LEVERLAB

Screw Calculator

Work out a screw’s mechanical advantage and the turning effort needed to overcome a load, from the lever-arm length and the screw’s pitch.

The force the screw must overcome, e.g. clamping resistance.
Radius at which you apply the turning force — a screwdriver handle or wrench length, in metres.
Linear distance the screw advances per full turn, in metres (e.g. 0.002 = 2mm).
100 = frictionless/ideal; real screw threads are often 20–50% efficient.

Screw result

Mechanical advantage
471.24
Ideal effort force
2.1221
Actual effort force
2.1221

The physics behind the screw

Picture unwrapping a screw's thread into a straight ramp: it's an inclined plane, just coiled around a cylinder instead of laid flat. Every full turn of the screw moves your hand through the circle traced by your lever arm, while the screw tip advances only by the thread's pitch — usually a few millimetres. That enormous mismatch between the circular distance and the tiny linear advance is where the screw's huge mechanical advantage comes from.

Screws famously trade almost all of that theoretical advantage away to friction, because the threads are pressed together under load across a large contact area. That same friction is what makes a screw self-locking — it will hold a clamped position or a raised car without slipping back, unlike a lever or pulley, which need something else to hold their position once you let go.

Frequently Asked Questions

How is a screw's mechanical advantage calculated?

A screw is an inclined plane wrapped around a cylinder. One full turn of your lever arm (a screwdriver handle radius, a jack handle, a wrench) sweeps a circular distance of 2π × the lever-arm length, while the screw itself advances by its pitch — the linear distance it travels per turn. Mechanical advantage is that circular distance divided by the pitch, so MA = (2π × lever-arm length) ÷ pitch.

Why does a finer thread (smaller pitch) give a bigger mechanical advantage?

A finer pitch means the screw advances less per turn, so the same turning distance at the lever arm is spread over a smaller linear advance — trading more turns (and more circular distance swept) for a much larger force at the tip. This is why a car jack or a bench vise uses a fine thread: enormous mechanical advantage from a hand-turned handle.

Why is a screw's actual efficiency often much lower than ideal?

Screw threads have a lot of sliding friction between the male and female threads compressed tightly together, so a real screw commonly runs at only 20–50% efficiency — meaning the actual effort force needed is 2 to 5 times the frictionless ideal. That friction is also what lets a screw hold its position without unwinding under load (self-locking), which is a feature, not just a loss.

Does a longer lever arm or a finer pitch matter more?

Both raise the mechanical advantage in direct proportion — doubling the lever-arm length doubles the MA, and halving the pitch also doubles it. In practice, lever-arm length is limited by what's comfortable to grip and swing, while pitch is limited by manufacturing and the thread's strength, so real designs balance both.

Educational estimate only. Real screw threads lose a large share of the ideal advantage to friction — verify load-bearing fasteners and jacks with a qualified engineer.