Horology - The Index Repair & Restoration Calculations Pendulum Length and Beats per Hour

Calculate Beats and Pendulum Length from Tooth Counts

If you know the number of wheel teeth, it is easy to calculate the correct pendulum length and the beats per minute.

Calculator: BPM and Pendulum Length
Number of Wheels
in Drive Train:		Wheel
Teeth		Pinion
Leaves
Escape Wheel
5 Wheels4th Wheel
4 Wheels3rd Wheel
Center Wheel
or Center Pinion
Results
Beats per Hour:
Beats per Minute:
Pendulum Length: inches

Tips
It can be a challenge to count the teeth on a wheel without losing your place. Here are a couple of tips.
- With a magic marker, place a dot next to the tooth that you will start counting. Now you will know when to stop counting.
- If the wheel is out of the movement, run the wheel across a sheet of paper and count the holes.

Formulae

BPM =   WE x W4 x W3 x WC
  x 2 ÷ 60
PE x P4 x P3
or
BPM =   WE x W3 x WC
  x 2 ÷ 60
PE x P3
LP =   141120
BPM2

where,
  • BPM is beats per minute
  • WE is the number of teeth on the escape wheel
  • W4 is the number of teeth on the fourth wheel
  • W3 is the number of teeth on the third wheel
  • WC is the number of teeth on the center wheel, or center pinion for a 4 wheel train
  • PE is the number of leaves on the escape wheel pinion
  • P4 is the number of leaves on the fourth wheel pinion
  • P3 is the number of leaves on the third wheel pinion
  • LP is the pendulum length

5 Wheel Drive Train

Gear Train with 5 Wheels

4 Wheel Drive Train

Gear Train with 4 Wheels

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