Gear Ratio Calculator: Speed, Torque, and Mechanical Advantage

Gears trade speed for torque (or vice versa) according to a simple ratio. Whether you're sizing a gearbox for a motor, designing a bicycle drivetrain, or figuring out the final drive ratio on a vehicle, the gear ratio calculation is the same — you just need to track which way the trade-off goes.

The CalcHub Gear Ratio Calculator calculates output speed, output torque, and mechanical advantage for simple and compound gear trains.

The Basic Gear Ratio

Gear Ratio = Driven Teeth ÷ Driver Teeth = Input Speed ÷ Output Speed = Output Torque ÷ Input Torque

For a 12-tooth driving gear meshing with a 48-tooth driven gear:

• Gear ratio = 48 ÷ 12 = 4:1 (speed reduction)


• If input is 1,200 RPM → output = 1,200 ÷ 4 = 300 RPM


• If input torque is 10 N·m → output torque = 10 × 4 = 40 N·m (× efficiency)


• Direction of rotation: reversed (external gears counter-rotate)

Speed-Torque Trade-Off

This is the fundamental principle:

Gear Ratio	Effect	Common Application
>1 (reduction)	Speed down, torque up	Conveyor, hoist, robot joint
<1 (overdrive)	Speed up, torque down	Bicycle high gear, overdrive transmission
1:1	Speed and torque unchanged	Direction change or shaft offset
High ratio (10:1+)	High torque multiplication	Worm drives, hoists, positioning

Compound Gear Trains

When multiple gear pairs are in series, multiply all ratios:

Total Ratio = Ratio₁ × Ratio₂ × Ratio₃ × ...

For a two-stage gearbox:

• Stage 1: 10T driver → 40T driven = 4:1


• Stage 2: 12T driver → 36T driven = 3:1


• Total ratio = 4 × 3 = 12:1

Input: 3,000 RPM, 5 N·m
Output: 3,000 ÷ 12 = 250 RPM, 5 × 12 = 60 N·m (before losses)

Compound gear trains allow large ratios with compact gear sizes.

Gear Efficiency

Real gearboxes lose some power to friction. Efficiency varies by type:

Gear Type	Efficiency per Stage
Spur gears	97–99%
Helical gears	97–99%
Bevel gears	95–98%
Worm gear	50–90% (depends heavily on lead angle)
Planetary gearbox	95–98%
Cycloidal drive	90–95%

For a 12:1 two-stage spur gear train at 98% per stage: Output torque = 60 N·m × 0.98 × 0.98 = 57.5 N·m (not 60)

Worm gears are particularly lossy at high ratios — a 50:1 worm drive might be only 50–60% efficient. However, they self-lock (the load can't back-drive the motor), which is useful for hoists and positioning applications.

Bicycle Example: Gear Inches

Bicycle gearing uses "gear inches" or a gear ratio expressed differently:

Gear ratio = Front chainring teeth ÷ Rear cog teeth

52T chainring / 13T cog = 4.0 gear ratio
52T chainring / 28T cog = 1.86 gear ratio

At the same cadence (pedal RPM), the 4.0 ratio gives you much higher wheel speed (but requires more force) compared to 1.86 (easier to pedal, more suited to climbing).

Planetary Gear Systems

Planetary gearboxes have sun, planet, and ring gears. The ratio depends on which element is held fixed:

• Ring fixed (sun in, planet carrier out): Ratio = 1 + (Ring teeth ÷ Sun teeth)
• Sun fixed (ring in, planet carrier out): Ratio = Ring teeth ÷ (Ring teeth − Sun teeth)

For a sun with 20 teeth and ring with 60 teeth, ring fixed: Ratio = 1 + (60/20) = 4:1

Planetary gears are compact for their torque capacity and are used in power tools, automatic transmissions, and industrial drives.

Does gear ratio affect the direction of rotation?

External (spur/helical) gears reverse direction at each mesh. An odd number of external gear meshes reverses overall direction. Internal gears (ring gear meshed with planet) maintain direction. Worm gears also change the shaft axis by 90°.

What's a differential gear and how is the ratio calculated?

A differential splits torque between two output shafts while allowing them to spin at different speeds (like in a car axle). The average output speed equals the input speed (for a 1:1 differential). The actual speed split depends on load distribution. This is more complex than fixed ratio gearing.

How do I convert between gear ratio and mechanical advantage?

They're the same thing here. A 4:1 gear reduction gives a mechanical advantage of 4 — you can output 4× the torque you input (at 1/4 the speed), before friction losses.

Related Tools

• Motor Torque Calculator — motor output that drives the gear train
• Pipe Flow Calculator — mechanical systems in pumping applications
• Acceleration Calculator — velocity and force related to rotating systems