Coil Math

How to Calculate Coil Yield, Slitting Loss, and Cut-to-Length Output

A step-by-step walk through the four calculations every coil line runs daily, with real gauges, widths, and worked numbers you can check against your own tags.

Start with coil length, because almost every downstream number depends on it. A steel coil weight of 20,000 lb at 0.048 in thick and 48 in wide converts to length using L = W / (t x b x rho), where rho for carbon steel is 0.2836 lb/in^3. That gives 20,000 / (0.048 x 48 x 0.2836) = 30,640 in, or 2,553 ft. For aluminum swap rho to 0.098 lb/in^3, which roughly triples length for the same weight. The Coil Yield calculator runs this both directions, so you can back out theoretical length before the coil ever hits the uncoiler.

Slitting yield is a width-fit problem, not a length problem. Take a 48.00 in master coil, subtract 0.25 in of edge trim per side, and you have 47.50 in of usable width. Cutting 3.125 in strips gives 47.50 / 3.125 = 15.2 strips, so you get 15 full mults and 0.625 in of scrap edge. Yield here is (15 x 3.125) / 48.00 = 97.7 percent by width. The Slitting Yield calculator lets you test strip widths against trim allowance so you pick the mult count that leaves the least skeleton; dropping to 3.00 in strips fits 15 and wastes 2.50 in, a worse fit.

Blanking utilization measures how much of a fed strip becomes parts. For a 200 mm wide strip stamping 90 mm round blanks on a single-row layout at 95 mm pitch, area in equals 200 x 95 = 19,000 mm^2 per hit, and blank area equals pi x 45^2 = 6,362 mm^2. Utilization is 6,362 / 19,000 = 33.5 percent, which is why round blanks push shops toward staggered double-row nesting. Two staggered rows on a 175 mm strip lift utilization past 60 percent. Feed the pitch, strip width, and blank geometry into the Blanking Utilization calculator to compare single-row against staggered before you cut die steel.

Cut-to-length throughput ties line speed to part length and shear cycle time. A line running 120 ft/min feeding 96 in (8 ft) sheets moves 15 sheets/min if the shear kept perfect pace, but every stop-to-shear costs settling time. With a 0.8 second shear dwell and 8 ft advance at 120 ft/min (4 seconds of feed), true cycle is 4.8 seconds per sheet, or 12.5 sheets/min, 750 sheets/hr. Run that through the Cut-To-Length Throughput calculator with your accel and decel ramps to see why shorter parts crater output: at 24 in sheets the shear dwell dominates and speed barely matters.

Gauge variation is a thickness calculation that quietly changes every weight and length number above. If a coil specced at 0.048 in actually runs 0.0495 in average, that 3.1 percent overage means a fixed-length order consumes 3.1 percent more weight than quoted. Measure with a micrometer at five points across width and average; the Gauge Variation calculator converts your readings into a percent deviation and a weight impact per 1,000 pieces. On a 0.060 in target, a 0.002 in high bias on a 40,000 lb monthly run is 1,300 lb of unbilled steel.

Coil changeover loss is a time-and-scrap calculation you should book on every setup. A changeover that threads 40 ft of strip to reach the shear, plus 25 ft of off-gauge lead and tail per coil, wastes 65 ft. On 0.048 in x 48 in steel that is 65 x 12 x 48 x 0.048 x 0.2836 = 509 lb per coil change. Multiply by changeovers per shift; six changes is over 3,000 lb of threading scrap daily. The Coil Changeover Loss calculator turns thread length and off-gauge allowance into pounds and dollars so you can justify wider min-order coils.

Tie the chain together with a single order example. A customer wants 5,000 blanks at 6,362 mm^2 each from 0.048 in steel. Working backward: blanks need strip, strip needs slit width, slit width comes off a master coil, and each stage carries its own yield. Multiply the stage yields, 97.7 percent slitting x 60 percent blanking x 98 percent net of changeover, to get 57.5 percent overall coil-to-part yield. That means the 5,000 good blanks demand roughly 8,700 blanks worth of input steel by area. Chaining Coil Yield, Slitting Yield, and Blanking Utilization prevents the classic error of quoting theoretical single-stage yield as if it were the whole line.

Published 2026-07-01.