Watch Gear Train Calculator

Enter the wheel and pinion counts below to calculate the watch movement's beats per hour (vph), frequency (Hz), and the turns per hour for each stage of the going train.

Understanding Watch Gear Trains

For horologists and watch repairers rebuilding or verifying a going train, understanding the beat rate is crucial. This calculator helps you determine the beats per hour (vph) that a watch movement will run at, based on the wheel and pinion counts you have on the bench. This allows you to confirm the movement's intended rate before you match a balance, order a staff, or confirm a replacement fourth wheel.

The calculation relies on the principle that vph = 2 x escape wheel teeth x escape wheel turns per hour. This formula applies to both lever and detent escapements, as both release one escape-wheel tooth per full oscillation (which equals two beats).

How to Use the Watch Gear Train Calculator

1. Enter the center wheel tooth count in the first field.
2. Enter the third wheel teeth count and the leaves of the pinion it drives (the third pinion, which the center wheel turns).
3. Enter the fourth wheel teeth count and the leaves of the fourth pinion it drives (which the third wheel turns).
4. Enter the escape wheel teeth count and the leaves of the escape pinion it drives (which the fourth wheel turns).
5. Read the vph headline figure and check the fourth-wheel turns per hour line to ensure it shows 60 turns per hour for a correctly timed seconds hand.

FAQ

Q: How do I calculate the beats per hour of a watch movement?

A: vph = 2 × escape wheel teeth × escape wheel turns per hour, where escape wheel turns per hour is built up from the wheel and pinion counts of the going train. With 80 center, 75/10 third, 80/10 fourth and 15/8 escape the train gives 60 fourth-wheel turns and 600 escape-wheel turns per hour, so vph = 2 × 15 × 600 = 18,000.

Q: Why does the fourth wheel turn 60 times an hour?

A: The seconds hand is mounted on the fourth wheel, so the train from the center wheel (taken as one turn per hour) must multiply up to 60 fourth-wheel turns per hour — one turn per minute. The calculator shows that figure separately so you can confirm the seconds hand will keep correct time.

Q: How do I convert beats per hour into Hz?

A: Hz = vph ÷ 7200. Each full oscillation is two beats, so vph ÷ 2 gives oscillations per hour and dividing by 3600 seconds gives oscillations per second — the same as vph ÷ 7200. An 18,000 vph train therefore runs at 2.5 Hz.

Q: Does a lever escapement and a detent escapement give the same beats per hour for the same train?

A: Yes. Both release one escape-wheel tooth per full oscillation, which is two beats, so vph = 2 × escape wheel teeth × escape wheel turns per hour applies to lever and detent escapements alike.