long-term friction changes.
- Critical speed, whip, screw deflection, alignment, backlash and lead accuracy are outside the model.
- Motor starting torque, acceleration torque, inertia, gearbox efficiency and transient drive behavior are not included in the steady-state torque and power results.
- Ball-screw rolling-contact behavior is outside the intended sliding power-screw model.
- For suspended loads or other safety-critical mechanisms, use independent holding and safety provisions as required by the governing application and applicable design requirements.
Validation
Input and calculation validation
- Operating direction must be raising or lowering.
- Nominal diameter and pitch must both be positive.
- Number of starts must be a positive integer.
- An entered mean diameter must be positive and no greater than the nominal diameter.
- Thread friction coefficient must be non-negative.
- Thread half-angle must be at least 0° and less than 90°.
- At least one of axial force or available raising torque must be supplied.
- Entered axial force and available raising torque must be positive.
- Collar friction coefficient and collar mean diameter must either both be entered or both be left blank.
- Collar friction must be non-negative and collar mean diameter must be positive.
- Entered rotational speed must be non-negative.
- The calculation rejects singular or numerically invalid raising-torque geometry and non-finite output states.