Gear Ratio Calculator

The torque-speed tradeoff every driver should understand

A gear ratio is a torque multiplier and a speed divider, and that tradeoff is non-negotiable. A 4:1 ratio quadruples the input torque at the output but cuts output rotational speed to one-quarter of the input. There is no free lunch in mechanical advantage; energy in equals energy out, minus what friction takes.

In a car, your engine makes peak power in a fairly narrow RPM band, which differs from engine to engine. The transmission and final drive's job is to keep the engine in that band across all road speeds. First gear's job is to multiply torque enough to overcome a stopped vehicle's inertia. Top gear's job is to cruise efficiently at highway speed without screaming the engine to redline.

Total ratio = transmission ratio × final drive ratio. A car with a 1.0 top gear and 3.55 differential has a 3.55 total ratio. A truck with a 4:1 low gear and 4.10 differential has a 16.4:1 ratio in first, meaning the engine spins 16.4 times for every wheel rotation. That is why the same engine can feel strong or relaxed depending on its gearing.

Worked example: regearing for 35-inch tires

Suppose you have an off-road vehicle with 31-inch tires and 3.73 differential gears. In a 1:1 gear at 65 mph the engine turns 2,629 RPM. You install 35-inch tires for clearance; bigger tires mean each revolution travels further, dropping effective gearing.

New effective ratio = old ratio × (old tire / new tire) = 3.73 × (31/35) = 3.30. In the same gear at 65 mph the engine now turns 2,328 RPM: sluggish acceleration, the transmission hunts gears on hills, and the engine lugs. To restore the original feel, you regear: target ratio = 3.73 × (35/31) = 4.21. Ring-and-pinion sets come in fixed steps, so you choose the nearest one offered for your axle.

Ratio that matches the original 31-inch, 3.73 gearing: 33-inch tires 3.97, 35-inch tires 4.21, 37-inch tires 4.45, 40-inch tires 4.81. Regearing is a real cost, which is why it belongs in a tire upgrade decision.

Where gear ratios show up beyond cars

• Bicycles: Gear inches = chainring teeth ÷ cog teeth × wheel diameter. On a wheel 27 inches across with its tire, a 50T chainring with 11T cog gives 122.7 gear inches, high speed, hard to start. 34T × 32T = 28.7 gear inches, a climbing gear.
• Power tools: Drill gearboxes reduce a fast, weak motor to a slow, strong chuck. Through a 50:1 reduction, 15,000 motor RPM becomes 300 RPM with 50 times the torque, before friction.
• Wind turbines: Many turbines use a gearbox to step the rotor's slow turning up to the much higher speed a generator needs.
• Clocks: A second hand turns once a minute. The hour hand turns once in 12 hours, 1/720th as fast. Ratios of 60:1 and 12:1 stacked together (60 × 12 = 720) produce the slowdown.
• Watches: A mechanical movement's balance wheel beats at a fixed rate. Gear trains step that down to drive the second, minute, and hour hands at exactly the right rates.

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