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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

InputDefaultAccepted range
Diameter (cm)The longest line across a circle — twice the radius.120 and up
Small circle diameter (cm)The diameter of the small circles being packed in.40 and up
Thickness (cm)How thick one layer is; times the number of layers gives the whole.0.020 and up

Step by step

FormulaWound length = π × (Diameter² − Small circle diameter²) ÷ (4 × Thickness)
With the default numbersWound length = π × (12² − 4²) ÷ (4 × 0.02)
AnswerWound length = 50.27 m

Quick reference table

Results when only Diameter (cm) changes and everything else stays put.

Diameter (cm)Wound length (m)TurnsArea (cm²)
67.855015.71
925.5312551.05
1250.27200100.53
18120.95350241.9
24219.91500439.82

What each result means

ResultAt 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.