Gear Speed Calculator: Formula & How to Use

A gear speed calculator works out the output speed (RPM) of a driven gear when you enter the input speed and the number of teeth on both gears. It also shows the gear ratio and often the torque change, so you can see how a gearset alters speed and force. You enter the driver gear’s RPM and tooth count plus the driven gear’s tooth count, and the calculator returns the driven gear’s RPM, the ratio, and the torque multiplier.

Formula

The basic gear speed formula comes from the fact that two meshing gears must have the same linear velocity at their contact point. That gives:

Output RPM = Input RPM × (Driver Teeth / Driven Teeth)

and the gear ratio is:

Gear Ratio = Driven Teeth / Driver Teeth

Where:

• Input RPM – rotational speed of the driving gear (revolutions per minute)
• Driver Teeth – number of teeth on the gear that is turning first
• Driven Teeth – number of teeth on the gear that is being turned
• Output RPM – rotational speed of the driven gear
• Gear Ratio – how many turns of the driver produce one turn of the driven gear (written as driven:driver, e.g., 2:1)

If the driven gear has more teeth than the driver, the output speed drops and torque increases. If it has fewer teeth, the output speed rises and torque drops. This is the same math used for bicycle gears, car transmissions, and industrial gearboxes.

Worked Example

Using the calculator defaults: input speed = 3000 RPM, driver teeth = 20, driven teeth = 40.

1. Gear ratio = 40 / 20 = 2.00 (written as 2:1)
2. Output RPM = 3000 × (20 / 40) = 3000 × 0.5 = 1500 RPM
3. Torque multiplier = 40 / 20 = 2.0 (the driven gear turns half as fast but with twice the torque, ignoring friction)

So a 3000 RPM motor driving a 20-tooth gear that meshes with a 40-tooth gear will spin the output at 1500 RPM. The calculator shows 1500.0 RPM, a ratio of 2.00, and a torque multiplier of 2.00.

When to Use a Gear Speed Calculator

You reach for a gear speed calculator whenever you need to know what speed a gearset will produce before you build it. Common situations include:

• Designing a gearbox for a robot or hobby project where motor RPM is known but wheel speed needs to be lower
• Choosing gears for a lathe or milling machine to get the right spindle speed
• Checking the final drive ratio on a car or motorcycle to estimate top speed or acceleration
• Replacing a gear on a conveyor or pump and needing to keep the same output speed
• Planning a bicycle gear setup for a specific cadence and speed

The same formula works for any pair of meshing gears – spur, helical, bevel, or worm – as long as you know the tooth counts. For a worm gear, the “teeth� on the worm are the number of starts (threads), usually 1, 2, or 4.

How to Choose the Right Gear Ratio

Choosing a gear ratio is about balancing speed and torque. Start with what you need at the output, then work backward.

1. Determine the required output speed (RPM) and the available input speed (motor RPM).
2. Calculate the ratio: Ratio = Input RPM / Output RPM.
3. Pick tooth counts that give that ratio. For a 2:1 reduction, you could use 20/40, 30/60, or 15/30 – all give the same ratio but different sizes.
4. Check the center distance: the sum of the two pitch diameters must match the spacing between shafts.
5. Consider the torque: a higher ratio increases torque but also increases stress on the teeth and bearings.

For example, if you have a 3000 RPM motor and want 750 RPM output, you need a 4:1 reduction. That means the driven gear must have four times as many teeth as the driver – e.g., 20 driver and 80 driven.

Common Mistakes and How to Avoid Them

The most frequent error is mixing up which gear is the driver. The driver is the gear that provides the power – the motor shaft or pedal crank. The driven gear is the one that receives power. If you swap them, you get the inverse ratio and a completely wrong speed.

• Unit mix-up: Make sure input speed is in RPM. If you have a speed in rad/s, multiply by 9.549 to get RPM (since 1 RPM = 2Ï€/60 rad/s).
• Tooth count vs. diameter: For standard gears, teeth are proportional to diameter, so the ratio works with teeth. But if you use the pitch diameter instead, the same formula works – just be consistent.
• Ignoring friction: The calculator gives the theoretical speed. Real gears lose 1–3% per mesh due to friction, so actual output speed will be slightly lower.
• Assuming torque stays constant: The torque multiplier is the inverse of the speed ratio only when power is constant. In reality, friction reduces the output torque a bit.

Limits of the Formula

The simple gear speed formula assumes ideal gears with no slip, no flex, and no power loss. That is accurate for most rigid metal or plastic gears, but there are cases where it falls short:

• Belt and chain drives: These can slip (belts) or have slight elongation, so the exact ratio may not hold. Chain drives are close to gears but not exact.
• Planetary gear sets: These have multiple meshing gears and a different formula that includes the sun, ring, and carrier.
• Worm gears: The ratio is driven teeth divided by the number of worm starts, but the worm also has an efficiency that varies with the lead angle.
• Variable speed drives: If the input speed changes, the output changes proportionally, but the calculator only gives a snapshot.

Also, the formula gives the speed ratio, not the absolute speed if the input RPM is unknown. You must know the input speed to get an output speed in RPM.

Gear Speed vs. Gear Ratio vs. Torque

These three are related but not the same. Gear ratio is a pure number describing the tooth relationship. Output speed is the ratio applied to the input RPM. Torque change is the inverse of the speed ratio (ignoring losses).

For a 2:1 reduction (driven has twice the teeth), the output speed is half the input, and the output torque is double the input. For a 1:2 overdrive (driven has half the teeth), the output speed is double, but torque is halved. This is why low gears (high ratios) are used for climbing hills and high gears for speed.

Frequently Asked Questions

Does the calculator work for metric or imperial gears?
Yes, because tooth count is unitless. The calculator only needs the number of teeth and the input RPM, so it works for any gear size or pitch (module, DP, etc.).

What if I only know the gear diameter, not the tooth count?
You can use the ratio of pitch diameters instead of teeth, as long as both gears are the same pitch. The formula becomes Output RPM = Input RPM × (Driver Diameter / Driven Diameter).

How do I find the output speed for a multi-stage gearbox?
Multiply the ratios of each stage together. For example, a 3:1 first stage and a 2:1 second stage gives a total 6:1 reduction. The output speed is input RPM divided by 6.

Why does my actual gear speed differ from the calculation?
Real gears have friction, backlash, and manufacturing tolerances. Also, if the load is heavy, the motor speed may drop below its no-load RPM. The calculation assumes the input speed you enter is the actual running speed.

Can I use this for a rack and pinion?
Yes, but the output is linear speed, not RPM. For a rack and pinion, the linear speed of the rack equals the pinion’s pitch circle circumference times the pinion RPM. The gear speed formula still gives the pinion RPM from the motor, but you then convert to linear velocity.

Is a higher gear ratio always better for torque?
Higher ratio means more torque at the output, but only up to the strength limits of the gears and bearings. Also, extremely high ratios may require multiple stages because a single pair with a huge tooth difference is impractical.

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in rpm | Input speed | RPM | 3000 | 0
in t1 | Driver teeth | teeth | 20 | 1
in t2 | Driven teeth | teeth | 40 | 1
out out_rpm | Output speed | RPM | rpm * t1 / t2 | 1
out ratio | Gear ratio | - | t2 / t1 | 2
out torque | Torque multiplier | - | t2 / t1 | 2