Gearbox Ratio Calculator: How to Use It

A gearbox ratio calculator works out the ratio between the number of teeth on two meshing gears (or the diameters of pulleys) and then uses that ratio to find output speed or torque. You enter the tooth counts (or diameters) and, if you like, the input RPM, and the calculator returns the gear ratio, output speed, and mechanical advantage. This page gives you the tool, the formula, and the practical details you need to use it correctly.

Formula

The gearbox ratio is simply the number of teeth on the driven gear divided by the number of teeth on the drive gear:

Gear ratio = N_driven / N_drive

Where:

• N_drive = number of teeth on the input (drive) gear
• N_driven = number of teeth on the output (driven) gear

Output speed is then input RPM divided by that ratio:

Output RPM = Input RPM / Gear ratio

And the torque multiplier equals the gear ratio itself (ignoring friction losses).

Worked Example

Using the default values from the calculator:

• Drive gear: 20 teeth
• Driven gear: 60 teeth
• Input speed: 1200 RPM

Step 1 – Calculate the ratio:

Gear ratio = 60 / 20 = 3.00 (written as 3:1)

Step 2 – Output speed:

Output RPM = 1200 / 3 = 400 RPM

Step 3 – Torque multiplier:

Torque multiplier = 3.00 (the driven gear turns slower but with three times the torque)

So the calculator shows a ratio of 3.00:1, an output speed of 400 RPM, and a torque multiplier of 3.00.

What the Ratio Actually Tells You

A gear ratio above 1 (e.g., 3:1) means the output gear is larger than the input gear. The output shaft turns slower than the input, but it gains torque. This is called a reduction gearbox, and it’s what you find in car differentials, winches, and conveyor drives. A ratio below 1 (e.g., 1:3) means the output turns faster but with less torque – an overdrive setup, common in bicycle high gears or certain machine spindles. A ratio of exactly 1:1 just transfers motion without changing speed or torque.

How to Choose a Gear Ratio

Choosing a ratio depends on what you need at the output shaft. For most practical purposes, you start with the required output speed and the available input speed:

1. Determine the input RPM of your motor or engine.
2. Determine the desired output RPM of the driven wheel, drum, or shaft.
3. Divide input RPM by desired output RPM – that’s the ratio you need.
4. Pick gear teeth counts that give that ratio and physically fit in your housing.

For example, if you have a 1750 RPM motor and want a drum to turn at 350 RPM, you need 1750 / 350 = 5, so a 5:1 reduction. That could be a 20-tooth drive gear and a 100-tooth driven gear, or any pair with that ratio.

Common Mistakes and Misconceptions

The most frequent error is mixing up which gear is the drive and which is the driven. The drive gear is on the input shaft (connected to the motor), and the driven gear is on the output shaft. Swapping them gives you the reciprocal ratio, which changes a reduction into an overdrive.

Another common mistake is using pitch diameters instead of tooth counts. For standard gears, tooth count is proportional to pitch diameter, so either works, but mixing the two (teeth on one gear, diameter on the other) gives a wrong answer. Also remember that the ratio is based on the number of teeth, not the physical size of the gear blank.

Finally, the torque multiplier formula assumes 100% efficiency. Real gearboxes lose a few percent to friction, so the actual output torque is slightly lower than the theoretical value. For planning purposes, this is usually fine, but for precise design you’d apply an efficiency factor (e.g., 0.95 for a single gear pair).

When You Need More Than One Gear Pair

If you need a very large reduction (say 50:1), a single pair of gears would need one gear with 50 times more teeth than the other – often too large to fit. Instead, you can use a compound gear train: two or more pairs in series. The total ratio is the product of each pair’s ratio. For instance, a 5:1 pair followed by a 10:1 pair gives 5 × 10 = 50:1 overall. The calculator above works for a single pair; for a compound train, multiply the individual ratios.

Limits of the Simple Ratio Formula

The formula works for standard spur gears, helical gears, and bevel gears, as long as you know the tooth counts. It does not account for gear tooth strength, backlash, or dynamic loads. It also assumes the gears are rigid and perfectly meshed. For belt or chain drives, you can use the same ratio formula but with pulley or sprocket diameters instead of tooth counts – just be consistent: both diameters in the same units, or both tooth counts if the pulleys have the same pitch.

Also note that the ratio alone doesn’t tell you the direction of rotation. Two external gears in mesh rotate in opposite directions. If you need the same direction, you add an idler gear (which doesn’t change the ratio) or use an internal gear arrangement.

Frequently Asked Questions

What does a 3:1 gear ratio mean?

A 3:1 ratio means the drive gear rotates three times for every one rotation of the driven gear. The output speed is one-third of the input speed, and the output torque is three times the input torque (ignoring losses).

How do I calculate gear ratio from RPM?

You can’t get the ratio from RPM alone – you need two RPM values. The ratio is input RPM divided by output RPM. For example, if input is 1500 RPM and output is 500 RPM, the ratio is 1500 / 500 = 3 (3:1).

Is a higher gear ratio faster or slower?

A higher ratio (like 5:1 vs 2:1) makes the output slower but with more torque. A lower ratio (like 1:2) makes the output faster but with less torque. So “faster� depends on whether you mean input or output speed – a higher ratio reduces output speed.

Does gear ratio affect torque or speed?

It affects both. The ratio directly sets the output speed (input RPM divided by ratio) and the torque multiplier (equal to the ratio). You can’t change one without the other; that’s the fundamental trade-off in gearboxes.

Can I use tooth count or diameter for the ratio?

Yes, for gears, tooth count is proportional to pitch diameter, so either works as long as you use the same method for both gears. For belt pulleys, use pitch diameters (or effective diameters) in the same units. For chain sprockets, use tooth counts because sprocket diameter is not directly proportional to tooth count in all cases.

Related

• Distribution Calculator With Withdrawals: How It Works
• Distribution Percentage Calculator: How It Works
• Distribution Rate Calculator: How It Works

in drive | Drive gear teeth | teeth | 20 | 1
in driven | Driven gear teeth | teeth | 60 | 1
in rpm | Input speed | RPM | 1200 | 0
out ratio | Gear ratio | :1 | driven / drive | 2
out out_rpm | Output speed | RPM | rpm / (driven / drive) | 0
out torque | Torque multiplier | x | driven / drive | 2