Horology Tool

Pendulum Clock Regulation Calculator

Enter your clock's drift and pendulum length — get the exact adjustment needed.

Length units:

① Clock Drift

Observe the clock for a measured interval, then enter how much it drifted.

days
hrs
min

② Current Pendulum

cm
°C

③ Regulation Results

Enter your values above and press Calculate.

④ Rating Log

Track your adjustments over multiple sessions. Saved in your browser.

Date Drift/day Old length New length Change
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How to Use This Calculator

  1. Observe your clock for at least 24 hours against a reliable reference (phone, GPS clock). Longer observation periods give more accurate results.
  2. Enter the drift — the total minutes and seconds it has gained or lost, and in which direction.
  3. Measure your pendulum length from the pivot point to the centre of the bob (not the bottom). Enter it in your chosen unit.
  4. Press Calculate. The tool shows the new target length, the exact change to make, the target BPH, and a temperature-correction note.
  5. Log the adjustment to track your progress over multiple sessions.

The Physics: Why Length Changes the Rate

A pendulum's period is governed by:

T = 2π × √(L / g) where: T = period (seconds per full swing) L = effective pendulum length (metres) g = local gravitational acceleration (≈ 9.80665 m/s²)

Because period is proportional to the square root of length, the corrected length is:

Gaining s seconds per day (clock too fast → lengthen): L_new = L_old × ((86400 + s) / 86400)² Losing s seconds per day (clock too slow → shorten): L_new = L_old × ((86400 − s) / 86400)² where s = total drift in seconds over the observation period, scaled to a 24-hour rate.

This formula is used by professional horologists and is derived from the relationship T ∝ √L documented in standard horology references and texts such as de Carle's Practical Clock Repairing.

Beats Per Hour (BPH) Explained

Every tick and every tock counts as one beat. A "seconds pendulum" (period = 2 s) produces 3600 BPH. This must match the gear-train design of your movement exactly. The formula is:

BPH = 7200 / T = 7200 / (2π × √(L / g))

Common values: longcase/grandfather clocks — 3600 BPH; Vienna regulators — 3600 BPH; French mantel clocks — commonly 3600 or 7200 BPH; American shelf clocks — often 3600 BPH.

Temperature & Seasonal Drift

Steel rods expand by about 11.7 parts per million per °C. For a 1-metre pendulum, a 1 °C rise lengthens it by 0.0117 mm, adding roughly 0.48 seconds per day. This explains why a clock regulated in summer may run slightly slow in winter. The temperature-correction panel in the results quantifies this effect for your rod material and the temperature change you enter.

Practical Tips

Frequently Asked Questions

How do I calculate pendulum length adjustment for a clock that gains or loses time?

Use the formula New Length = Current Length × ((86400 + drift_s) / 86400)² to correct a fast clock (gaining), or × ((86400 − drift_s) / 86400)² for a slow clock (losing), where drift_s is the daily drift in seconds. This calculator does all the arithmetic instantly.

How much does one full turn of the rating nut change the rate?

Typically 1–2 minutes per day per full 360° turn, but it varies by clock. The best approach: make one turn, measure the rate change over 24 hours, and use that as your per-turn coefficient going forward. Some finer-threaded movements have far smaller per-turn effects (as little as 30 seconds per turn).

Why does a longer pendulum make the clock run slower?

Period T = 2π√(L/g). Longer L → larger T → each escapement release takes longer → clock runs slow. Raising the bob (shortening effective length) makes the clock run faster.

What is BPH and why does it matter?

BPH (beats per hour) counts every individual tick and tock. A clock movement's gear train is designed for a specific BPH. If the pendulum delivers the wrong BPH, the clock will gain or lose time no matter how the hands are set. Matching measured BPH to the design value is a precise way to regulate without waiting 24 hours per trial.

Does temperature affect pendulum accuracy?

Yes — steel rods expand about 11.7 ppm/°C, lengthening the pendulum and slowing the clock. A 10 °C seasonal change can cause ~5 seconds/day drift on a steel-rod clock. Invar rods (1.2 ppm/°C) or compensated (gridiron/mercury) pendulums dramatically reduce this effect.

What's the difference between "effective length" and physical length?

Effective length is measured from the pivot (suspension spring axis) to the centre of mass of the bob — not to the bottom of the bob or the tip of the rod. For most simple bobs this is close to the geometric centre. For complex or asymmetric bobs, the centre of mass must be calculated or determined by experiment.

This calculator is for guidance only. Pendulum regulation involves many real-world variables (suspension spring stiffness, oil viscosity, air resistance, local gravity). Results are estimates to inform adjustment direction and magnitude; always verify with timed observation after each change. Not a substitute for professional clock servicing.