Screw Jack Calculator
Enter load, handle radius, pitch and efficiency to compute effort F=W·p/(2πr·η) and mechanical advantage MA=2πr/p. W=1000 N, r=0.3, p=0.005, η=0.3 → F≈8.84 N, MA≈377.
Input Data
Results
At a glance:A screw is an inclined plane wrapped around a cylinder (the sixth simple machine). The thread cross-section is triangular or square; the pitch p is the distance between adjacent threads (advance per turn). Ideal mechanical advantage MA=2πr/p (r handle radius). Actual effort F=W·p/(2πr·η) (η efficiency; friction increases F). Self-locking: if the thread friction angle exceeds the lead angle, releasing the handle won't let it descend (the jack's safety key). Physical meaning: a screw is an inclined plane of height p and base 2πr, so MA=base/height=2πr/p. Smaller pitch → larger MA (easier) but less advance per turn (slower). Efficiency: triangular thread η=0.2–0.4 (high friction, self-locking); square thread η=0.3–0.5; ball screw η=0.9 (no self-lock, needs a brake). Applications: (1) car jacks; (2) C-clamps and vises (clamping); (3) threaded fasteners (bolts, nuts); (4) wine presses, printing presses; (5) CNC ball screws (precision positioning).
Formula
Mechanical advantage: MA = 2π·r / p
Effort: F = W·p / (2π·r·η)
Lead angle: tanφ = p/(2π·r)
Self-lock: friction angle > lead angle
Energy conservation: F·(2πr) = W·p / η
$$MA = \frac{2\pi r}{p}, \quad F = \frac{W\,p}{2\pi r\,\eta}$$How to Use
- Enter load W (N).
- Enter handle radius r (m) and pitch p (m).
- Enter efficiency η (triangular 0.3, ball screw 0.9).
- The tool gives F=W·p/(2πr·η) and MA.
Case Studies
Car jack and C-clamp
Car jack: W=15000 N, r=0.3, p=0.005, η=0.3 → F=15000×0.005/(2π×0.3×0.3)≈132.6 N, MA=2π×0.3/0.005≈377.
A person pushes 132 N to lift a 15000 N car — the screw amplifies ~113× (η cut it from 377 to ~113 actual).
C-clamp: small r and p gives huge clamping force with little hand torque; triangular thread self-locks so it holds.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.