Calculate finished roll outside diameter from core size, material thickness, and length, or find roll length from measured OD in inches and metric units.

Roll Outside Diameter Calculator

Enter your core size, material thickness, and length to get the finished roll diameter.

Find Outside Diameter
Find Length on Roll
Not sure? use typical values

Roll Outside Diameter Formula

The roll outside diameter is based on the area of material wound around the core. The calculator uses the same unit system internally, converting all diameter, thickness, and length inputs to inches before calculating.

Find outside diameter:

OD = sqrt(ID² + (4*L*t) / pi)

Find length on roll:

L = pi*(OD² - ID²) / (4*t)
  • OD = outside diameter of the finished roll
  • ID = inside diameter, or core diameter
  • L = length of material on the roll
  • t = material thickness
  • pi = 3.14159...

Use Find Outside Diameter when you know the core size, material thickness, and total length. Use Find Length on Roll when you have a measured outside diameter and want to estimate how much material remains on the roll.

Typical Material Thickness Values

Thickness has a large effect on roll diameter and length estimates. Use the actual measured thickness when possible.

Material Typical thickness Approx. mm
Aluminum foil 0.0005 in 0.013 mm
Plastic film / poly 0.001 in 0.025 mm
Masking tape 0.002 in 0.051 mm
Office paper 0.003 in 0.076 mm
Receipt paper / newsprint 0.004 in 0.102 mm
Cardstock 0.007 in 0.178 mm
Corrugated cardboard 0.016 in 0.406 mm

Roll Diameter Reference

Outside diameter General interpretation
Under 2 in Small roll, similar to some tape or ribbon rolls
2 to 5 in Common small roll size, such as tape, labels, or small paper rolls
5 to 10 in Medium roll, often seen with receipt paper, labels, film, or craft material
10 to 20 in Large roll, common for shipping paper, sign vinyl, and production materials
Over 20 in Industrial-size roll

Example Calculations

Example 1: Find the outside diameter

You have a 3 in core, 500 ft of material, and the material is 0.004 in thick.

OD = sqrt(3² + (4*6000*0.004) / pi)
OD = sqrt(9 + 30.558) = 6.289 in

The finished roll outside diameter is about 6.29 in.

Example 2: Find the length on a roll

You measure an 8 in outside diameter roll with a 3 in core. The material thickness is 0.004 in.

L = pi*(8² - 3²) / (4*0.004)
L = 10799 in = 899.9 ft

The roll contains about 900 ft of material.

FAQ

Why does material thickness matter so much?

Roll diameter depends on the total cross-sectional area of material wound around the core. A small thickness error is repeated across many wraps, so the final diameter or length estimate can change noticeably. For the best result, measure the material thickness with calipers or use a verified product specification.

Should I use radius or diameter?

Use diameter. Enter the full distance across the core or finished roll, not the radius. The formula uses squared diameters, so entering a radius by mistake will give a result that is far too small.

Why is the result an estimate?

The formula assumes the material winds evenly with no air gaps, compression, stretching, wrinkles, or loose winding. Real rolls can vary depending on tension and material behavior. Flexible materials such as foam, fabric, tape, and film may differ more than paper or other stable materials.