Gear Ratio Calculator Formula & How to Use It

This calculator works out the gear ratio between two gears, and then gives you the output speed and torque change based on the teeth counts you enter. You input the number of teeth on the driving gear and the driven gear, and you get the ratio, the speed multiplier, and the torque multiplier. The formula is simple: gear ratio = driven teeth ÷ driving teeth, and that number tells you how many times the driving gear turns for each full turn of the driven gear.

Formula

The gear ratio formula is written as:

Gear Ratio (GR) = Number of teeth on driven gear (T_driven) ÷ Number of teeth on driving gear (T_drive)

Where:

• T_drive = teeth on the input gear (the one connected to the motor or pedals), unit: teeth (dimensionless)
• T_driven = teeth on the output gear (the one connected to the wheel or shaft), unit: teeth (dimensionless)
• GR = gear ratio, usually written as “X:1â€� (e.g., 2:1 means the driving gear turns twice for every one turn of the driven gear)

The inverse of the ratio gives the speed factor: output speed = input speed × (T_drive ÷ T_driven). Torque changes in the opposite direction: output torque = input torque × (T_driven ÷ T_drive).

Worked Example

Using the default values from the calculator above:

• Driving gear teeth = 20
• Driven gear teeth = 40

Step 1: Divide driven by driving: 40 ÷ 20 = 2.0

Step 2: The gear ratio is 2.0:1. This means the driving gear makes 2 full rotations for each rotation of the driven gear.

Step 3: Speed factor = 20 ÷ 40 = 0.5. So if the input shaft spins at 1000 RPM, the output spins at 500 RPM.

Step 4: Torque multiplier = 40 ÷ 20 = 2.0. So the output torque is double the input torque (ignoring friction losses).

The calculator rounds to 2 decimal places, so the displayed result is exactly 2.00:1.

How Gear Ratios Work

A gear pair transfers rotational motion and force. When two gears mesh, their teeth must match in size (module or pitch), so the number of teeth is directly proportional to the gear’s diameter. The ratio of teeth determines the mechanical advantage:

• Ratio greater than 1 (driven has more teeth): speed decreases, torque increases. This is a “reductionâ€� gear, common in car differentials, winches, and bicycle low gears.
• Ratio less than 1 (driven has fewer teeth): speed increases, torque decreases. This is an “overdriveâ€� gear, used in high-speed applications like drill presses or bicycle high gears.
• Ratio equal to 1: speed and torque stay the same (just a direction change, often used to reverse rotation).

The key trade-off is always speed vs. torque. You cannot get both more speed and more torque from the same gear pair without adding external power.

How to Choose a Gear Ratio

Choosing the right ratio depends on what you are trying to achieve. Here are the main factors to consider:

• Desired output speed: If you need a wheel to spin at a certain RPM, divide the motor RPM by the target RPM to get the ratio.
• Required torque: If you need to lift a heavy load, you need a ratio greater than 1. Multiply the motor torque by the ratio to estimate output torque.
• Space constraints: Large ratios require a big driven gear or multiple stages. A single pair can only give about 10:1 max practically; beyond that, use compound gears.
• Efficiency: Each gear mesh loses about 1-3% due to friction. More stages = more loss.

For example, a small DC motor spins at 3000 RPM but you want a wheel at 300 RPM. Ratio = 3000 ÷ 300 = 10:1. So you need a driven gear with 10 times the teeth of the driving gear (e.g., 12 teeth driving, 120 teeth driven).

Common Mistakes and Misconceptions

One frequent error is reversing the ratio. Remember: driven ÷ driving. If you swap them, a 2:1 reduction becomes a 0.5:1 overdrive, which is the exact opposite.

Another mistake is ignoring tooth size. Two gears with the same tooth count but different module (tooth pitch) will not mesh. The ratio formula only works when the gears actually fit together.

Also, people often confuse gear ratio with gear train ratio in multi-gear systems. For a compound gear train (multiple pairs), you multiply the individual ratios. For example, two 2:1 pairs give an overall 4:1.

Finally, the ratio formula assumes ideal conditions. Real gears have friction, backlash, and wear, so actual output torque is slightly lower than calculated. For most design work, a 1-3% loss per mesh is a reasonable estimate.

Gear Ratio vs. Pulley Ratio vs. Sprocket Ratio

Gears, pulleys, and sprockets all use the same ratio concept, but the input changes:

• Gears: ratio based on teeth count.
• Pulleys (belt drive): ratio based on pulley diameter (or radius).
• Sprockets (chain drive): ratio based on teeth count, just like gears.

The speed and torque formulas are identical once you have the ratio. For pulleys, you measure diameter instead of teeth. For example, a 2-inch pulley driving a 4-inch pulley gives a 2:1 reduction.

This is why the same calculator can be used for any of these, as long as you enter the correct tooth count or diameter.

Compound Gear Trains

When you need a ratio larger than about 10:1, a single pair becomes impractical because the driven gear would be huge. Instead, use multiple pairs on shared shafts:

1. Gear A (driving) meshes with Gear B (driven).
2. Gear B is fixed to Gear C on the same shaft.
3. Gear C meshes with Gear D (final output).

Total ratio = (B/A) × (D/C). For example, A=10, B=40, C=12, D=60 gives (40/10) × (60/12) = 4 × 5 = 20:1. This is much more compact than a single 20:1 pair.

Compound trains are common in gearboxes, clocks, and automotive transmissions. The same torque/speed trade-off applies at each stage, and the total efficiency is the product of each mesh’s efficiency.

Frequently Asked Questions

What does a 2:1 gear ratio mean?

A 2:1 ratio means the driving gear turns twice for every one turn of the driven gear. This is a reduction gear: output speed is half the input speed, but output torque is doubled (ignoring friction).

How do I calculate gear ratio from RPM?

If you know input RPM and desired output RPM, divide input by output. For example, 3000 RPM in, 1000 RPM out = 3000 ÷ 1000 = 3:1. Then choose gears with teeth counts matching that ratio (e.g., 20 teeth driving, 60 teeth driven).

Does gear ratio affect horsepower?

No. Gear ratio changes torque and speed, but the power (horsepower) stays the same (minus friction losses). Power = torque × angular speed. If torque doubles and speed halves, power remains constant.

What is the difference between gear ratio and gear train ratio?

Gear ratio usually refers to a single pair of meshing gears. Gear train ratio refers to the overall ratio of a multi-gear system, which is the product of all individual pair ratios. For a single pair, they are the same.

Can I use this formula for pulleys?

Yes, but use pulley diameters instead of teeth. The ratio is driven diameter ÷ driving diameter. The speed and torque relationships are identical.

Why does my gear ratio calculation seem too high?

Check that you didn’t swap driving and driven. Also, if you have multiple gears, you need to multiply each pair’s ratio, not add them. A common error is adding ratios instead of multiplying.

Related

• E30 Gear Ratio Calculator: Speed & RPM
• Easy Run Pace Calculator: Find Your Zone
• Gear Ratio Calculator: RPM, Speed & Torque

in drive | Driving gear teeth | teeth | 20 | 1
in driven | Driven gear teeth | teeth | 40 | 1
out ratio | Gear ratio | :1 | driven / drive | 2
out speed | Output speed factor | x | drive / driven | 2
out torque | Torque multiplier | x | driven / drive | 2