Gear Reduction Calculator

| Added in Automotive

What Is Gear Reduction?

Whenever two gears of different sizes mesh together, they trade speed for torque. Gear reduction describes the specific case where a small drive gear (the one connected to the motor) turns a larger driven gear (the one doing the work). The driven gear completes fewer revolutions per minute than the drive gear, but each revolution carries more twisting force.

This trade-off is everywhere: the reduction gears in a power drill let a small, fast motor turn a bit slowly but with enough torque to drive a screw; a car's low gears do the same thing to get a heavy vehicle moving from a stop.

The Gear Reduction Formula

The ratio itself is a straightforward comparison of tooth counts:

[
\text{Gear Ratio} = \frac{\text{Driven Teeth}}{\text{Drive Teeth}}
]

Once you know the ratio, it tells you exactly how torque and speed change between the drive shaft and the driven shaft:

[
\text{Output Torque} = \text{Input Torque} \times \text{Gear Ratio}
]

[
\text{Output RPM} = \frac{\text{Input RPM}}{\text{Gear Ratio}}
]

A ratio greater than 1:1 is a reduction — torque goes up, speed goes down. A ratio less than 1:1 is an overdrive — speed goes up, torque goes down. Either way, the product of torque and RPM stays roughly constant, because gears can't create power out of nothing; they only trade one for the other.

Worked Example: A 3:1 Reduction

Say a motor's drive gear has 20 teeth, meshing with a driven gear that has 60 teeth. The motor delivers 50 Nm of torque at 3,000 RPM.

First, the ratio:

[
\text{Gear Ratio} = \frac{60}{20} = 3 : 1
]

Then the output values:

[
\text{Output Torque} = 50 \times 3 = 150 \text{ Nm}
]

[
\text{Output RPM} = \frac{3{,}000}{3} = 1{,}000 \text{ RPM}
]

The driven shaft turns at exactly a third of the input speed — 1,000 RPM instead of 3,000 — but delivers three times the torque, 150 Nm instead of 50 Nm. Notice that torque × RPM stays close to constant (50 × 3,000 = 150,000 versus 150 × 1,000 = 150,000): that's the power being conserved, just redistributed between speed and twisting force.

Reduction vs Overdrive: What Different Ratios Mean

Ratio Drive : Driven teeth Effect
3:1 (reduction) 20 : 60 Torque ×3, speed ÷3 — strong pulling power, slower rotation.
1:1 (direct drive) 30 : 30 No change — torque and speed pass straight through.
1:3 (overdrive) 60 : 20 Speed ×3, torque ÷3 — fast rotation, less twisting force.

Try the calculator above with the numbers reversed — a 60-tooth drive gear turning a 20-tooth driven gear — and you'll get a 0.33:1 ratio: output RPM triples while output torque drops to a third. That's exactly how a vehicle's overdrive gear works, letting the engine spin slower than the wheels at cruising speed.

Why the Formula Uses Teeth, Not Diameter

Teeth counts are the most reliable way to get a gear ratio because every tooth on a meshing pair of gears is the same size — that's what lets them mesh at all. Counting teeth (or reading them off a parts spec) avoids the measurement error you'd get trying to measure gear diameters by hand, and it's the number manufacturers print in their catalogs.

Quick Recap

  • Gear Ratio = driven gear teeth ÷ drive gear teeth.
  • Ratios above 1:1 are reduction: more torque, less speed.
  • Ratios below 1:1 are overdrive: more speed, less torque.
  • Torque × RPM stays roughly constant through an ideal gearset — gears redistribute power, they don't create it.
  • Real gearboxes lose a small percentage to friction; check the gearbox efficiency calculator to account for that loss.

Frequently Asked Questions

Gear reduction is what happens when a smaller drive gear turns a larger driven gear. The driven gear turns slower than the drive gear, but with more torque, because the same amount of power is spread across a slower rotation.

Divide the number of teeth on the driven gear by the number of teeth on the drive gear: Gear Ratio = Driven Teeth ÷ Drive Teeth. A drive gear with 20 teeth turning a driven gear with 60 teeth gives a ratio of 3:1.

More teeth means a larger gear, and a larger gear takes longer to complete one revolution for the same input speed. That slower rotation is exactly what "reduction" refers to — reduced output speed in exchange for increased output torque.

It increases torque. Output torque equals input torque multiplied by the gear ratio, so any ratio greater than 1:1 multiplies torque while dividing speed by the same amount, roughly conserving power.

Overdrive is the opposite of reduction: the drive gear has more teeth than the driven gear, so the ratio is less than 1:1. Output speed increases and output torque decreases, which is how a car's top gear lets the engine spin slower at highway speed.

No, it calculates ideal output assuming no losses. Real gearboxes lose a few percent of torque to friction and heat, so measured output is always slightly lower than the ideal figure — use a gearbox efficiency calculator to account for that loss.

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