Mainspring calculator
Explore how barrel dimensions and spring material affect the available turns.
Your dimensions
Axis to inner wall; radius, not diameter.
Axis to arbor surface; radius, not diameter.
Full length along the spring strip.
Strip thickness, not width or coil spacing.
Values update as you type. Length and thickness are shared between calculations.
Available barrel turns
8.73 turns
From fully wound to unwound inside the barrel.
Compare spring lengths
With the same barrel, arbor and thickness, 357.356 mm gives the most geometric turns: 8.82.
The optimum fills half the annular area. Your spring fills 56%.
Replaces spring length. This maximizes geometric travel, not running time.
L = π(R² − r²) / (2e)
ΔNbmax = [√(2(R² + r²)) − r − R] / e
Where the turns come from
Wound coil count minus unwound coil count gives the available barrel travel.
ΔNb = N″ − N′
N″ = (√(r² + Le/π) − r) / e
N′ = (R − √(R² − Le/π)) / e
Assumptions & limits
These calculations estimate ideal spring behavior. Torque, energy, running time and winding losses require additional definitions and are not calculated here.
The geometry model treats the strip as packed against the arbor or barrel wall. Attachments and working clearances are not modeled. Geometric turns do not guarantee a running reserve.
k = r / e
Dimensionless. No acceptable design range is assumed.
Torque & energy h, Mb24
Mbmax = [Ee³h / (12L)] · 2π · ΔNr
Mbmax = (e²h / 6) · σmax
β = Mb24 / Mbmax
Wbmax = (ehL / 6) · (σmax² / E)
Torque and energy require a confirmed definition of h. The ratio β also requires the measurement conditions for Mb24. If h is a length in mm, torque is in N·mm and energy in mJ; that unit check alone does not establish what h measures.
The torque equations are equivalent after substituting ΔNr. The energy equation equals ½ Mbmax · 2πΔNr; it does not account for energy lost in the gear train.
Running time D, f, ze, ibe
ΔNbmax = 3600 · D · f / (ze · ibe)
Converting turns to running time requires D’s time unit, whether f counts full oscillations or beats, what ze counts, and the direction of the gear ratio ibe. These conventions must be established before using this equation.
Winding losses Mwinding, η
ΔMb = Mwinding · (1 − η)
Calculating winding loss requires a defined efficiency η and the measurement conditions for Mwinding. No default efficiency is assumed.