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HoroCalc support

Help, formulas, and frequently asked questions · Last updated 26 June 2026

Mainspring Sizer

What it does

Calculates the target length, width, and thickness of a replacement mainspring from the barrel dimensions, using the industry-standard ⅓ barrel-fill rule.

Inputs

Formulas

The ⅓ fill rule states that the wound spring should occupy one-third of the annular space between the arbor and barrel wall:

L = π(D² − d²) / (12 × t)

Width is calculated as 85% of the barrel height, allowing clearance:

Width = h × 0.85

Turns in the barrel:

Turns = (D − d) / (2 × t)

If thickness is not provided, it is estimated as:

t = (D − d) / 75

This targets approximately 38 turns, which is typical for most watch barrels.

Notes

These results are estimates. Actual spring selection depends on the material (blue steel, stainless), end-piece and bridle design, and the torque curve the watchmaker wants to achieve. The calculated length gives a good starting point; consult the movement’s technical sheet or established spring catalogues (e.g. Cousins, Ranfft) to cross-reference.

Beat Rate

What it does

Converts between BPH (beats per hour), Hz (oscillations per second), beat interval (ms), and beat period (seconds). Also calculates a rate deviation in ppm from a measured daily error.

Inputs

Formulas

Hz = BPH / 7200
Beat interval (ms) = 3,600,000 / BPH
Beat period (s) = 7200 / BPH
Rate (ppm) = (error s/day) / 86,400 × 1,000,000

Why 7200? One beat is a single tick of the escapement — one tooth advance. A balance oscillation (one full swing and return) produces two beats. So BPH = Hz × 2 × 3600 = Hz × 7200.

Rate indicator

The ppm deviation is colour-coded: green (within ±50 ppm), orange (±50–150 ppm), red (over ±150 ppm). This follows typical COSC chronometer limits as a rough benchmark; the actual tolerance for any given movement will differ.

Hairspring

What it does

Works out how the active (vibrating) length of a hairspring relates to rate, so you can calculate how much to lengthen or shorten it to correct a measured daily error — and see how sensitive the regulator is at the current length.

Inputs

Formulas

Balance frequency scales with the inverse square root of active length, so the required length for a corrected rate is:

L_required = L × (1 + error / 86,400)²

Because a fast watch needs a longer active spring and a slow watch a shorter one, the app reports the required length and the change (lengthen or shorten) explicitly. Regulator sensitivity — the rate change for a 0.1 mm change in length — is:

Δrate ≈ 86,400 / 2 × (0.1 / L)   [s/day per 0.1 mm]

Notes

This models the active length only; it does not account for spring material, terminal-curve geometry, or temperature effects. Use it to estimate a regulator move or a stud-to-pin adjustment, then confirm on the timegrapher.

Gear Depthing

What it does

Relates the module, tooth counts, and centre distance of a meshing wheel and pinion — in both directions. Use it to find the correct centre distance for a known module, or to recover an unknown module from a measured centre distance.

Inputs

Formulas

Pitch diameter = m × z
Centre distance = m × (z₁ + z₂) / 2
Module = 2 × centre distance / (z₁ + z₂)

Two meshing gears must share the same module. Recovering the module from a measured centre distance helps identify or cut a replacement wheel.

Pendulum

What it does

Converts between pendulum length and beat rate in both directions, and calculates the bob adjustment needed to correct a measured rate error.

Inputs

Formulas

The standard pendulum formula (simple pendulum approximation using g = 9.80665 m/s²):

T = 2π√(L / g)     [T in seconds, L in metres]
BPH = 7200 / T

L = g × (7200 / BPH)² / (4π²)   [result in metres × 1000 for mm]

Bob adjustment for a rate error of e seconds/day with current pendulum length L mm:

ΔL = 2 × L × |e| / 86,400

The app tells you the direction explicitly — no need to remember which way.

Notes

The simple pendulum formula assumes a massless rod and point bob. For accurate clock servicing, use it as a starting point and trim to rate. Temperature compensation (e.g. gridiron pendulums) is not modelled.

Gear Train

What it does

Calculates the beat rate and key intermediate wheel speeds from the tooth counts of a watch or clock gear train.

Inputs

Formulas

All derived from the centre wheel making exactly one revolution per hour (1/60 RPM):

BPH = 2 × C × tw × fw × ew / (tp × fp × ep)

Fourth wheel RPM = C × tw / (tp × fp) / 60

Escape wheel RPH = C × tw × fw / (tp × fp × ep)

Notes

Enter only the teeth that mesh in series: centre → third → fourth → escape. A cannon pinion or motion work (which drives the dial train) sits in parallel and does not affect the beat rate calculation. Some movements (e.g. certain pocket watch calibres) have more or fewer wheel stages — this calculator models the standard four-wheel train.

Power Reserve

What it does

Estimates the power reserve in hours from the barrel and spring dimensions and a barrel rate figure.

Inputs

Formulas

Max turns = (D − d) / (2 × t)
Useful turns = Max turns × (efficiency / 100)
Power reserve (h) = Useful turns × hours per barrel revolution

Notes

This is a geometric estimate. Real-world power reserve depends on spring material, heat treatment, the bridle, gear train friction, and how the escapement is set up. Use it to sanity-check a spring selection or compare barrel configurations; measure the actual reserve on the timegrapher for a definitive figure.

Regulation worksheet

What it does

Takes the rate measured in up to six positions and reports the overall quality of regulation: the mean rate, the positional spread, and the flat-versus-vertical delta, with a grade against COSC-style limits.

Inputs

How the grade works

The worksheet computes the mean of all entered positions, the spread (best minus worst), and the difference between the mean flat and mean vertical rates, then grades:

These thresholds are a practical guide based on COSC-style limits, not the certification test itself. A healthy watch typically loses no more than about 50° of amplitude from flat to vertical, and beat error under 0.5 ms is excellent.

Saved Movements

What it does

Stores a movement’s specification so you can return to it, and keeps a timing log over time. Everything is saved locally on your device.

Saving a movement

Give it a name (e.g. “ETA 2824-2”) and, optionally, a maker, caliber, beat rate, barrel and mainspring dimensions, power-reserve figures, and notes. From these HoroCalc derives the frequency, beat interval, mainspring length, and estimated power reserve automatically, using the same formulas as the individual calculators.

Logging timing

Add rate readings with a date, position, rate (s/day), amplitude, and beat error. The detail screen plots the rate trend on a chart and shows the positional spread, colour-coded green (< 15 s/day), orange (< 30), or red. Tap a reading to remove it, or swipe to delete.

Exporting

The share menu produces a plain-text spec sheet — identity, derived specification, notes, and the full timing log — that you can send anywhere via the system share sheet. The export is created only when you tap Share.

Converters

What it does

Converts between the everyday units of movement and case work: lignes, millimetres, and inches.

Conventions

1 ligne (‴) = 2.2558 mm
1 inch = 25.4 mm

The ligne is the traditional Swiss unit for movement diameter — an 11½‴ movement is about 25.6 mm across.

Service & Lubrication

What it does

A set of bench-reference tables for service work. These are read-only guides, not calculators.

What’s included

These are general guides. Always follow the manufacturer’s technical sheet for a given caliber.

Reference library

What it does

Built-in articles explaining the theory behind the tools, so you can check the reasoning as well as the number.

What’s included

Units and conventions

Contact

For bug reports, feature requests, or questions not answered here:

Whiteforge Technologies Ltd
support@whiteforgetech.co.uk

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