Rolled Length Calculator
Divide the area of the wound cross-section by the material thickness. Counting by area rather than turn by turn keeps the error under one percent as long as the winding is tight.
Your numbers
Wound length
50.27m
Turns
200
Area
100.53cm²
Formula
Wound length = π × (Diameter² − Small circle diameter²) ÷ (4 × Thickness)
Accuracy hangs on the thickness figure. Masking tape runs about 0.13 mm, label stock about 0.1 mm.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Diameter (cm)The longest line across a circle — twice the radius. | 12 | 0 and up |
| Small circle diameter (cm)The diameter of the small circles being packed in. | 4 | 0 and up |
| Thickness (cm)How thick one layer is; times the number of layers gives the whole. | 0.02 | 0 and up |
Step by step
Quick reference table
Results when only Diameter (cm) changes and everything else stays put.
| Diameter (cm) | Wound length (m) | Turns | Area (cm²) |
|---|---|---|---|
| 6 | 7.85 | 50 | 15.71 |
| 9 | 25.53 | 125 | 51.05 |
| 12 | 50.27 | 200 | 100.53 |
| 18 | 120.95 | 350 | 241.9 |
| 24 | 219.91 | 500 | 439.82 |
What each result means
| Result | At default values |
|---|---|
| Wound length (m)The length you get when it is fully unrolled; thinner means longer. | 50.27 |
| TurnsHow many full turns it makes. | 200 |
| Area (cm²)The space a shape covers — length squared. | 100.53 |
Common mistakes
Accuracy hangs on the thickness figure. Masking tape runs about 0.13 mm, label stock about 0.1 mm.
Glossary
- Diameter
- The longest line across a circle — twice the radius.
- Small circle diameter
- The diameter of the small circles being packed in.
- Thickness
- How thick one layer is; times the number of layers gives the whole.
- Wound length
- The length you get when it is fully unrolled; thinner means longer.
- Turns
- How many full turns it makes.
- Area
- The space a shape covers — length squared.
Frequently asked questions
Q. How is Rolled Length Calculator calculated?
Wound length = π × (Diameter² − Small circle diameter²) ÷ (4 × Thickness) — Divide the area of the wound cross-section by the material thickness. Counting by area rather than turn by turn keeps the error under one percent as long as the winding is tight.
Q. Can you walk through an example?
With Diameter 12cm, Small circle diameter 4cm, Thickness 0.02cm, the answer is Wound length 50.27m.
Q. What do I need to enter?
Enter Diameter, Small circle diameter, Thickness. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Diameter (cm) moves the answer to Diameter (cm) 6 → Wound length (m) 7.85 and Diameter (cm) 24 → Wound length (m) 219.91. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Accuracy hangs on the thickness figure. Masking tape runs about 0.13 mm, label stock about 0.1 mm.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.