Gear Ratio & RPM Calculator (Mechanical)

Mechanical Power Transmission: Understanding Gear Ratios

In mechanical engineering, robotics, and automotive design, motors rarely spin at the exact speed or with the exact torque required for the job. To adapt the power of a motor to a real-world task, engineers use a series of interlocking gears.

[Image of gear ratio driver and driven gears]

By changing the size (and therefore the tooth count) of the gears, you can mathematically trade rotational speed for twisting force, or vice versa. Our Gear Ratio Calculator allows you to reverse-engineer any gear train by simply inputting three known variables to find the fourth.

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Glossary of Mechanical Variables

• Driver Gear (T1): The input gear that is attached directly to the power source (like an electric motor or engine). Measured by its physical number of teeth.
• Driven Gear (T2): The output gear that is attached to the workload (like a car's wheels or a robotic arm). Measured by its physical number of teeth.
• RPM (Revolutions Per Minute): The standard unit of rotational speed. It dictates how many full 360-degree rotations the gear makes in 60 seconds.
• rad/s (Radians Per Second): The SI derived unit for angular velocity, often used in advanced physics equations (1 RPM ≈ 0.1047 rad/s).
• Torque (τ): The twisting, rotational force produced by the system. While not directly inputted here, torque and speed are completely inversely proportional in a gear train!

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The Golden Rule of Gears: Speed vs. Torque

The most critical concept to understand in gear mechanics is the law of conservation of energy. You cannot create free power. Therefore, a gear ratio acts as a mathematical seesaw:

• Gear Reduction (Ratio > 1:1): A small Driver Gear spins a large Driven Gear. The output speed decreases, but the output torque increases by the exact same multiplier. Used in tractors, heavy machinery, and first-gear in your car.
• Overdrive (Ratio < 1:1): A large Driver Gear spins a small Driven Gear. The output speed increases dramatically, but the torque drops. Used in highway cruising gears in vehicles or high-speed centrifuges.

The Gear Kinematic Formula

Because the teeth of both gears interlock perfectly, the number of teeth passing the contact point per minute must be identical for both gears. This gives us our core algebraic equation: