Mechanical Advantage & Gear Ratio Calculator
Calculate the efficiency and mechanical output of simple machines and gear systems.
1. Gear Ratio Calculation
2. Lever Mechanical Advantage
3. Pulley System Advantage
Understanding Mechanical Advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device, or machine system. In simpler terms, it tells you how many times a machine multiplies the input force to make a task easier.
Gear Ratios Explained
A gear ratio is the relationship between the number of teeth on two gears that are meshed together. It determines how the speed and torque of the input (driver) gear are transformed at the output (driven) gear.
- High Gear Ratio (>1): Increases torque but decreases speed (good for climbing hills).
- Low Gear Ratio (<1): Increases speed but decreases torque (good for high-speed cruising).
| Machine Type | Input Variable | Output Variable | Calculation Formula |
|---|---|---|---|
| Gears | Driver Teeth | Driven Teeth | Driven / Driver |
| Lever | Effort Arm | Load Arm | Effort / Load |
| Pulley | Force Applied | Number of Ropes | Total Rope Sections |
Real-World Examples
Bicycle Gears: If your front chainring (driver) has 44 teeth and your rear sprocket (driven) has 11 teeth, the gear ratio is 0.25:1. This is a "tall" gear used for high speeds. Conversely, a 22-tooth front and 34-tooth rear gives a ratio of 1.54:1, providing high torque for steep inclines.
The Lever: Archimedes famously said, "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world." If you have an effort arm of 10 meters and a load arm of 1 meter, your mechanical advantage is 10, meaning you only need 100kg of effort to lift a 1,000kg load.
How to Use This Calculator
This mechanical calculator is designed for engineers, students, and hobbyists to quickly determine the physics properties of common mechanical setups. Simply select the section relevant to your machine (Gears, Levers, or Pulleys), enter your measurements in consistent units, and click calculate.