What are simple machines?
Simple machines are six basic mechanical devices defined by Renaissance scientists. In essence, they are elementary mechanisms that amplify the force you use to move objects. Each of the simple machines takes advantage of the fact that work is equal to force multiplied by distance. Each device increases the output force at the cost of decreasing the distance traveled by the load — the work done stays the same.
How do I calculate the mechanical advantage?
By definition, the mechanical advantage (MA) is the ratio between the output force and the input (effort) force:
MA = Output Force / Input Force
If MA > 1, the machine amplifies your force. If MA < 1, it reduces force but increases speed or distance. If MA = 1, there is no mechanical advantage.
How do I find the mechanical advantage of a lever?
A lever multiplies your input force using a rigid bar and a fulcrum. The mechanical advantage depends only on the lengths of the arms:
MA (Lever) = Effort Arm Length / Load Arm Length
The effort arm is the distance from the fulcrum to where you apply force. The load arm is the distance from the fulcrum to the load. If your effort arm is 100 cm and the load arm is 25 cm, MA = 100 / 25 = 4. You multiply your force by four.
Mechanical advantage of a wedge
A wedge converts a downward force into horizontal forces that push material apart (e.g., an axe splitting wood):
MA (Wedge) = Wedge Length / Wedge Width (thickness)
A long, thin wedge has a higher mechanical advantage. A wedge with length 20 cm and width 4 cm gives MA = 5.
Mechanical advantage of a pulley
A single fixed pulley only changes the direction of force (MA = 1). A movable pulley gives MA = 2. A compound block-and-tackle system has:
MA (Pulley) = Number of rope segments supporting the load (n)
For example, if 4 rope segments support the load, MA = 4 — you need only one quarter of the load's weight as effort force.
Mechanical advantage of a screw
A screw converts rotational motion into linear motion. The mechanical advantage depends on the radius of the effort arm (handle) and the thread pitch (distance between threads):
MA (Screw) = 2π × R / p
Where R is the effort arm radius and p is the thread pitch (lead per revolution). A screwdriver handle with radius 15 cm and pitch 0.2 cm gives MA = 2π × 15 / 0.2 ≈ 471.
Mechanical advantage of a ramp (inclined plane)
A ramp reduces the force needed to lift a load by increasing the distance traveled:
MA (Ramp) = Ramp Length / Ramp Height = 1 / sin(θ)
A ramp of length 300 cm and height 60 cm gives MA = 5. The angle of inclination is θ = arcsin(60/300) ≈ 11.54°.
Mechanical advantage of a wheel and axle
The wheel and axle is essentially a rotating lever. Effort applied at the wheel is amplified at the axle:
MA (Wheel & Axle) = Wheel Radius / Axle Radius
A wheel of radius 30 cm attached to an axle of radius 5 cm gives MA = 6. Steering wheels, doorknobs, and screwdrivers all use this principle.
FAQs
What units does mechanical advantage have?
Mechanical advantage is a dimensionless ratio — it has no units. The lengths or forces used to calculate it cancel out.
Can mechanical advantage be less than 1?
Yes. When MA < 1, the machine reduces your applied force but increases speed or the distance the load moves. Tweezers and fishing rods are examples.
What is ideal vs. actual mechanical advantage?
The ideal mechanical advantage (IMA) is calculated purely from geometry (as in this calculator) and assumes no friction. The actual mechanical advantage (AMA) is the true output force divided by the true input force, and is always lower due to friction.
How do I calculate output force from mechanical advantage?
Once you know MA, multiply it by the effort (input) force: Output Force = MA × Effort Force. Enter the effort force in the optional field to see the result directly.
What is the most efficient simple machine?
In theory, all simple machines are 100% efficient (IMA = AMA) when friction is ignored. In practice, the screw has the highest mechanical advantage but also the most friction losses.