Roll Length Calculator
Calculate the length of material wound on a roll using diameter and thickness measurements
Calculate Roll Length
The total diameter of the entire roll
The diameter of the core or center tube
The thickness of a single layer of material
Roll Length Results
Additional Measurements
Formula Used
L = π × (D² - d²) / (4 × T)
Where:
- L = Length of material
- D = Outer diameter
- d = Inner diameter
- T = Material thickness
Calculation based on: Outer Ø 0cm, Inner Ø 0cm, Thickness 0mm
Cross-sectional area: 0.000000 m²
Calculation Status
Example Calculation
Toilet Paper Roll
Outer diameter: 12 cm
Inner diameter: 4 cm (cardboard core)
Paper thickness: 0.1 mm per layer
Calculation
L = π × (12² - 4²) / (4 × 0.01)
L = π × (144 - 16) / 0.04
L = π × 128 / 0.04
L = 10,053 cm ≈ 100.5 meters
Common Applications
Paper Products
Toilet paper, paper towels, newsprint
Tapes & Films
Adhesive tape, plastic films, foils
Textiles
Fabric rolls, carpets, vinyl
Industrial
Wire, cable, metal sheets
Measurement Tips
Measure diameter at the widest point for accuracy
For thin materials, measure multiple layers and divide
Ensure the roll is tightly wound for best estimates
Account for compression in soft materials
Use calipers for precise thickness measurements
Understanding Roll Length Calculations
How the Formula Works
The roll length calculation is based on the principle that when a roll is unwound, the material forms a rectangle. The cross-sectional area of the annulus (ring shape) formed by the material equals the area of this rectangle.
Key Assumptions
- •No gaps between layers when wound
- •Material doesn't stretch or compress
- •Uniform thickness throughout
- •Material makes complete revolutions
Mathematical Derivation
Cross-sectional area = π(D²/4 - d²/4)
Rectangle area = L × T
Setting equal: π(D²/4 - d²/4) = L × T
Solving for L: L = π(D² - d²)/(4T)
Practical Considerations
- Compressible materials: May give overestimates
- Loose winding: Actual length may be less
- Tapered rolls: Use average diameter
- Variable thickness: Use average thickness