calculate gear ratios

What does it mean to calculate gear ratios?

A gear ratio describes how the rotational speed and torque change from one gear to another. Whether you are tuning a bike drivetrain, designing a gearbox, or sizing gears for a robotics project, calculating the ratio helps you predict performance before you build.

In simple terms, the ratio tells you how many turns of the input are needed to produce one turn of the output, or vice versa, depending on how you define it. Higher reduction ratios usually trade speed for torque. Lower ratios tend to increase output speed but reduce torque multiplication.

Core formulas you should know

Standard external gear pair formula

Gear Ratio = Teeth on Driven Gear ÷ Teeth on Driving Gear

• If the result is greater than 1, you have a reduction (more torque, less speed).
• If the result is less than 1, you have an overdrive (more speed, less torque).
• With two external gears, input and output rotate in opposite directions.

Bicycle drivetrain formula

Bicycle Ratio = Chainring Teeth ÷ Rear Cog Teeth

This tells you how many rear-wheel revolutions happen for each crank revolution (ignoring wheel slip and drivetrain losses). From there, you can estimate speed using wheel circumference and cadence.

How to use the calculator above

For machines, go-karts, robots, or gear trains

• Enter the input (driving) gear tooth count.
• Enter the output (driven) gear tooth count.
• Click Calculate Ratio to see reduction, speed factor, and torque factor.

For bicycles

• Enter chainring and rear cog teeth.
• Add wheel diameter in inches.
• Enter cadence (RPM) and optional internal hub ratio.
• Click Calculate Bike Metrics for gear ratio, gear inches, rollout, and estimated speed.

Worked examples

Example 1: 20T driving, 60T driven

Ratio = 60/20 = 3.0:1. The output turns one revolution for every three input revolutions. Output speed is one-third of input speed, and ideal torque is multiplied by about three.

Example 2: Road bike 50/17 at 90 RPM

Bicycle ratio = 50/17 ≈ 2.94. With a typical ~27-inch wheel, this produces a high rollout per pedal stroke. At 90 RPM cadence, speed is in a strong cruising range for flat terrain and fast group riding.

How to choose the right ratio

• For climbing or pulling loads: choose more reduction (higher driven/driving value).
• For top speed: choose less reduction or overdrive, if motor torque allows.
• For bicycles: lower gears for hills, higher gears for flats and descents.
• For efficiency: avoid ratios that force operation far from optimal RPM or cadence.

Common mistakes when calculating gear ratios

• Mixing up which gear is driving and which is driven.
• Ignoring additional stages in a multi-stage gearbox.
• Forgetting to include internal hub or transmission multipliers.
• Assuming theoretical speed equals real speed without accounting for drag, losses, and tire growth/slip.

Quick FAQ

Is a bigger gear ratio always better?

No. Bigger reduction improves torque but lowers output speed. “Better” depends on your goal.

What is gear inches?

Gear inches = wheel diameter (inches) × bicycle ratio. It is a classic way cyclists compare how hard or easy a gear feels.

Can I use this for multi-stage systems?

Yes. Calculate each stage ratio and multiply them together for total ratio. For example, stage 1 of 2:1 and stage 2 of 3:1 gives total 6:1.

Final thoughts

When you calculate gear ratios correctly, design decisions become clearer: speed targets, acceleration expectations, climbing behavior, and drivetrain feel all become predictable. Use the calculator as a quick planning tool, then validate with real-world testing.