The reel capacity formula

The formula, term by term

Every wooden reel is named by three numbers: flange diameter F, traverse T and drum diameter D, written F x T x D in inches. Those three, plus the outside diameter of the cable and a clearance figure, are all the formula needs.

Anixter's Wire and Cable Technical Information Handbook prints the same method as Footage = 0.262 × T × (H − C) × (D + H − C) / d², where its H is the full flange height above the drum, (F − D) / 2. Our H already has the clearance taken off, so the two read differently but give the same answer. Anixter introduces it as the NEMA WC 26 formula for approximate cable capacity per reel.

C, the clearance, is the gap between the outer layer of cable and the edge of the flange. It protects the cable when the reel is rolled, chocked or set down, and leaves room for lagging. Anixter's capacity table uses 1 inch for 16 to 28 inch flanges, 2 inches for 30 to 48 inch flanges and 3 inches for 54 to 96 inch flanges. Each cable maker sets its own standard clearances, Okonite notes, so a maker's chart can differ slightly.

Where 0.2618 comes from

The cable sits in a ring around the drum. Seen from the side, that ring is the space between a circle of diameter D and a larger circle of diameter D + 2H. Its area is π/4 × ((D + 2H)² − D²), which simplifies to π × H × (D + H). Multiply by the traverse T and you have the volume of winding space in cubic inches.

Now picture each foot of cable taking up a square channel of side d, 12 inches long: 12 × d² cubic inches per foot. Divide the winding volume by that and you get feet, π × H × (D + H) × T / (12 × d²). Pull π / 12 out as a constant and it is 0.2618.

The square-channel picture is the key assumption. Round cable laid in neat layers, each wrap sitting directly on the one below, fills that kind of grid. Real winding differs a little, which is why every source that prints the formula calls the answer approximate. Superior Essex adds on its own reel charts that they apply to round cable only and show maximum calculated capacity, and that actual lengths may be less.

Six worked examples, checked against Anixter's table

Each row runs the formula with Anixter's clearance for that flange size. Step one is H: half the difference between flange and drum, less the clearance. Step two is the product (H + D) × H × T. Step three multiplies by K. The last column is the figure Anixter's Table 10.2 prints for the same reel and cable; the small gaps come from Anixter's rounder 0.262 constant.

Example: 48x36x24 with 1.00 inch cable. H = (48 − 24) / 2 − 2 = 10. (10 + 24) × 10 × 36 = 12,240. 12,240 × 0.2618 = 3,204 feet.

Cable diameter matters more than anything

Because d is squared, small changes in cable size move the answer a lot. Double the diameter and the footage drops to a quarter. That is why two cables that look alike on a spec sheet can need different reels, and why you use the measured outside diameter over the jacket, never the conductor size.

Holding the reel fixed at 48x36x24 with 2 inches of clearance, the winding product is 12,240 every time. Only K changes.

Anixter's table gives 12,828 feet for this reel at 0.50 inch and 3,207 feet at 1.00 inch.

What the clearance costs you

Clearance comes straight off the depth, and the depth appears twice in the formula, so each extra inch costs more than you might expect. On the same 48x36x24 reel with 1.00 inch cable, footage falls from about 4,072 feet with no clearance to about 2,413 feet with 4 inches. Zero clearance is shown for comparison only; a reel wound flush with the rim loses its outer wraps the first time it is rolled.

Running it backwards: which reel holds my length?

Often you know the length and want the reel. Divide the length by K to get the winding product you need, then look for a reel whose (H + D) × H × T is at least that large.

Say you need 5,000 feet of a cable with a 0.75 inch outside diameter. K is 0.2618 / 0.5625 = 0.4654, so the required product is 5,000 / 0.4654, about 10,743. A 42x26x24 gives H = (42 − 24) / 2 − 2 = 7 and a product of (7 + 24) × 7 × 26 = 5,642, about 2,626 feet. Too small. A 48x36x24 gives 12,240, about 5,697 feet, with margin for uneven winding. The 48-inch reel is the answer.

Then check the drum. NEMA WC 26, as tabled by Anixter, sets minimum drum diameters as a multiple of cable outside diameter: 10 for nonshielded cable up to 2,000 volts, 14 to 20 for tape-shielded cable, 16 for wire armored, 20 for fiber optic cable and never under 12 inches. A reel that holds the length is no use if its drum is below that line.

The wire rope version of the same formula

Wire rope suppliers print the method as L = (A + D) × A × B × K, with A the depth of rope space, B the traverse and D the barrel. It is the same arithmetic with different letters. Their published K tables differ from 0.2618 / d², though, because, as Paducah Rigging puts it, the K values take normal rope oversize into account. For 1-inch rope the table K is 0.239 rather than 0.2618.

Paducah's worked example is 1-1/4 inch rope on a reel with a 36-inch flange, 24-inch drum and 30 inches between flanges: (6 + 24) × 6 × 30 × 0.152 = 821 feet. That example subtracts no clearance. Industrial Rope advises about 2 inches unless rope-end fittings need more, which would cut the depth to 4 inches and the answer to about 511 feet.

Mistakes we see most often

Most wrong answers come from a wrong input rather than the formula. Run down this list before trusting a result, and remember the formula ignores nesting of wraps, hand winding and soft products like braided rope. For metric work, convert to inches, run the formula, then multiply feet by 0.3048 for meters.

• Using the conductor gauge or kcmil size instead of the overall outside diameter. Insulation, shield and jacket can double the figure.
• Using out-to-out width for T. Traverse is the inside gap between flanges; out-to-out includes both flange thicknesses.
• Mixing radius and diameter. F and D are both full diameters; the halving happens inside the H step.
• Measuring the drum over leftover cable, tape or lagging scraps instead of bare staves.
• Forgetting to square d. A cable twice as thick takes four times the space per foot.
• Ignoring weight. Okonite checks gross cable weight against the reel's loading weight; its table rates a 36x24x17 at 2,000 pounds of cable, and some sizes come in a light and a heavy build with different ratings.