FRC Gear Calculator: Ratios & Speed

The FRC gear calculator works out the output speed and torque of a gearbox for a FIRST Robotics Competition (FRC) robot, given the motor free speed, the gear ratio, and the wheel or mechanism diameter. You enter those three values and get the theoretical maximum robot speed (or mechanism speed) and the output torque at the motor stall point. This page explains the math behind the calculator, how to use it for drivetrain and shooter design, and what real-world factors it does not capture.

Formula

The core formula converts motor RPM to linear speed using the circumference of the driven wheel:

Speed (ft/s) = (Motor free speed / Gear ratio) × (Wheel diameter × π / 12) / 60

• Motor free speed – the RPM of the motor with no load (e.g., a CIM is about 5310 RPM, a mini CIM about 5840 RPM, a 775pro about 18730 RPM). Check the motor datasheet for the exact value.
• Gear ratio – the reduction from motor to output, written as motor turns per one output turn. For example, a 10.71:1 reduction means the motor spins 10.71 times for each wheel revolution.
• Wheel diameter – the outside diameter of the wheel or sprocket in inches. For a mecanum or traction wheel, use the actual rolling diameter.
• Output speed – the linear speed of the robot (or the surface speed of a shooter roller) in feet per second and miles per hour.

The torque formula uses the motor stall torque (e.g., 3.56 oz-in for a CIM) multiplied by the gear ratio, ignoring gearbox efficiency:

Output stall torque (oz-in) = Motor stall torque × Gear ratio

This gives the theoretical maximum torque at zero speed, which is always higher than what the robot will actually produce due to friction and gearbox losses.

Worked Example

Using the default values from the calculator: a CIM motor (free speed 5310 RPM), a 10.71:1 gear ratio, and a 4-inch diameter wheel.

1. Find the output RPM: 5310 / 10.71 = 495.8 RPM (approximately).
2. Find the wheel circumference: 4 in × π = 12.566 in.
3. Convert to feet: 12.566 in / 12 = 1.0472 ft.
4. Output speed in ft/s: 495.8 RPM × 1.0472 ft / 60 = 8.65 ft/s.
5. Convert to mph: 8.65 × 0.681818 = 5.90 mph.
6. Stall torque: 3.56 oz-in × 10.71 = 38.1 oz-in (about 2.38 lb-in).

The calculator shows 8.65 ft/s, 5.90 mph, and 38.1 oz-in – matching the manual calculation.

How to Use This Calculator for Your Robot

In FRC, gearboxes are used for two main purposes: drivetrains and mechanisms (shooters, arms, elevators). For a drivetrain, you typically want a top speed between 10 and 15 ft/s, depending on the field and your strategy. For a shooter, you need the roller surface speed to match the required launch speed of the game piece.

• Start with the motor free speed from the manufacturer datasheet. For a CIM, that is 5310 RPM; for a NEO, it is 5880 RPM (free speed at 12V).
• Pick a gear ratio based on the desired top speed. A lower gear ratio (e.g., 8:1) gives higher speed but less torque; a higher ratio (e.g., 12:1) gives more torque but lower speed.
• Measure the actual wheel diameter. A 4-inch wheel is common, but many teams use 6-inch or even 8-inch wheels. The diameter directly affects speed – a larger wheel goes faster for the same gear ratio.
• For a shooter, measure the roller diameter (the part that contacts the ball) and use that as the wheel diameter. The output speed is the surface speed of the roller.

Common Mistakes and Misconceptions

One frequent error is mixing up gear ratio direction. A 10.71:1 ratio means the motor turns 10.71 times per output turn – that is a reduction. If you enter 10.71 as the gear ratio, the calculator divides the motor speed by 10.71. If you accidentally use 1:10.71, you would get a speed 100 times too high.

Another mistake is using the wheel radius instead of diameter, or using inches when the formula expects feet. Always convert to consistent units. The calculator uses inches for wheel diameter and outputs speed in ft/s, so the conversion factor 12 (inches per foot) is built in.

A common misconception is that the free speed is the actual speed under load. In reality, the motor slows down as load increases. The free speed is the no-load maximum; the actual speed at operating torque is lower, often 70-80% of free speed for a well-designed drivetrain. This calculator gives the theoretical maximum, not the real-world speed.

Real-World Factors the Calculator Ignores

The calculator assumes 100% efficiency and no losses. Real gearboxes have friction, and the efficiency of a planetary gearbox is typically around 80-90% per stage. A multi-stage gearbox might have overall efficiency of 70-80%. This means the actual speed will be lower than calculated, and the actual torque will also be lower (because friction consumes some of the motor torque).

Battery voltage also matters. The free speed is specified at 12V, but during a match the battery voltage can drop to 10V or lower under heavy load, reducing motor speed proportionally. At 10V, a CIM free speed would be about 5310 × (10/12) = 4425 RPM.

Other factors include wheel slip, tire deformation, and the weight of the robot. The calculator gives a theoretical maximum; a typical robot might achieve 80-90% of that speed on a flat surface with good traction.

Choosing a Gear Ratio for Your Drivetrain

The right gear ratio depends on your robot’s weight, the torque needed to accelerate, and the desired top speed. A heavier robot needs more torque to accelerate quickly, so a higher gear ratio (more reduction) is better. A lighter robot can use a lower ratio for higher speed.

As a rule of thumb, many FRC teams use a gear ratio between 8:1 and 12:1 for a standard 6-wheel drivetrain with 4-inch wheels. That gives a top speed of roughly 10-15 ft/s. For a 6-inch wheel, a ratio of 10:1 to 14:1 might be more appropriate.

To decide, start with the desired top speed and work backward using the formula. For example, if you want 12 ft/s with a 4-inch wheel and a CIM motor (5310 RPM), solve for the gear ratio:

Gear ratio = (5310 × 4 × π / 12) / (12 × 60) = 7.72

So a ratio around 8:1 would give about 11.6 ft/s. If you need more torque, go to 10:1 (about 9.3 ft/s).

Alternatives and Other Calculators

This calculator is specific to FRC gearboxes, but the same math applies to any motor-driven wheel. If you are working with a different motor, just replace the free speed and stall torque with the values from that motor’s datasheet. For example, a NEO motor has a free speed of 5880 RPM and a stall torque of about 3.6 N·m (or about 510 oz-in) – actually, the NEO stall torque is around 3.6 N·m, but in oz-in that is about 510 oz-in. The calculator uses the CIM’s stall torque of 3.56 oz-in as a default, but you should change it if you use a different motor.

For shooter design, you might also need to calculate the required roller speed to launch a game piece a certain distance. That involves projectile motion, which is beyond the scope of this calculator. Similarly, for arms and elevators, you need to consider gravity and the moment of inertia, which this calculator does not handle.

Frequently Asked Questions

What is the difference between gear ratio and gear reduction?

Gear ratio and gear reduction are often used interchangeably, but technically the gear ratio is the ratio of input speed to output speed. A reduction is a gear ratio greater than 1:1, meaning the output turns slower than the input. In FRC, when someone says “10.71:1 gearbox,� they mean a reduction of 10.71:1 – the motor turns 10.71 times per output turn.

How do I find the free speed of my motor?

The free speed is listed on the motor’s datasheet, usually under “free speed� or “no-load speed.� For common FRC motors, the values are well-known: CIM is 5310 RPM, mini CIM is 5840 RPM, 775pro is 18730 RPM, NEO is 5880 RPM, and Falcon 500 is 6380 RPM. Always check the datasheet for the exact number, as different versions may vary.

Why does my robot not go as fast as the calculator says?

Several factors reduce real speed: gearbox friction (efficiency), battery voltage drop under load, wheel slip, and the motor not reaching free speed because it has to overcome rolling resistance and inertia. A typical robot might only reach 70-90% of the theoretical speed. To get closer, use a more efficient gearbox, keep the robot light, and use a good battery.

Can I use this calculator for a shooter?

Yes, for a shooter you enter the roller diameter (the part that contacts the ball) and the gear ratio. The output speed is the surface speed of the roller in ft/s. This is the speed at which the ball leaves the roller, assuming no slip. You then need to account for the ball’s compression and the shooting angle, which are not covered here.

What is the best gear ratio for an FRC drivetrain?

There is no single best ratio – it depends on your robot’s weight, the field, and your strategy. A common starting point is 10:1 with 4-inch wheels, which gives about 9.3 ft/s with a CIM. For a lighter robot or if you want more speed, try 8:1 (11.6 ft/s). For a heavier robot or if you need more torque for pushing, try 12:1 (7.7 ft/s). Test with your actual robot to find the best balance.

Does the calculator account for gearbox efficiency?

No, it assumes 100% efficiency. To account for efficiency, multiply the output speed by the efficiency factor (e.g., 0.85 for 85% efficiency). You can also adjust the gear ratio slightly to compensate. For example, if you want a real speed of 10 ft/s with 85% efficiency, aim for a theoretical speed of about 11.8 ft/s.

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in motor_free_rpm | Motor free speed | RPM | 5310 | 0
in gear_ratio | Gear ratio (motor:output, e.g. 10.71:1) | - | 10.71 | 0.1
in wheel_diam | Wheel or sprocket diameter | in | 4 | 0.1
out speed_fps | Robot speed | ft/s | (motor_free_rpm / gear_ratio) * (wheel_diam * 3.14159 / 12) / 60 | 2
out speed_mph | Robot speed | mph | ((motor_free_rpm / gear_ratio) * (wheel_diam * 3.14159 / 12) / 60) * 0.681818 | 2
out torque_stall | Stall torque at output | oz-in | 3.56 * gear_ratio | 1