Gear Ratio Calculator: RPM, Speed & Torque

This gear ratio calculator works out the output speed and torque of a driven gear when you enter the number of teeth on the driving and driven gears, and the input RPM. You get the gear ratio, the output RPM, and the torque multiplication factor instantly, which is exactly what you need for planning a drivetrain, a gearbox, or a simple chain-and-sprocket setup.

Formula

The fundamental gear ratio equation is simple: Gear Ratio = (Number of teeth on driven gear) ÷ (Number of teeth on driving gear). In symbols, that is GR = N_driven / N_drive.

• N_drive – number of teeth on the input (driving) gear, unitless.
• N_driven – number of teeth on the output (driven) gear, unitless.
• GR – the ratio, expressed as X:1.

Output RPM is then RPM_out = RPM_in ÷ GR, and torque multiplication is numerically equal to GR (ignoring friction losses). For example, a 20-tooth driving gear turning a 40-tooth driven gear gives a 2:1 reduction: output speed halves, torque doubles.

Worked Example

Using the calculator defaults: a 20-tooth driving gear, a 40-tooth driven gear, and 1500 RPM input.

1. Gear ratio = 40 ÷ 20 = 2.00 (2:1).
2. Output RPM = 1500 ÷ 2.00 = 750 RPM.
3. Torque multiplication = 2.00 (ideal, frictionless).

So the driven gear spins at 750 RPM with twice the torque of the input shaft. This matches the calculator’s headline output of 2.00 for the ratio.

How Gear Ratios Work

Gears transfer rotational motion and force. When two gears mesh, their teeth must move at the same linear speed at the contact point, so the smaller gear must spin faster than the larger one. The ratio of teeth directly sets the speed and torque trade-off: a reduction (driven gear larger than driving gear) lowers speed and raises torque; an overdrive (driven gear smaller) does the opposite. This is the core principle behind bicycle gears, car transmissions, and industrial gearboxes.

For compound gear trains (multiple meshing pairs), multiply each individual ratio together. For example, a 2:1 first stage and a 3:1 second stage give a total 6:1 reduction. The calculator handles a single pair; for multiple stages, enter the overall ratio as the driven/drive teeth values.

How to Choose a Gear Ratio

Choosing the right ratio depends on what you are optimizing: top speed, acceleration, or torque. Start with the desired output RPM and your available input RPM, then divide input by output to get the needed ratio.

• For speed – you want a ratio less than 1 (overdrive), so the driven gear is smaller than the driving gear.
• For torque – you want a ratio greater than 1 (reduction), so the driven gear is larger.
• For a balance – pick a ratio near 1:1, common in transfer cases and simple machinery.

Also consider the physical space: a very large driven gear may not fit, and very small pinions can undercut teeth. When in doubt, check the manufacturer’s spec for minimum teeth on the smaller gear (often 12–18 for standard involute gears).

Common Mistakes and Misconceptions

The most frequent error is inverting the ratio – dividing driving by driven instead of driven by driving. A 20-tooth drive and 40-tooth driven is 2:1, not 0.5:1. Double-check which gear is the input.

Another misconception is that torque multiplication is free. In reality, gear meshing has friction losses (typically 1–2% per mesh for spur gears), so output torque is slightly less than the ideal ratio. Also, the ratio only affects torque and speed, not power; power in equals power out minus losses. Finally, do not confuse the gear ratio with the gear module or pitch – those are about tooth size, not the number of teeth.

Comparison: Gears vs. Belts and Chains

Gears, belts, and chains all achieve speed/torque conversion, but with different trade-offs. Gears are compact, positive (no slip), and can handle high torque, but they are noisy and need precise alignment. Chains (like on bicycles) are also positive and efficient, but they require tensioning and lubrication. Belts are quiet and forgiving of misalignment, but they can slip under shock loads unless they are toothed timing belts. The ratio calculation is the same for all three if you use the number of teeth on the sprockets or pulleys instead of gears.

Safety and Accuracy Notes

When using gear ratios for any real machine, always verify the calculated values with a tachometer or encoder after assembly – manufacturing tolerances and friction can shift actual output. Never exceed the rated speed of a gear or belt; overspeed can cause catastrophic failure. For high-torque applications, ensure the gear material and tooth width are rated for the load, and always use proper guards to prevent clothing or fingers from being caught in moving parts. For a prototype, start at low speed and check for unusual noise or heat.

Frequently Asked Questions

What is a good gear ratio for a go-kart?

There is no single “good� ratio; it depends on your engine RPM, tire diameter, and desired top speed. A common starting point is around 6:1 for a typical 200cc engine with 15-inch tires, but you should work backwards from your target speed using the formula: engine RPM ÷ (final ratio × tire circumference) gives wheel RPM, then multiply by tire circumference to get speed.

Does a higher gear ratio mean more speed or more torque?

A numerically higher ratio (e.g., 4:1 vs. 2:1) means more torque and lower speed at the output. A lower ratio (e.g., 0.8:1) means more speed but less torque. The ratio is a trade-off, not a way to get both.

How do I calculate gear ratio from RPM?

Divide the input RPM by the output RPM. For example, if your motor spins at 3000 RPM and you want the output at 750 RPM, the ratio is 3000 ÷ 750 = 4. So you need a 4:1 reduction.

What is the difference between gear ratio and final drive ratio?

Gear ratio refers to a single pair of gears. Final drive ratio is the total reduction from the engine/input shaft to the wheels, including the transmission gear, differential, and any other stages. Multiply all individual ratios together to get the final drive ratio.

Can I use this calculator for pulley or sprocket ratios?

Yes, as long as you use the number of teeth on the sprockets or the pitch diameter of the pulleys. For belts and chains, the same ratio formula applies: driven teeth ÷ drive teeth. For friction pulleys, use the diameter instead of tooth count.

Why does my measured output RPM differ from the calculation?

Real-world losses from friction, belt slip, gear backlash, and manufacturing tolerances cause the actual output to be slightly lower than the ideal calculation. Also, verify that you are measuring the correct gear as the input – a simple inversion error is the most common cause of a large discrepancy.

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in drive | Driving gear teeth | teeth | 20 | 1
in driven | Driven gear teeth | teeth | 40 | 1
in rpm | Input RPM | rpm | 1500 | 0
out ratio | Gear ratio (driven/drive) | :1 | driven / drive | 2
out outrpm | Output RPM | rpm | rpm / (driven / drive) | 0
out torque | Torque multiplication | x | driven / drive | 2