Gear Ratio Calculator

How to Use This Calculator

1. Enter the number of teeth on the Driving Gear (input) and Driven Gear (output).
2. Enter Input RPM to see output speed.
3. Use the Single Stage tab to add input torque and see output torque.
4. Use Multi-Stage for compound gear trains, or Vehicle Final Drive to compute car speed from engine RPM.

Formula

Example

Frequently Asked Questions

• What is a gear ratio and why does it matter? ▼
  A gear ratio is the relationship between the number of teeth on two meshing gears — specifically the driven gear divided by the driving gear. A ratio of 3:1 means the output shaft turns once for every three turns of the input shaft. This is fundamental to mechanics because it defines two competing quantities: speed and torque. High gear ratios (large number) reduce rotational speed but multiply torque, making it easier to move heavy loads but slower. Low gear ratios (close to 1:1) preserve speed while providing less torque multiplication. Gear ratios appear everywhere: bicycle gears, automotive transmissions, industrial gearboxes, power tools, clock mechanisms, and robotic actuators. Understanding gear ratios allows engineers and hobbyists to match motor or engine characteristics to the load requirements — a critical skill in mechanical design, from selecting the right rear axle ratio for a truck to choosing chain rings on a bicycle.
• How does gear ratio affect a car's performance? ▼
  In a car, lower numerical first-gear ratios (like 3.5:1 vs. 2.8:1) multiply engine torque more aggressively, giving stronger low-speed acceleration. Higher numerical ratios (like 4.10:1 vs. 3.55:1 rear axle) similarly increase torque at the wheels at the cost of higher RPM at cruise speeds, which reduces fuel economy. Sports cars and trucks towing heavy loads benefit from numerically higher axle ratios for stronger pull. Highway-oriented vehicles use lower ratios (3.23:1 or less) so the engine can cruise at low RPM for efficiency. Modern automatics with 8–10 speed ranges use a wide ratio spread — a very low first gear (4.7:1 or higher) for launch combined with a tall overdrive (0.65:1) for efficient highway cruising. The total drive ratio at any given moment is the product of the transmission gear ratio and the rear axle ratio.
• What is the difference between low and high gear ratios? ▼
  The terms "low" and "high" are sometimes confusing because they are used in two ways. "Low gear" in driving parlance means a numerically high ratio — first gear multiplies torque significantly (e.g., 3.5:1) and produces slow output speed, which is useful for climbing hills, towing, or starting from rest. "High gear" means a numerically low ratio — like fifth or sixth gear — which produces fast output speed with minimal torque multiplication, ideal for efficient highway cruising. In the gearbox engineering world, a "high numerical ratio" (e.g., 4.10) is described as "taller" or "lower" numerically than a 3.55, but it provides more torque at the expense of RPM. The confusion arises because colloquial "high gear" (top gear in a car) corresponds to numerically low ratios. When comparing axle ratios for trucks or race cars, always check whether you need more low-end torque (go higher numerically) or better top speed and fuel economy (go lower numerically).
• How do I calculate the final drive ratio in my car? ▼
  The final drive ratio at any moment is calculated by multiplying the current transmission gear ratio by the rear axle (differential) ratio. For example, if your transmission is in first gear at 3.35:1 and your axle ratio is 3.73:1, the total final drive ratio is 3.35 × 3.73 = 12.5:1. This means for every 12.5 engine revolutions, the rear wheels turn once. You can find your transmission gear ratios in the owner's manual or manufacturer technical documentation. The axle ratio is often stamped on the differential housing or listed in your vehicle's RPO (Regular Production Option) codes. Using this calculator's Vehicle Final Drive tab, you can also back-calculate your vehicle speed at any engine RPM once you know the tire diameter and both ratios. This is useful for understanding cruise RPM, checking speedometer calibration after a gear swap, or planning performance modifications.
• Why do bicycles have so many gears? ▼
  Bicycle gears exist because the human body produces peak power efficiently only within a narrow cadence range — typically 70–100 RPM for most cyclists. Too slow (mashing a big gear uphill) wastes muscular energy and stresses joints. Too fast (spinning a tiny gear downhill) loses power to excess motion and becomes inefficient. Multiple gears allow the rider to maintain optimal cadence across a wide range of terrain and speeds. A modern road bike with a 2×11 drivetrain has up to 22 gear combinations covering roughly a 5:1 speed range at constant cadence. Mountain bikes with a 1×12 drivetrain offer an even wider range in a simpler system. The gear-inches metric (wheel diameter × chainring teeth / sprocket teeth) is used to compare gearing across bikes: a high gear-inch value means high speed at a given cadence, while a low value means easier pedaling for climbing. Modern electronic shifting systems like Shimano Di2 and SRAM AXS allow automatic optimization of cadence by continuously adjusting the drivetrain.

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