Torque Multiplier Mathematics

Home X4 Torque Multiplier Mathematics

Mathematics of the X-4 Torque Multiplier

Manual torque multipliers are a speed reducing "transmission" to increase the torque force applied by the user.

Torque multipliers have a mechanical gear ratio which indicates the number of turns of the input tool to achieve one turn of the output. A so-called 4 to 1 multiplier, therefore, means that one turn of the input will result in 1/4 turn of the output; four input rotations will result in one output turn.

This does not mean, however, that "force" is similarly multiplied. All multipliers have losses (inefficiency) which must be recognized in estimating the resultant force transmitted.

In X-4 tools that inefficiency will range between 10% and 20%; 15% is a reasonable mid-range estimate to use.

A 4 to 1 multiplier with a 15% inefficiency results in a 3.4 to 1 actual force transmission. Larger multipliers may have greater "pure" ratios; be sure to use this information in calculating your "net" ratio.

By using 3.4 in your calculations you will be within ± 5% with the result.


  • Output required 1500 lb.ft.
  • "Pure" ratio 4 to 1
  • Inefficiency 15%
  • "Net" ratio 3.4 to 1
  • 1500-3.4 = 441 lb.ft. of input

Using X-4 Torque Multipliers in Combination

X-4 Torque Multipliers in CombinationThis photo shows the possibilities for and advantages of using X-4 Tool Torque Multipliers in tandem. The technician is using the output torque generated by an X-4 Tool model TD1000 to provide the input torque to drive an X-4 Tool model TD2000 resulting in a multiplication factor greater than 13X (when taking efficiency losses into consideration). In this particular application, 50 ft-lbs of torque applied by the technician would result in more than 650 ft-lbs of torque applied to the fastener! X-4 Tool Torque Multipliers have proven to be both invaluable and essential tools for remote field applications.

NOTE: If the user is interested in achieving a minimum torque and doesn't care if the fastener is slightly over-torqued, use a 3.2 ratio. If the user wants to be sure he doesn't over torque and doesn't care if the fastener is slightly under-torqued use a 3.6 ratio. For exact (±2%) readings use an output torqmeter.

Phone: 781-933-1400

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