Gear Ratio Explained: Formula, Speed vs Torque, and Real-World Tables

What Is a Gear Ratio?

A gear ratio describes the relationship between the number of teeth on two meshing gears — or, equivalently, the relationship between their rotational speeds and torques. It is always expressed as driver:driven or as a single decimal number (the result of dividing driver by driven).

Two gears meshing have a simple mechanical constraint: every tooth on the driver gear must move one tooth on the driven gear. This means:

• If the driver has 20 teeth and the driven has 40 teeth, the driver must rotate twice for every one rotation of the driven gear → gear ratio 2:1
• If the driver has 40 teeth and the driven has 20 teeth, the driver rotates once for every two rotations of the driven gear → gear ratio 0.5:1 (or 1:2 expressed the other way)

The same relationship applies to sprocket-and-chain systems (bicycles) and pulley-and-belt systems. The formula is identical; only the mechanism of power transfer differs.

The Gear Ratio Formula

The fundamental formula:

Gear Ratio = T_driver ÷ T_driven

Where T = number of teeth (or diameter, or radius — the ratio is the same either way).

From this single formula, three other quantities fall out immediately:

The speed-torque tradeoff is a direct consequence of energy conservation. Ignoring friction losses, input power equals output power (Power = Torque × RPM). If a gear ratio multiplies torque by 3×, output RPM drops to 1/3 of input RPM. You never get more energy out than you put in — you only change the form it arrives in.

Worked Examples

Example 1 — Basic Gear Pair

A motor spins at 1,800 RPM with 10 Nm of torque. It drives a gear with 15 teeth. That gear meshes with a second gear that has 45 teeth.

• Gear ratio = 15 ÷ 45 = 0.333 (1:3)
• Output RPM = 1,800 ÷ 0.333 = 600 RPM (speed reduced)
• Output torque = 10 × 3 = 30 Nm (torque tripled)

This is a speed reduction — trading rotational speed for torque. Used in conveyor systems, winches, and first gear in vehicles where maximum pulling force is needed from a standstill.

Example 2 — Speed Increase

An engine output shaft turns at 3,000 RPM with 200 Nm of torque. It drives a 60-tooth gear meshing with an 20-tooth gear on the output shaft.

• Gear ratio = 60 ÷ 20 = 3:1
• Output RPM = 3,000 × 3 = 9,000 RPM (speed tripled)
• Output torque = 200 ÷ 3 = 66.7 Nm (torque reduced to 1/3)

This is a speed multiplier — sacrificing torque for higher rotational speed. Used in the final drive of high-speed spindles, some electric tools, and overdrive gears in transmissions at highway speeds.

Example 3 — Gear Train (Multiple Stages)

When gears are chained in sequence (a gear train), multiply the individual ratios:

Stage 1: 10-tooth driving 30-tooth → ratio 3:1
Stage 2: 30-tooth driving 15-tooth → ratio 0.5:1
Overall ratio = 3 × 0.5 = 1.5:1

A 1,000 RPM input becomes 667 RPM output with 1.5× the input torque. Gear trains allow very large ratios to be achieved in compact spaces — useful in clocks, gearboxes, and industrial reducers.

Bicycle Gear Ratios

A bicycle drivetrain uses a chainring (front, driver) and a cassette sprocket (rear, driven). The gear ratio determines how far the bike travels per pedal revolution — called the gear inches or development.

Development (metres per pedal stroke) = (Chainring ÷ Sprocket) × Wheel circumference

For a typical 700c road wheel (2.096m circumference):

Road Bicycle — Common Gear Combinations

The lowest usable ratio is typically around 1:1 on road bikes and 0.7:1 on mountain bikes. Below that, cadence becomes too high relative to forward progress to be efficient. Above 4.5:1, most cyclists cannot generate enough RPM (cadence) to sustain it.

Mountain Bike vs Road Bike — Ratio Ranges

Car Transmission Gear Ratios

A car transmission uses multiple gear ratios to match engine RPM to wheel speed across a wide range of driving conditions. First gear provides maximum torque for starting from rest; top gear (or overdrive) is optimized for fuel efficiency at highway speeds.

Typical 6-Speed Manual Transmission Ratios

These ratios are multiplied by the final drive ratio (axle ratio, typically 3.5:1–4.1:1) to give the total gear reduction from engine to wheel. A 1st gear of 3.5:1 combined with an axle ratio of 3.73:1 gives a total ratio of 13.1:1 — meaning the engine spins 13 times for every 1 wheel rotation.

How Automakers Choose Gear Ratios

The spread between first and top gear has grown significantly with 8-, 9-, and 10-speed automatic transmissions, which now commonly offer a ratio spread of 7:1 or more compared to 4:1 for older 4-speeds. Closer-spaced ratios keep the engine in its power band longer during acceleration, improving both performance and fuel economy.

Speed vs Torque — Choosing the Right Ratio

Compound and Planetary Gear Systems

Compound Gear Trains

When a large ratio is needed in a small space, compound gear trains stack multiple gear pairs. The output shaft of each pair becomes the input shaft of the next, and the overall ratio is the product of all individual ratios.

A 3-stage compound train with ratios 4:1, 3:1, and 2:1 produces a total ratio of 4 × 3 × 2 = 24:1. This is how watches and clocks achieve ratios of thousands-to-one using small gears that fit in a wristwatch case.

Planetary (Epicyclic) Gear Systems

Automatic transmissions, hybrid vehicle drive systems, and electric vehicle single-speed reducers often use planetary gear sets rather than simple gear pairs. A planetary set consists of:

• Sun gear — at the centre
• Planet gears — 3–4 gears orbiting the sun
• Ring gear — outer gear that the planets mesh with
• Planet carrier — the arm holding the planet gears

By holding different members fixed (via clutches and brakes), the same planetary set produces different ratios. A Toyota-style automatic transmission uses three planetary sets to generate 6 forward ratios from a compact package that would require a much longer gear train if built from simple spur gears.

Frequently Asked Questions

Summary

The gear ratio formula — driver teeth divided by driven teeth — is the foundation of all mechanical power transmission. The key practical takeaways:

• Ratio > 1: driver larger than driven → torque multiplied, speed reduced (reduction drive)
• Ratio < 1: driver smaller than driven → speed multiplied, torque reduced (overdrive)
• Ratio = 1:1: direct drive — no mechanical advantage; speed and torque pass through unchanged
• Compound trains: multiply individual ratios to get overall ratio
• Energy is conserved: more torque always comes at the cost of less speed, and vice versa

Whether you are selecting a cassette for a mountain pass, diagnosing why a conveyor belt is running too slowly, or understanding why a car labours in too high a gear, the same arithmetic applies. Driver ÷ driven = ratio. Input RPM ÷ ratio = output RPM. Input torque × ratio = output torque.