About the Gear Ratio Speed Calculator
Gears trade speed for torque. A small gear driving a large one slows the output and multiplies its turning force; a large gear driving a small one speeds it up. This simple principle runs everything from wristwatches to wind turbines, robot drive trains, electric scooters, bicycles and industrial gearboxes. Designing or modifying any of them starts with the gear ratio.
This gear ratio speed calculator takes an input speed in rpm and the tooth counts of one or two pairs of gears. It gives the overall gear ratio, the output speed, the ideal torque multiplication and, if you enter a wheel diameter, the linear speed of a wheel on the output shaft in mph or km/h.
How to Use the Gear Ratio Speed Calculator
Enter the input speed in revolutions per minute, such as a motor's rated rpm.
Enter the driving gear teeth, the gear on the input shaft, and the driven gear teeth.
For a compound train, enter the second-stage driving and driven teeth; leave them at 0 for a single pair.
Optionally choose inches or millimetres and enter the wheel diameter to get the linear speed.
The Formulas
stage ratio = driven teeth ÷ driving teeth
overall ratio = stage 1 ratio × stage 2 ratio
output rpm = input rpm ÷ overall ratio
ideal torque = input torque × overall ratio
wheel speed = output rpm × π × diameter (per minute)
mph = rpm × π × diameter (in) × 60 ÷ 63,360Step-by-Step Example
A 3,000 rpm motor with a 12 tooth pinion driving a 48 tooth gear, on a 10 inch wheel.
ratio = 48 ÷ 12 = 4:1
output = 3,000 ÷ 4 = 750 rpm
torque = 4 × the motor torque (ideal)
circumference = π × 10 = 31.42 in
wheel speed = 750 × 31.42 = 23,562 in/min
= 23,562 × 60 ÷ 63,360 ≈ 22.31 mph (35.91 km/h)A two-stage train: a 1,450 rpm motor, a 15 to 45 tooth first stage and a 12 to 36 tooth second stage. Each stage is 3:1, so the overall ratio is 9:1 and the output turns at about 161 rpm with about nine times the torque.
Reduction, Overdrive and Direct Drive
When the driven gear has more teeth than the driver, the ratio is greater than 1 and the gear train is a reduction: the output turns slower and with more torque. This is the most common arrangement, since electric motors spin fast but have modest torque. When the driven gear is smaller, the ratio is below 1 and the train is an overdrive: faster output, less torque. Equal gears give direct drive.
Torque and Efficiency
In an ideal gear train, power in equals power out, so if speed falls by a factor of four, torque rises by four. Real gears lose some power to friction: well-made spur gears lose roughly 2 to 5 percent per stage, and worm gears can lose much more. For a design, multiply the ideal torque by the efficiency of each stage, and size the motor with a margin for losses and starting loads.
Compound Gear Trains
A single pair of gears becomes impractical for large ratios, because the driven gear would be enormous. Compound trains put two gears on an intermediate shaft: the first stage drives a large gear, and a small gear on the same shaft drives the next stage. The overall ratio is the product of the stage ratios, so two 3:1 stages give 9:1 and three give 27:1, all in a compact space.
Direction of Rotation
Each pair of meshing external gears reverses the direction of rotation. With one stage the output turns the opposite way to the input; with two stages it turns the same way. An idler gear placed between two gears reverses the direction again without changing the ratio, because its tooth count cancels out. Belt and chain drives, by contrast, keep the same direction.
Choosing Gear Sizes
Gears that mesh must have the same tooth size, called the module in metric systems or the diametral pitch in inch systems. Within a compatible set, avoid very small pinions, since gears with fewer than about 12 to 17 teeth can suffer undercutting and wear. When a ratio is not a whole number, choosing tooth counts with no common factor, such as 13 and 47, spreads wear across all the teeth.
From Motor to Wheel
For a vehicle or robot, work backwards from the speed you want. If a 6 inch wheel should move at 5 mph, it must turn at 5 × 63,360 ÷ 60 ÷ (π × 6), or about 280 rpm. A motor running at 3,000 rpm then needs a ratio of about 10.7:1, which suits a two-stage train such as 3:1 and 3.6:1. Checking the torque at the wheel against the load ensures the motor can start and climb.
Gears Versus Belts and Chains
Belt and chain drives follow the same ratio rule using pulley diameters or sprocket tooth counts, and keep the direction of rotation. A bicycle is a familiar example: a 50 tooth chainring driving a 25 tooth sprocket gives the rear wheel two turns per pedal turn.
Understanding Your Result
The headline gives the output speed in rpm.
The ratio line gives the overall gear ratio and whether it is a reduction or overdrive.
The torque line gives the ideal torque multiplication and typical losses.
The wheel speed line gives the linear speed of a wheel on the output shaft.
When Should You Use This Calculator?
Use it to choose gears for a robot, model, cart or machine.
Use it to work out the output speed of an existing gearbox.
Use it to convert motor rpm into vehicle or conveyor speed.
Common Mistakes
Inverting the ratio. Divide driven teeth by driving teeth.
Adding stage ratios. Multiply them instead.
Ignoring losses. Real torque is lower than the ideal figure.
Using radius instead of diameter. Circumference is π times the diameter.