Clock Mainspring Length Calculator
Enter the barrel, arbor, and spring dimensions to compare common mainspring-length rules. The result also shows how closely an available replacement length matches the rule you selected.
Selected target length (mm)1,588.25
- Selected target length (m)
- 1.59
- Theoretical half-fill length (mm)
- 1,985.31
- Practical 80%-of-half length (mm)
- 1,588.25
- One-third-fill length (mm)
- 1,323.54
- Available spring barrel fill
- 40.3%
- Length difference from target (mm)
- 11.75
- Fit comparison
- Available spring is 11.75 mm longer than the selected target.
Lengths are idealized ribbon-area estimates; hooks, eyes, bridles, and inactive end sections reduce usable length.
Area fill alone does not establish torque, running duration, or mechanical suitability.
How to use this calculator
- Measure the clear inside diameter of the barrel and the diameter of the arbor in the same unit.
- Measure the spring ribbon thickness with a micrometer away from worn or damaged ends.
- Choose the fill convention you want to use as the target length.
- Enter the listed or measured length of the available spring and compare its idealized barrel fill.
How mainspring length is estimated
A coiled mainspring occupies the annular space between the barrel wall and the arbor. This calculator first estimates that space as an area, then divides the chosen share of it by the spring thickness. It is a sizing comparison, not a prediction of how a movement will run.
With D for the inside barrel diameter, d for the arbor diameter, and t for spring thickness, the available annular area is:
A = π(D² − d²) ÷ 4
For a selected fill fraction p, the target length is:
Lp = pπ(D² − d²) ÷ (4t)
The half-fill result uses p = 0.50, giving L50 = π(D² − d²) ÷ (8t). The practical reference is 80% of that result, or 40% area fill. The one-third rule uses p = 1/3. Showing all three makes the convention visible instead of treating one published rule as universal.
What moves the result most
Thickness has a direct inverse effect: a spring twice as thick has half the calculated length at the same fill. Barrel diameter has a large effect because the formula uses its square, while a larger arbor reduces the available annular area. Small measuring errors matter most in compact barrels and with thin springs, so use the clear internal dimensions rather than nominal outside dimensions.
The available-spring fill is F = 4tLa ÷ [π(D² − d²)], where La is the candidate length. A value at or above 100% cannot fit under this simplified area model. A shorter spring may fit, but that does not show whether it provides adequate running duration.
What the calculation leaves out
Real barrels are not perfect annuli. Hook clearance, eyes, bridles, barrel-arbor geometry, lubrication, and the inactive portions at the ends all reduce usable space or length. Width does not appear in this area calculation because it is common to both sides of the ribbon-volume comparison, but width still matters to torque and the movement's design.
Spring alloy, temper, thickness, width, train friction, and the original maker's design determine whether a replacement is appropriate. Use a verified original or movement specification where possible, and treat the comparison as one part of fitting a replacement.
Worked example
For a 50 mm inside barrel, a 15 mm arbor, and a 0.45 mm-thick spring, the annular area is π(50² − 15²) ÷ 4 = 1,786.78 mm². The theoretical half-fill length is 1,985.31 mm. The practical 80%-of-half target is 1,588.25 mm, and the one-third target is 1,323.54 mm.
With the practical rule selected, a 1,600 mm candidate is 11.75 mm longer than the target. Its idealized barrel fill is 40.30%. Those figures describe length and area only; they do not establish that the spring has the right strength or end form for the movement.
Common questions
Why do mainspring formulas use different barrel-fill percentages?
Different procedures use different allowances for the way a real spring packs into a barrel and for the performance they seek. A 50% area-fill calculation is a geometric reference, while lower rules leave more allowance. The right convention depends on the movement and the source you are following.
What is the 50% up-and-down-circle rule?
It is a traditional geometric sizing reference that treats the spring as occupying half of the area between the barrel and arbor. In this calculator it is the theoretical half-fill length, L50. It is useful for comparison, but it is not a complete replacement specification.
Why use 80% of the theoretical half-fill length?
The 80% reference is a practical 40% area-fill rule used in published clock-repair guidance. It reduces the theoretical half-fill length to allow for real-world packing and end details. It should be treated as a convention, not proof that a spring will suit every barrel.
Should barrel and arbor diameters include hook clearance?
No. Enter the clear inside barrel diameter and the arbor diameter where the coils run. Hook clearance, eyes, and bridle geometry are excluded from this idealized model and must be judged separately when selecting the spring and end form.
Can a replacement mainspring be shortened?
Shortening changes the end geometry and can create a dangerous installation or an unreliable attachment. It also does not correct a mismatch in thickness, width, alloy, temper, or end type. Use appropriate mainspring winding equipment and established repair practice before altering a spring.