Gear Train Calculator: Speed Ratio, Output Speed and Torque

The speed ratio, output speed and output torque of a one or two stage gear train.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

For a pair of meshing gears the speed ratio is the number of teeth on the driven gear divided by the number on the driver. A larger driven gear turns more slowly and delivers more torque. Over two stages the ratios multiply.

Each stage loses a little power to friction, typically 2 to 3 percent for good spur or helical gears, so the output torque is the input torque times the ratio times the combined efficiency.

Formulas used

  • i = \frac{z_2}{z_1}\cdot\frac{z_4}{z_3}
  • N_{out} = N_{in}/i
  • T_{out} = T_{in}\, i\, \eta^n

Worked example

With the default numbers in the calculator above:

  1. Overall ratio: 3 : 1 reduction
  2. Output speed: 483 rev/min
  3. Output torque: 29.1 N m
  4. Input and output power: 1.52 kW in

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why does torque go up when speed goes down?

Power is torque times speed. Apart from losses, the power stays the same, so torque rises as speed falls.

What efficiency per stage?

About 97 to 98 percent for good spur or helical gears. Worm gears are much lower.

Does the direction reverse?

Each external mesh reverses the direction of rotation.

Related calculators

Further reading: Shigley, Mechanical Engineering Design; Norton, Machine Design.

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