Gear Ratio Calculator: Teeth, RPM & Torque

This gear ratio calculator finds the ratio between the driver and driven gears from their tooth counts, then gives output RPM, torque and power for single or multi-stage gear trains.

It also works as a gearbox calculator and gear torque calculator: add input RPM, torque and efficiency to see how a gear reduction changes speed and torque. A second mode estimates the vehicle gear ratio from engine RPM, tire size and road speed.

Gear Ratio Formula

A 20-tooth gear driving a 60-tooth gear gives 3:1: the output turns 3× slower with 3× more ideal torque. Meshing teeth move at the same speed where they touch, so the bigger gear must turn slower. Revolutions follow the same rule: 1800 input revolutions through 3:1 give 600 output revolutions.

Real transmitted torque is lower than ideal; how much depends on gear type, speed, load, lubrication, bearings and the number of stages.

How to Calculate Gear Ratio (Step by Step)

Example: a 1500 rpm, 5 N·m motor drives a 20T gear meshing with a 60T gear on a conveyor roller.

1. Count the teeth. Driver (on the motor) = 20T. Driven (on the load) = 60T.
2. Find the ratio. 60 ÷ 20 = 3:1.
3. Find output speed. 1500 ÷ 3 = 500 rpm.
4. Find output torque. 5 × 3 = 15 N·m (ideal, 100% efficiency).
5. Check power. 5 N·m at 1500 rpm = 15 N·m at 500 rpm ≈ 0.785 kW. A passive gear train cannot create power; real losses reduce the output power slightly.

Common Gear Ratio Table: Output RPM and Torque

Input: 1500 rpm and 5 N·m. Torque shown is ideal (100% efficiency).

Actual output torque = ideal torque × total efficiency. Ratios of 10:1 and above are shown as two stages, the usual practical choice.

Gear Ratio From Diameter, Radius or Speed

Meshing gears share the same tooth size (module or diametral pitch). So pitch diameter, pitch radius and shaft speeds give the same ratio as tooth count:

Measure pitch diameter, not tip (outside) diameter. On a standard gear the tip diameter is about two modules larger than the pitch diameter (one addendum on each side), which skews small gears most.

Four Ways to Write a Gear Ratio

The 20T → 60T pair can be written as:

• Fraction: 60/20, reduced to 3/1
• Decimal: 3.0 (input turns per output turn)
• Colon ratio: 3:1 (catalog and datasheet style)
• Torque multiplier: ×3

Watch the notation direction. A 20T gear driving a 40T gear is 2:1 in the driven ÷ driver form used here. Some sources write the same pair as 1:2 (driver : driven), so check which way a figure is quoted.

Compound Gear Train Ratio Calculator (Multiple Gears)

A compound train stacks gear pairs on shared shafts. Multiply the stage ratios, never add them:

Example (4 gears, 2 stages): 1800 rpm, 2 N·m input.

1. Stage 1: 15T drives 45T → 45 ÷ 15 = 3.
2. Stage 2: a 20T gear on the 45T shaft drives 60T → 60 ÷ 20 = 3.
3. Overall: 3 × 3 = 9:1.
4. Output: 1800 ÷ 9 = 200 rpm, 2 × 9 = 18 N·m.

Two moderate-ratio stages can be more practical than one very high single-stage reduction, depending on gear geometry, centre distance, strength and allowable size. In the calculator, press "+ Add stage" for up to four stages.

Gear Torque Calculator: Torque From Gear Ratio

Example: 5 N·m through a 3:1 pair at 95% efficiency gives 5 × 3 × 0.95 = 14.25 N·m (15 N·m ideal).

1. Get the overall ratio (single pair or compound product).
2. Multiply: Output torque = Input torque × Ratio.
3. Apply efficiency: multiply by the manufacturer's rated gearbox efficiency. It varies with gear type, size, speed, lubrication, load and number of stages. To get torque from shaft power and speed, use the Shaft Torque Calculator.

The tooth-count ratio sets the ideal (kinematic) speed relationship. Efficiency is applied to the transmitted torque and power. This calculator does not model tooth deflection, backlash, bearing losses or load-dependent gearbox behaviour.

Gearbox Calculator: Ratio, RPM and Torque

A gearbox (gear reducer) is a housed gear train. Its ratio equals input speed ÷ output speed, or the product of its stage ratios.

Used as a gear reduction calculator, a ratio above 1 lowers output speed and raises available output torque, subject to efficiency and other losses. For a catalog gearbox with a known ratio such as 5:1, enter any tooth pair with the same ratio (for example 20T and 100T) plus the gearbox's rated efficiency.

Industrial Gear Ratio Examples

1. Conveyor drive: 1450 rpm motor, 20T driver, 80T driven.

1. Ratio: 80 ÷ 20 = 4:1.
2. Roller speed: 1450 ÷ 4 = 362.5 rpm. Convert it to belt surface speed with the Belt Speed Calculator.

2. Motor gearbox (gearmotor): 7.5 kW motor at 1475 rpm, 5:1 gearbox, 95% efficiency.

1. Motor torque: 9549 × 7.5 ÷ 1475 ≈ 48.6 N·m. Rating in HP? Convert first with the HP to kW Converter.
2. Output speed: 1475 ÷ 5 = 295 rpm.
3. Output torque: 48.6 × 5 × 0.95 ≈ 230.6 N·m (output power ≈ 7.13 kW). Size the output shaft with the Shaft Diameter Calculator.

3. Pump or fan drive (finding the ratio): 1440 rpm motor, shaft needs 480 rpm. Estimate the motor size first with the Pump Power Calculator.

1. Required ratio: 1440 ÷ 480 = 3:1.
2. Pick gears: any pair with driven = 3 × driver, such as 20T → 60T (or 19T → 57T). Using a belt instead? Use the Pulley Ratio Calculator.
3. Check torque: enter the motor torque and gearbox efficiency in the calculator to confirm the shaft torque.

Motor → gearbox → shaft → load workflow: check the motor's full-load current with the Motor Current Calculator (or the kW to Current Calculator), set the speed and torque here, then size the shaft and belt stages.

Hunting Tooth Effect and Gear-Tooth Wear

The tooth-pair repeat period is N₂ ÷ gcd(N₁, N₂) driver revolutions: the number of driver turns before the same driver tooth meets the same driven tooth again.

• 20T → 60T: gcd = 20, so 60 ÷ 20 = 3 driver revolutions. Tooth pairs repeat quickly, and a local tooth defect keeps loading the same few spots.
• 17T → 60T: gcd = 1, so 60 ÷ 1 = 60 driver revolutions. This "hunting tooth" pair spreads repeated contact over many more revolutions.

Actual wear still depends on load, lubrication, alignment and tooth geometry. The calculator shows this repeat period for every stage.

Common Gear Ratio Mistakes

• Swapping driver and driven. Always driven ÷ driver, or a reduction becomes an overdrive.
• Ignoring efficiency. 100% is ideal. Real output torque is lower, especially over many stages.
• Using one stage's ratio for a multi-stage gearbox. Multiply all stages.
• Counting an idler as a stage. An idler only changes direction, not the ratio.
• Mixing modules or pitches. The diameter form only works if both gears share one module (or diametral pitch).
• Treating any tooth count as buildable. Very small pinions (roughly below 17 teeth on a standard 20° profile) may need profile shift to avoid undercut. The ratio alone does not check geometry or strength.
• Mixing up the cycling convention. Cyclists quote chainring ÷ cog, the inverse of driven ÷ driver.

Reference: Standard mechanical power-transmission relationships. For preliminary, educational sizing only. Does not replace manufacturer gearbox data or a qualified engineer's review.

Every time two external gears mesh, the direction of rotation flips. Put a third gear in the middle and the output flips back, turning the same way as the input. That middle gear is an idler, and its tooth count has no effect on the overall ratio. The algebra shows why: with a driver (N₁), idler (N_i) and driven gear (N₂), the ratio is (N_i ÷ N₁) × (N₂ ÷ N_i) = N₂ ÷ N₁. The idler's teeth cancel out completely.

Toggle the demo below. The 20-tooth input and 30-tooth output keep the same 1.5:1 ratio in both cases; only the output's direction changes.

The rule generalises to any chain of external gears: count the meshes. An odd number of meshes reverses the output; an even number keeps it turning the same way. The calculator applies this rule using the number of stages plus the number of idlers you enter. A few related cases are worth knowing:

• Reverse gear in a manual car gearbox usually works by sliding a small idler into the gear path, which is why reverse can sound different (it often uses straight-cut teeth) and why the car's wheels turn backward with the engine still turning the same way.
• Internal (ring) gears don't reverse direction. A pinion meshing inside a ring gear turns the same way as the ring, which is one reason planetary sets behave differently from simple gear pairs.
• Open belts and chains keep the direction; a crossed belt reverses it. A bicycle chain turns the rear wheel the same way as the pedals for this reason.
• Idlers also bridge distance. When two shafts are too far apart to mesh directly, an idler fills the gap without forcing either gear to become oversized.

A gear is a toothed wheel that passes rotation, torque and speed from one shaft to another by positive engagement: the teeth lock into each other. A set of gears working together is a gear train. The first gear to receive power (from a motor, an engine, or a hand crank) is the driver, the last one is the driven or output gear, and the way their shafts are arranged decides which type of gear you need.

Gear pairs provide positive tooth engagement with a fixed kinematic ratio, unlike belt drives that can slip under some conditions, and are the usual choice wherever the shafts are close together and precise, backlash-controlled motion matters. Chain and belt drives let the two shafts sit farther apart without an intermediate gear train — chains handle higher torque with minimal slip, while belts run quieter and tolerate minor misalignment but can slip under sudden overload unless properly tensioned.

A worked worm example: a 40-tooth wheel driven by a single-start worm gives 40:1 in one stage; a two-start worm on the same wheel gives 20:1. A worked planetary example: with a 12-tooth sun as input, a 36-tooth ring held still and the planet carrier as output, the ratio is 1 + 36 ÷ 12 = 4:1, and the carrier turns in the same direction as the sun. This formula applies only to that arrangement; holding the sun or the carrier instead gives a different ratio.