Mechanical Advantage Calculator

Simple machines are six basic mechanical devices identified by Renaissance scientists: the lever, pulley, screw, wedge, inclined plane (ramp), and wheel and axle. They work by redirecting or amplifying an input force to make moving objects easier. Most complex machines are combinations of these fundamental building blocks.

Mechanical advantage (MA) is defined as the ratio of output force to input force: MA = Output Force / Input Force. For each simple machine, this ratio translates into a geometric formula based on dimensions — for example, for a lever it's the effort arm divided by the load arm. A higher MA means you apply less force to move a heavier load.

For a lever, MA = Effort Arm Length / Load Arm Length. The effort arm is the distance from the fulcrum to the point where you apply force, and the load arm is the distance from the fulcrum to the load. For example, if your effort arm is 2 m and load arm is 0.5 m, the MA is 4 — meaning you multiply your force by 4.

Using the wedge formula MA = Length / Width, a wedge that is 20 cm long and 4 cm wide has a mechanical advantage of 20 ÷ 4 = 5. This means the wedge multiplies your driving force by a factor of 5. A longer, thinner wedge always produces a higher mechanical advantage.

For a ramp, MA = Slope Length / Height. If a ramp is 5 m long and rises 1 m vertically, the MA is 5. This means you only need one-fifth of the force to push an object up the ramp compared to lifting it straight up, though you must push it over a longer distance.

For a system of movable pulleys, MA = 2 × n, where n is the number of movable pulleys. A single fixed pulley gives MA = 1 (it only changes direction), while two movable pulleys give MA = 4. More movable pulleys mean greater force multiplication, but you must pull the rope a greater distance.

The mechanical advantage of a screw is MA = π × Diameter / Lead, where the lead is the distance the screw advances per full rotation (also called pitch for single-start screws). A larger diameter or finer thread pitch produces a higher MA, allowing a small rotational force to generate a large linear force.

Not necessarily. While a higher MA means less input force is needed, it also means you must apply that force over a greater distance or through more rotations — the total work done remains the same (conservation of energy). Real machines also have friction losses, so the actual (real) MA is always less than the theoretical (ideal) MA calculated here.