Balance Spring Stiffness Calculator
For horologists sizing or auditing a balance assembly, this converts a balance's inertia in mg·cm² and its beat rate in vph into the hairspring stiffness the oscillator actually demands, using the trade's 7200 vph-per-Hz constant rather than a generic SI converter.
Calculate Hairspring Stiffness
How to Use This Calculator
- Enter the balance wheel's moment of inertia in mg·cm² in the inertia field.
- Choose the movement's beat rate — 18000, 21600 or 28800 vph — from the dropdown.
- Read the stiffness k in µN·m/rad from the large result, with the derived frequency in Hz and the substituted formula shown underneath.
- Change either input to recompute; clear the inertia field to reset the display.
FAQ
Q: How do I convert vibrations per hour to Hertz for a balance?
A: Divide vph by 7200 — the constant this calculator applies — so 18000 vph is 2.5 Hz, 21600 vph is 3 Hz and 28800 vph is 4 Hz.
Q: What formula does the balance spring stiffness calculator use?
A: k = I × (2πf)², with the inertia converted from mg·cm² to kg·m² and f taken as vph ÷ 7200, giving k in µN·m/rad.
Q: Why is the required stiffness higher at 28800 vph than at 21600 vph for the same balance?
A: Because frequency is squared in k = I × (2πf)²: going from 3 Hz to 4 Hz multiplies the stiffness by (4/3)², about 1.78×.
Q: What happens if I enter zero or negative inertia?
A: The calculation is rejected — stiffness is directly proportional to inertia, so zero inertia gives no meaningful spring stiffness and a negative inertia is not physically possible.