Clock Rate Error Calculator (Seconds Per Day)

Clock regulation is small adjustments based on observed error. Set a clock to the correct time, wait a known interval, compare. The math:

Seconds per day = (observed error in seconds) / (interval in days)

A clock that gained 35 seconds in 7 days runs 35 / 7 = 5 seconds fast per day. To regulate it, you slow it down. To slow a pendulum clock, you LOWER the bob (longer effective pendulum = slower swing). To speed it up, raise the bob.

Pendulum length adjustment formula. Period scales with the square root of length:

T = 2π × √(L / g)

A 1% change in length gives roughly a 0.5% change in period. For a 1-meter (39.4 inch) seconds pendulum that beats once per second:

• 1 mm length change ≈ 43 seconds per day rate change
• 0.1 mm change ≈ 4.3 seconds per day
• For a “lyre” pendulum or shorter clocks, the multiplier is smaller (proportional to L).

The regulation nut on a pendulum bob typically moves the bob up or down by about 0.4 mm per full turn. So one full clockwise turn (raises bob) speeds up a 1-m pendulum clock by about 17 seconds per day. Most clocks have finer regulation, so plan on a quarter or half turn.

Allowed tolerance.

• Quartz wristwatch: ±15 sec/month (0.5 sec/day) is normal
• Mechanical wristwatch (COSC certified): -4 to +6 sec/day
• Mechanical wristwatch (uncertified): ±20 sec/day is acceptable
• Pendulum mantel clock: ±30 sec/day before customers complain
• Tower clock: ±2 sec/day is high quality
• Atomic clock: 1 second per 100 million years

Mechanical clocks need temperature stability. Cold thickens oil and slows things down. Warm thins oil and may speed things up but increases wear. A clock running well in summer may need re-regulation in winter. The pros use a “mean position” averaging summer and winter rates.

Worked example. A mantel clock loses 2 minutes 30 seconds in 5 days. That is 150 seconds / 5 = 30 sec/day slow. Raising the bob 0.7 mm should bring it to within 1 sec/day if all goes well.

Other regulation methods.

• Quartz movements: trim capacitor adjustment (specialist tools).
• Balance wheel watches: raise/lower regulator pin to shorten or lengthen hairspring effective length.
• Atmos clocks: temperature-driven motor; check the bellows seal first.