HoroCalc support
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
- Barrel bore — D: the internal diameter of the barrel, measured in mm.
- Arbor diameter — d: the diameter of the mainspring arbor (the central post the spring is coiled around), in mm.
- Barrel height — h: the internal height of the barrel (the space the spring actually occupies), in mm.
- Spring thickness — t (optional): if you know the spring thickness from the original or from catalogue data, enter it for an exact calculation. If left blank, the app estimates it from the arbor-to-barrel ratio, targeting approximately 38 turns.
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
- BPH: beats per hour. Select a common frequency from the chip buttons or type any value.
- Daily rate error (optional): a positive value means the watch is gaining time; negative means losing. Entered in seconds per day.
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
- Active spring length: the free vibrating length, from the stud to the regulator pins (or to the collet if free-sprung), in mm.
- Nominal beat rate: tap a common frequency or enter the target BPH.
- Measured daily error: positive if the watch gains, negative if it loses, in seconds per day.
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
- Module → geometry: enter the module (m), wheel teeth (z₁), and pinion leaves (z₂).
- Centre distance → module: enter the measured distance between the two arbors and the tooth counts.
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
- Pendulum length: measured in mm from the pivot to the centre of the bob.
- Target BPH: the intended beat rate of the clock.
- Daily rate error: positive = gaining (clock runs fast); negative = losing (clock runs slow).
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
- If the clock is gaining (e > 0): lower the bob by ΔL mm.
- If the clock is losing (e < 0): raise the bob by ΔL mm.
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
- Centre wheel teeth (C): the main driving wheel, assumed to rotate once per hour.
- Third pinion leaves (tp) and Third wheel teeth (tw)
- Fourth pinion leaves (fp) and Fourth wheel teeth (fw)
- Escape pinion leaves (ep) and Escape wheel teeth (ew)
- Layout: selects how the fourth wheel RPM result is interpreted:
- Watch — centre seconds: fourth wheel should rotate at 1.000 RPM; reading turns green when within 5%.
- Watch — sub-seconds: same check applies.
- Clock: fourth wheel check is not shown.
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
- Barrel bore — D: internal barrel diameter, in mm.
- Arbor diameter — d: arbor diameter, in mm.
- Spring thickness — t: mainspring thickness, in mm.
- Hours per barrel revolution: how long one full rotation of the barrel takes. For most wristwatches this is approximately 1.0 hour. An 8-day clock barrel turning once in 8 hours → enter 8.
- Efficiency (%): the fraction of total turns that deliver usable driving torque. Typical values are 75–85%. Turns at the very end of the run-down (where torque falls below the movement’s threshold) do not count.
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
- Flat positions: dial up (DU) and dial down (DD), in s/day.
- Vertical positions: crown up (PU), crown down (PD), crown left (PL), crown right (PR), in s/day.
- Amplitude — flat and vertical, and beat error (optional): adds an amplitude-drop figure and records beat error.
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:
- Chronometer grade — spread ≤ 8 s/day, small mean, flat−vertical within −6 to +8.
- Well regulated — spread ≤ 15 s/day.
- Serviceable — spread ≤ 30 s/day.
- Needs regulation — spread over 30 s/day.
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
- Lubrication points — each part of the movement mapped to a recommended oil or grease.
- Lubricant guide — common Moebius and Kluber products and what each is for.
- Service intervals — rough guidance by watch type.
- Torque conversions — gram-millimetres to micro-newton-metres for mainspring torque.
- Swiss / NIHS screw threads — common diameters and pitches.
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
- Formulas — beat rate, mainspring sizing, power reserve, gear-train ratios, and pendulum length, each with the equation and an explanation.
- Concepts — lift angle and amplitude, beat error, the six positions, and lever-escapement geometry (lock, draw, lift, drop).
- Standards & tables — the full COSC chronometer limits, common balance frequencies, and ligne-size tables.
- Glossary — concise definitions of the everyday watchmaking terms.
Units and conventions
- All lengths are in millimetres.
- Beat rates are in beats per hour (BPH). One beat = one tooth advance of the escapement.
- Gravity is taken as 9.80665 m/s² (standard gravity).
- The pendulum formula is the simple pendulum (massless rod, point bob).
- The mainspring formula uses the ⅓ barrel-fill rule, which is the standard industry starting point.
Contact
For bug reports, feature requests, or questions not answered here:
Whiteforge Technologies Ltd
support@whiteforgetech.co.uk