Slit Coil Outer Diameter & Strip Length Calculator
Industrial coil dimension engineering tool designed for slitting lines, stamping shops, and metal service centers. Precision calculation of coil outer diameter (OD), uncoiled strip length, and batch coil mass across carbon steel, stainless steel, and aluminum alloys.
- • Strip Length Formula: L = (π × (Dod² - Did²)) / (4 × t)
- • Outer Diameter Formula: Dod = √(Did² + (4 × L × t) / π)
- • Carbon Steel Density: 7.85 g/cm³ (0.2836 lb/in³)
- • Aluminum Alloys Density: ~2.70 g/cm³ (0.0975 lb/in³)
1. Material & Calculation Method
Mathematical Derivation for Metal Coil Annular Geometry
A coiled metal strip forms a series of concentric cylindrical wraps. Assuming a tight wrap with negligible air gap, the total cross-sectional area of the annular ring between the inner diameter ( Did) and outer diameter ( Dod) equals the longitudinal cross-sectional area of the uncoiled strip.
Slitting Recoil Tension & Compaction Factor
In high-speed slitting operations (compliant with ASTM A568 or EN 10131), recoil arbor tension introduces a slight compaction factor. Thick hot-rolled coil stock may exhibit a wrap efficiency of 98.5%, whereas precision cold-rolled thin strip approaches 99.8% solid density.
Frequently Asked Questions
Q: What is the standard inner diameter (ID) for steel slitting arbors?
The standard core inner diameter for industrial steel slitting lines is 508 mm (20 inches) or 610 mm (24 inches). Fiber cores or expanding mandrel rubber sleeves may alter these dimensions slightly.
Q: How do you estimate the weight per millimeter of width (PIW / PIMM)?
Pounds Per Inch of Width (PIW) or kg per mm of width measures coil buildup density regardless of slit width. It is calculated by dividing total master coil weight by master coil width.