Clock Escapement Beat Rate Calculator

What is beat rate?

The beat rate (or vibration rate) of a clock is the number of ticks per hour (abbreviated BPH or vph). Each “tick” is one swing of the pendulum in one direction, so a full back-and-forth swing produces two beats. The beat rate determines how finely a clock can divide time and is critical for accurate timekeeping.

Pendulum period formula: The period (time for one full swing) of an ideal simple pendulum is:

T = 2π × √(L / g)

Where:

• T = period in seconds (one complete cycle)
• L = effective pendulum length in meters (center of suspension to center of bob)
• g = standard gravity, 9.80665 m/s². Real gravity varies by latitude and altitude, which is why a clock moved a long way needs re-regulating

From period to beat rate: Beats per hour = 3600 / (T / 2) = 7200 / T

Each full period T contains 2 beats (tick and tock).

Common clock beat rates:

The first four columns are exact arithmetic. The last one is a trade convention and nothing more.
Clocks sold as Vienna regulators turn up beating both seconds and half-seconds, and a cuckoo pendulum has a sliding leaf specifically so it can be tuned to whatever movement is behind it. Count your own beats or measure your own pendulum, then read the row. Do not pick the row by the name on the dial. The pendulum length calculator carries the identical figures worked from beat rate to length.

Two families of clock are missing from that table, and neither one belongs in it.

400-day anniversary clocks use a torsion pendulum, a disc rotating on a suspension spring, whose period comes from the spring’s torsional stiffness and the disc’s moment of inertia rather than from length and gravity. Feeding their roughly 900 BPH into the formula above would demand a pendulum nearly sixteen metres long.

French carriage clocks and most travel clocks are missing for the opposite reason: they beat fast, typically 14,400 an hour, but they do it with a balance wheel on a platform escapement rather than a pendulum. That was the whole point of the design, since a pendulum will not keep time in something you carry about. The rate there is set by the balance and its hairspring, so this calculator has nothing useful to say about one. If you can see a swinging platform rather than a hanging rod, you want a watch timing machine, not this page.

Gear train verification: The escapement beat rate can also be calculated from the gear train. Count the teeth on each wheel and pinion from the center wheel to the escape wheel:

BPH = (Teeth product ÷ Pinion product) × 2 × Escape wheel teeth

The centre wheel turns once an hour, so that product gives the escape wheel’s revolutions per hour directly, and each revolution produces two beats per tooth. A seconds-beating movement with a 30-tooth escape wheel checks out: the escape wheel turns 60 times an hour, and 60 × 2 × 30 = 3,600 BPH.

If the pendulum-based figure and the gear-train figure disagree, trust the gear train. It is fixed by the movement; the pendulum length is the thing you can adjust.

Worked example: A grandfather clock with a 994 mm pendulum:

• T = 2π × √(0.994 / 9.80665) = 2π × 0.3184 = 2.0004 seconds
• BPH = 7200 / 2.0004 = 3,599 beats per hour
• That is 60 beats per minute, one tick per second, the classic grandfather clock rhythm. Trim the rod to 993.6 mm and it lands on 3,600 exactly.

Adjusting beat rate:

• To speed up (increase BPH): shorten the pendulum by raising the bob
• To slow down (decrease BPH): lower the bob
• One turn of the rating nut typically changes rate by 10–30 seconds per day
• A 1 mm change in a seconds pendulum changes the rate by about 43 seconds per day. The general figure is 43,200 ÷ L in millimetres, so shorter pendulums are far more sensitive: a 250 mm Vienna regulator shifts about 173 seconds a day per millimetre

Temperature compensation: Metal pendulum rods expand with heat, making the clock run slower in summer. A 1°C rise expands a steel rod by ~11 parts per million, slowing a seconds pendulum by ~0.5 seconds/day. Compensated pendulums (mercury, wood-and-metal, invar) minimize this drift.