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Gear Ratio Torque & Speed Calculator

Calculate the output torque and rotational speed of a gear system from its gear ratio.

Result

Gear Ratio
3:1
Output Torque
15 N·m
Output Speed
333 RPM

A gear system trades speed for torque (or vice versa) but can't increase both - output torque multiplies by the gear ratio while output speed divides by the same ratio, so total mechanical power (torque × angular speed) stays constant aside from small friction losses.

About the Gear Ratio Calculator

The Gear Ratio Torque & Speed Calculator determines how a pair of meshed gears transforms input torque and rotational speed into output torque and speed, based on the number of teeth on each gear. It's built for anyone designing or analyzing a simple gear train, from hobbyist robotics to mechanical engineering coursework.

How It Works

Enter the number of teeth on the driving gear and the driven gear, along with the input torque and input rotational speed. The calculator divides driven teeth by driving teeth to get the gear ratio, then multiplies input torque by that ratio to get output torque, and divides input speed by the same ratio to get output speed.

Gear ratio = driven teeth / driving teeth. Output torque = input torque x gear ratio. Output speed = input speed / gear ratio.

Formula & Methodology

To calculate by hand, first find the gear ratio by dividing the number of teeth on the driven (output) gear by the number of teeth on the driving (input) gear. A ratio greater than 1 means the output gear turns slower but with more torque; a ratio less than 1 means the opposite. Multiply input torque by this ratio for output torque, and divide input speed by the same ratio for output speed, reflecting that mechanical power stays essentially constant through the gear train aside from friction losses.

Examples

Reduction Gearbox

A 12-tooth driving gear meshes with a 36-tooth driven gear, carrying 5 N·m of input torque at 1000 RPM. Gear ratio = 36 / 12 = 3:1, output torque = 5 x 3 = 15 N·m, and output speed = 1000 / 3, or about 333 RPM.

Speed-Increasing Gear Pair

A 40-tooth driving gear meshes with a smaller 10-tooth driven gear, carrying 15 N·m of input torque at 500 RPM. Gear ratio = 10 / 40 = 0.25:1, output torque = 15 x 0.25 = 3.75 N·m, and output speed = 500 / 0.25 = 2000 RPM.

Advantages

  • Converts raw tooth counts directly into a practical gear ratio, output torque, and output speed in a single step.
  • Makes the fundamental torque-for-speed tradeoff visible, useful for choosing gear sizes when a system needs a specific torque or speed target.
  • Works equally well for torque-multiplying reduction gears and speed-increasing gear pairs using the same formula.

Common Mistakes

  • Swapping the driving and driven gear tooth counts, which inverts the gear ratio and flips whether the system is a speed reducer or a speed increaser.
  • Forgetting that this calculator models a single gear pair; a multi-stage gear train needs the ratios of each stage multiplied together, not just the first and last gear's tooth counts entered directly.
  • Assuming output torque and output speed can both increase at the same time, when the formulas guarantee that one rises only as the other falls, aside from small friction losses.

Edge Cases to Watch For

  • The driving gear's tooth count is automatically floored at a minimum of 1 internally, even if a smaller or zero value is entered, preventing a division-by-zero error when calculating the gear ratio.
  • If driven teeth is entered as zero, the gear ratio becomes zero, which zeroes out output torque and makes output speed mathematically undefined in the underlying division; a zero-tooth driven gear isn't a physically real input and should be avoided.
  • The calculator assumes an idealized gear pair with no friction or backlash losses, so a real-world output torque will be slightly lower than the calculated value due to mechanical inefficiency.

Common Use Cases

  • Hobbyist and student robotics builders selecting gear combinations for a desired motor output.
  • Mechanical engineering students verifying gear train torque and speed relationships from coursework.
  • Anyone designing a simple drivetrain, such as a bicycle, winch, or small machine, who needs to estimate output torque and speed from available gears.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

Why can't a gear system increase both torque and speed at the same time?

This would violate conservation of energy - a gear system is a mechanical energy transfer device, not an energy source, so it can only redistribute the input power between torque and speed, never increase the total power output beyond what went in (and real systems lose a small amount to friction, meaning output power is always slightly less than input power).

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Conclusion

A gear pair's tooth-count ratio determines everything about how torque and speed trade off between input and output, and this calculator applies that relationship directly from real gear tooth counts. It's a fast way to check a gear selection before committing to a physical build.