Gear Ratio Calculator by Diameter

This calculator works out the gear ratio you need when you know the diameter of the driving and driven pulleys, gears, or wheels. Enter the two diameters (or the diameter and the desired speed ratio) and it returns the gear ratio, plus the speed of the driven component if you also enter the input speed. The result is a dimensionless number that tells you how many turns the input makes for each turn of the output.

Formula

The basic gear ratio formula for two pulleys or gears connected by a belt or chain is:

Gear ratio = Driven diameter / Driving diameter

Symbolically: GR = D_driven / D_driving

Where:

• D_driving is the diameter of the input pulley, gear, or wheel (same unit as the driven diameter).
• D_driven is the diameter of the output pulley, gear, or wheel.
• GR is the gear ratio (dimensionless).

If you also know the input speed (in rpm), the output speed is:

Output speed = Input speed / Gear ratio

That is, N_out = N_in / (D_driven/D_driving).

Worked Example

Using the default values from the calculator above: driving diameter = 6 inches, driven diameter = 12 inches, input speed = 100 rpm.

1. Compute the gear ratio: 12 / 6 = 2.00.
2. Compute the output speed: 100 / 2 = 50 rpm.

The calculator shows a gear ratio of 2.00 and an output speed of 50.0 rpm. This matches the formula exactly.

When to Use Diameter Instead of Teeth

For gears with teeth, the ratio is normally calculated from the number of teeth, not the diameter, because teeth are discrete and the ratio must be a whole number fraction (e.g., 20 teeth driving a 40-tooth gear gives 2.00). However, for belt drives, chain drives, and friction wheel drives, the pitch diameter (or effective diameter) is the correct basis. For a belt drive, use the pitch diameter of each pulley—the diameter at the centerline of the belt. For a chain drive, use the pitch diameter of the sprockets, which is slightly larger than the outer diameter. For a friction drive (two wheels pressed together), the outer diameters are used.

How to Choose the Right Diameter

When designing a drive system, you typically start with the desired speed ratio and then pick diameters that are physically available. For example, if you need a 2:1 reduction and your motor runs at 1750 rpm, you could use a 2-inch driving pulley and a 4-inch driven pulley. But you could also use 3-inch and 6-inch, or 4-inch and 8-inch—all give the same ratio. The choice depends on belt length, center distance, and torque requirements. Larger pulleys generally reduce belt wear and allow higher torque transmission, but they take up more space.

Common Mistakes and Misconceptions

• Using outer diameter instead of pitch diameter for belt drives: this introduces a small error, usually 2-5%, which can be significant in precision applications.
• Mixing units: both diameters must be in the same unit (inches, mm, cm) before dividing. The calculator assumes you enter both in the same unit, but it does not convert.
• Reversing the ratio: many people accidentally divide the driving by the driven. The gear ratio as defined here is driven/driving. A ratio greater than 1 means speed reduction (output slower than input); a ratio less than 1 means speed increase (output faster than input).
• Confusing gear ratio with torque ratio: torque is inversely proportional to speed ratio (ignoring losses). A 2:1 reduction doubles torque at the output, but the gear ratio number itself is just the diameter ratio.

Limits of the Diameter-Based Formula

The diameter method assumes no slip and perfect contact. In real belt drives, slip can occur under load, so the actual output speed may be slightly lower than calculated. Chain drives have negligible slip, but the pitch diameter must be used, not the outer diameter. For gear trains with multiple stages, you multiply the individual ratios. The formula also assumes the two diameters are measured at the same reference point (e.g., both pitch diameters). If you mix pitch diameter with outer diameter, the result is wrong.

Frequently Asked Questions

What is the difference between gear ratio and speed ratio?

They are the same thing. The gear ratio (driven/driving) equals the speed ratio (input speed / output speed). A gear ratio of 2 means the input turns twice for every one turn of the output.

Can I use this calculator for gears with teeth?

Yes, but only if you use the pitch diameter of each gear, not the outer diameter. For standard gears, the pitch diameter is proportional to the number of teeth, so using teeth count is simpler and more accurate. The diameter method works fine if you have the pitch diameters.

What if I only know the number of teeth?

Then you don’t need diameters. The gear ratio is simply teeth on the driven gear divided by teeth on the driving gear. For example, a 20-tooth gear driving a 60-tooth gear gives a ratio of 3.0. This calculator is for when you have diameters, not tooth counts.

How do I measure the pitch diameter of a pulley?

For a V-belt pulley, the pitch diameter is approximately the outer diameter minus the belt cross-section height. For a timing belt pulley, it is the diameter at the belt’s pitch line, which is usually marked on the pulley or can be calculated from the number of teeth and the belt pitch. When in doubt, consult the manufacturer’s specifications.

Does the distance between centers affect the gear ratio?

No. For a belt or chain drive, the center distance only affects belt length and tension, not the speed ratio. The ratio depends solely on the diameters of the two pulleys or sprockets.

What is a good gear ratio for a project?

It depends on your application. For a reduction drive (e.g., from a motor to a wheel), ratios between 2 and 5 are common. For high-speed applications, you might use a ratio less than 1 (overdrive). The calculator helps you find the ratio for given diameters, but the ‘good’ ratio is determined by your speed and torque requirements.

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in d1 | Driving diameter | in | 6 | 0
in d2 | Driven diameter | in | 12 | 0
in rpm | Input speed | rpm | 100 | 0
out ratio | Gear ratio (d2/d1) | - | d2 / d1 | 2
out speed | Output speed | rpm | rpm / (d2 / d1) | 1