Screw Jack Force Calculator

Screw jack force calculator for Acme, trapezoidal and square threads. It finds handle force, raising and lowering torque, efficiency, self-locking and screw buckling for each load.

Screw Jack Force Calculator Example: 5 Tons on a 1-1/2 in Acme

Raising 10,000 lbf on a 1-1/2 in, 4-TPI Acme screw with a 20 in handle takes 106.6 lbf of push at the handle end. The screw needs 177.6 ft·lbf of torque, with an oiled bronze nut (μ = 0.13) and a 2 in steel-on-bronze thrust collar (μc = 0.08).

Only 18.7% of that work lifts the load. The rest goes into friction: 110.9 ft·lbf in the thread and 66.7 ft·lbf at the collar. The screw also holds the load on its own, and lifting it 6 in takes 24 turns.

A screw jack force calculator gets there in three steps: the lead angle from pitch and diameter, the thread torque from friction, then the handle force from torque and handle length. Each step below uses the same 5-ton example.

Screw Jack Formula for Raising and Lowering Torque

The method comes from Shigley's Mechanical Engineering Design, the standard power-screw reference. It starts with the lead angle, which is how steep the thread climbs around the screw.

$$\tan \lambda =\frac{l}{\pi \times d_m}$$

Lead l is pitch times the number of starts, and d_m is the mean thread diameter. For the 1-1/2-4 Acme, l = 0.25 in and d_m = 1.375 in, so tan λ = 0.0579 and λ = 3.31°. Every later screw jack force calculator step depends on this angle.

$$T_R=\frac{W{d}_m}{2}\times \frac{\tan \lambda +\mu \sec \alpha }{1-\mu \sec \alpha \tan \lambda }+\frac{W{\mu }_c{d}_c}{2}$$

T_R is the raising torque, W the load, μ the thread friction, α the thread half-angle, μ_c the collar friction and d_c the mean collar diameter. The first term is thread torque, 1,331 in·lbf here; the second is collar torque, 800 in·lbf.

$$F=\frac{T_R}{R}$$

F is the handle force and R is the distance from the screw axis to your hand. That is 2,131 in·lbf ÷ 20 in = 106.6 lbf. Doubling the handle to 40 in halves the push to 53.3 lbf but doubles the arc you walk per turn.

$$T_L=\frac{W{d}_m}{2}\times \frac{\mu \sec \alpha -\tan \lambda }{1+\mu \sec \alpha \tan \lambda }+\frac{W{\mu }_c{d}_c}{2}$$

T_L is the torque to lower the load. In the example it is 1,321 in·lbf, or 110.1 ft·lbf. A positive value means you have to turn the screw to bring the load down; a negative one means the load runs down by itself.

The sec α factor is why square threads lift with the least torque and V-threads with the most. An Acme thread adds only 3.3% to the friction term, so it gives up very little efficiency against a square thread while carrying the load on a stronger, wider-rooted tooth.

A 60° V-thread adds 15.5%, so a screw jack force calculator set to the wrong thread form misses torque.

Acme and Trapezoidal Screw Sizes for Jacks

Thread size changes both torque and holding. Larger screws need more torque per pound of load because the friction acts at a bigger radius, but their flatter lead angle gives a wider self-locking margin.

The table runs Shigley's thread torque on standard general-purpose Acme sizes, oiled bronze nut (μ = 0.13), single start, no collar. Mean diameter is major diameter minus half the pitch.

Self-lock margin is the friction angle minus the lead angle, 7.65° minus λ at μ = 0.13. Every single-start Acme size in the table holds its load, with at least 3.1° to spare.

Collar friction, when present, adds to that holding, so a screw jack force calculator that skips the collar under-counts both raising torque and holding.

A screw jack force calculator in metric uses the same equations with millimeters and newtons. For trapezoidal threads, the table gives thread torque in N·m per kN of load, again at μ = 0.13 with no collar.

Use the real pitch diameter from the thread standard when you have it. The Pitch Diameter Calculator finds it from size and pitch, and the Thread Calculator gives the other dimensions of common threads.

Thread and Collar Friction Values for Screw Jacks

Friction sets most of the torque, so it is the input most worth getting right. Shigley's tables give ranges for screw and nut pairs, plus running and starting values for the thrust collar.

The friction range swings a screw jack force calculator answer more than people expect. On the 5-ton example, oiled steel-on-bronze at μ = 0.10 needs 95.7 lbf at the handle; at μ = 0.16 it needs 117.4 lbf. Size the handle and operator effort for the high end.

Use the low end of the range when you check holding. Low friction is the worst case for a load that must stay up, so a screw that self-locks only at high μ can creep once the thread is freshly greased.

Starting torque is higher than running torque

Breaking a loaded screw free takes more torque than keeping it turning. With the starting collar value of 0.10 instead of 0.08, the 5-ton example needs 116.6 lbf to start, not 106.6 lbf, and the thread adds its own breakaway on top.

Running values give the force to keep turning; starting values give the force to break the load free.

Manufacturers publish both numbers. In the Joyce/Dayton machine screw jack data, starting torque runs about 1.4 to 2 times the operating torque across their 2 to 20 ton models, plus a fixed tare torque for seals and assembly drag.

Screw Jack Efficiency and Mechanical Advantage

Efficiency is the share of input work that ends up lifting the load. For one turn, the load rises one lead while the handle torque turns through 2π radians.

$$\eta =\frac{W\times l}{2\pi \times T_R}$$

For the example, 10,000 × 0.25 ÷ (2π × 2,131) = 18.7%. Without the collar, the thread alone would reach 29.9%, so the collar costs more than a third of the screw's efficiency on this jack.

Mechanical advantage follows from the same numbers. The actual ratio is W ÷ F = 10,000 ÷ 106.6 = 93.8 to 1. A frictionless screw would give 2πR ÷ l = 502.7 to 1, and the gap between the two is the friction loss.

Low efficiency is normal. Joyce/Dayton lists 9.4% to 24.2% for its standard machine screw jacks, which include worm gearing. A screw jack force calculator result in that band is a working jack, not a design error.

Worm-gear screw jacks

Most machine screw jacks drive the lifting screw through a worm gear. The gear ratio cuts the input torque, and the gearbox efficiency adds it back, so both belong in the handle force.

$$F=\frac{T_R}{i\times {\eta }_g\times R}$$

Here i is the worm gear ratio and η_g is the gearbox efficiency. Overall jack efficiency is the screw efficiency times η_g, which is why catalog jacks sit below the screw-only figures in the tables above.

Leave the gear stage out and a screw jack force calculator over-states handle force on a worm-driven jack by the ratio, less the gear loss.

Joyce/Dayton's 20-ton WJ820, with an 8:1 worm, lists operating torque as 0.051 × W and starting torque as 0.075 × W in in·lbf, plus 40 in·lbf of tare. At its full 40,000 lbf, that is 170 ft·lbf to keep it moving and 253 ft·lbf to start it.

A self-locking screw can never pass 50% thread efficiency. With no collar, thread efficiency is tan λ ÷ tan(λ + φ), and when φ is at least λ that ratio stays below one half. Higher efficiency always costs you the self-locking.

When a Screw Jack Holds the Load by Itself

A screw jack self-locks when the thread friction angle is larger than the lead angle. Then the load cannot spin the screw backward, and it stays up with no brake.

$$\pi \times \mu \times d_m\times \sec \alpha >l$$

In the example, the friction angle is 7.65° against a 3.31° lead angle, so it holds with a 4.34° margin. Going to a two-start thread doubles the lead to 0.50 in, raises the lead angle to 6.60°, and shrinks the margin to 1.05°.

Faster leads lose the lock. Joyce/Dayton states that its double-lead screw jacks are not self-locking and may lower under load, and recommends brake motors or external locks for them.

A self-locking thread can still creep. Vibration can let a loaded screw back off a little at a time, so a jack under a vibrating machine or a moving vehicle needs a lock nut, ratchet or brake even when the math says it holds.

How Much Weight Can a Screw Jack Lift

A screw jack lifts its rated capacity at the load cup, as long as the screw stays below yield and does not buckle at full extension. A 20-ton jack is rated for 40,000 lbf, and a 1.5-ton jack for 3,000 lbf.

The table runs the screw jack force calculator math on the example screw, a 1-1/2-4 Acme with a 20 in handle, from 1 to 20 tons. Yield safety factor uses 54 ksi steel; buckling uses a 12 in free length with a fixed base and free top.

Torque and handle force rise in step with the load, but safety falls fast. At 20 tons this screw still clears yield and buckling, though with factors near 1.2 to 1.3, and a 426 lbf push is far past what one person can apply to a 20 in bar.

Buckling often decides capacity before thread strength does. Joyce/Dayton's column-load charts include a 2:1 factor of safety on the Euler-Johnson column formula, and allowable load drops as the lifting screw extends.

A screw jack force calculator that checks thread torque alone will pass a screw that buckles, so run the column check at the longest extension the jack will reach.

Design of a Screw Jack, Step by Step

Designing a screw jack runs in a fixed order, because each choice feeds the next. The load and stroke come first; the handle comes last.

Start with the screw body. Size the root diameter so compressive and torsional stress, combined as von Mises stress, stay well below yield, then check column buckling at full extension with the right end condition: 0.25 for a fixed base and free top.

Next size the nut. Thread bearing pressure is 2W ÷ (π d_m n_t p), where n_t is the threads engaged. The 2 in nut on the example screw engages 8 threads and runs at 2.3 ksi; compare that with the nut material's published limit.

Then check holding with low-end friction, and finally size the handle from raising torque at high-end friction and starting values. A screw jack force calculator covers the torque and holding steps, but nut bearing limits and drive gearing come from the maker's data.

Screw weight matters for portable jacks. Steel weighs about 0.284 lb per cubic inch, so a 24 in length of the 1-1/2 in screw weighs roughly 10 to 12 lb, between its mean-diameter and full-diameter volume.

Clamping Force From Screw Torque

A screw clamp, vise or press works the same way as a jack, run backward: torque in, axial force out. Divide the applied torque by the torque per pound of load to get the clamping force.

$$W=\frac{T}{k},k=\frac{d_m}{2}\times \frac{\tan \lambda +\mu \sec \alpha }{1-\mu \sec \alpha \tan \lambda }+\frac{{\mu }_c{d}_c}{2}$$

Run backward, a screw jack force calculator turns torque into clamping force. On the example screw, k = 0.213 in. A 150 ft·lbf input, which is 1,800 in·lbf, gives 1,800 ÷ 0.213 = 8,445 lbf of clamping force. With no collar, k drops to 0.133 in and the same torque gives 13,520 lbf.

For bolts, the same idea is usually written as T = K × F × d with a single nut factor K. The Bolt Preload Calculator finds clamping force from torque, and the Bolt Friction Coefficient Calculator backs out friction from a measured torque and preload.

How a Hydraulic Jack Calculation Differs

A hydraulic jack multiplies force with fluid pressure instead of a thread. Pressure is the same on both pistons, so the force grows with the ratio of piston areas.

$$F_{ram}=F_{pump}\times \frac{A_{ram}}{A_{pump}}$$

A 2 in ram fed by a 0.75 in pump piston gives (2 ÷ 0.75)² = 7.1 times the pump force, and the pump handle's own lever multiplies that again.

Unlike a screw, a hydraulic jack holds only as long as its check valve seals, so lead angle and thread friction from a screw jack force calculator do not apply to it.

What Is a Screw Jack Force Calculator?

A screw jack force calculator finds the handle force, torque, efficiency and self-locking margin needed to raise or hold a load with a power screw. It works from load, mean thread diameter, lead, thread angle, thread and collar friction, and handle length.

What is a rough starting value for screw jack friction?

Use μ = 0.15 for a first pass on a steel screw in a bronze or steel nut, then refine it. Shigley's ranges run from 0.10 oiled to 0.25 dry, and collar friction from 0.06 to 0.12 running, so a first pass at 0.15 sits in the middle.

How many turns does a screw jack take to lift?

Divide the lift height by the lead. The 1-1/2-4 Acme rises 0.25 in per turn, so a 6 in lift takes 24 turns; at 30 rpm that is 48 seconds and about 1 hp of input power at 10,000 lbf.