Sorting Calculations

How to Calculate Optical Sorter Throughput, Contamination Rate, and Screen Efficiency

The five formulas that govern a municipal sort line, worked with real units and realistic single stream inputs: optical throughput, contamination rate, screen efficiency, conveyor power, and baler capacity.

A materials recovery facility lives or dies on five numbers: optical sorter throughput, contamination rate, screen efficiency, conveyor energy, and baler capacity. Every one of them comes from a short formula with inputs you can measure on the tipping floor with a scale, a stopwatch, and a tape measure. This guide works each calculation with real units and realistic values from a 20 ton per hour single stream line receiving residential material at roughly 18 percent inbound contamination. Run your own inputs through the Optical Sorter Throughput, Contamination Rate, and Screen Efficiency calculators as you go, and keep every mass figure in metric tons so the mass balance closes at the end.

Optical sorter throughput is belt geometry times material density: Q (t/h) = W x d x v x rho x k x 3600, where W is working width in meters, d is burden depth in meters, v is belt speed in m/s, rho is bulk density in t/m3, and k is belt occupancy, typically 0.25 to 0.40. Example: a 2.0 m machine running 3.0 m/s with a 30 mm burden of container stream at 0.045 t/m3 and 30 percent occupancy gives 2.0 x 0.030 x 3.0 x 0.045 x 0.30 x 3600 = 8.7 t/h. Sanity check against vendor rules of thumb, roughly 1 to 3 t/h per meter of width on containers and 4 to 6 t/h per meter on fiber, then confirm with the Optical Sorter Throughput calculator.

Contamination rate is simple division done carefully: contamination percent = contaminant mass divided by total sample mass, times 100. The discipline is in the sampling. Pull at least 90 kg (200 lb) per sample, quarter it, and audit weekly per stream rather than monthly for the whole plant. A 91 kg sample of inbound single stream containing 16.4 kg of film, food waste, and tanglers gives 16.4 / 91 = 18.0 percent, right in the typical residential range of 15 to 25 percent. Run the same math on outbound bales, where the stakes flip: PET reprocessors commonly reject loads above 2 percent, and mixed paper specs allow 2 to 3 percent outthrows. The Contamination Rate calculator handles the conversion and tracks samples over time.

Screen efficiency measures how much of the undersize material actually reports to the unders stream: E = (undersize mass in unders / undersize mass in feed) x 100. Get the feed fraction from a belt cut: stop the conveyor, remove everything on a 1 m section, and size it by hand over a test sieve matching the screen aperture. Example: a glass breaker screen fed 20 t/h containing 30 percent minus 50 mm material carries 6.0 t/h of true unders; if 5.1 t/h reports through the deck, efficiency is 5.1 / 6.0 = 85 percent. Pair it with purity of the unders stream, targeting above 90 percent glass and fines, and let the Screen Efficiency calculator resolve both from your sample weights.

Conveyor power splits into friction and lift: P (kW) = (f x L x g x (2 x qB + qG) x v) / 1000 + (Q x H) / 367, where f is the friction factor (0.02 to 0.03), L is length in m, qB is belt mass and qG is material mass per meter in kg/m, v is speed in m/s, Q is throughput in t/h, and H is lift in m. A 30 m incline moving 20 t/h up 5 m needs only 20 x 5 / 367 = 0.27 kW for lift; friction and drive losses push the installed motor to 4 to 7.5 kW. Multiply across 40 to 80 conveyors and the Sort Line Conveyor Energy calculator shows why conveyance takes 30 to 40 percent of plant load.

Baler capacity is bale mass times cycle rate: t/h = bale volume (m3) x bale density (kg/m3) x bales per hour / 1000. A single ram machine making 1.1 x 1.1 x 1.5 m bales of OCC at 400 kg/m3 produces 726 kg bales; at a 3 minute cycle, 20 bales per hour, that is 14.5 t/h. PET typically bales at 300 to 380 kg/m3, so the same cycle yields 10 to 12.5 t/h. Size the baler at least 20 percent above peak line output, because it becomes the choke point during commodity changeovers, and use the Baler Capacity calculator to run the cycle math in both directions.

Chain the five results into a mass balance before trusting any of them: feed = recovered products + residue + moisture loss, and the total should close within 3 percent over a week of scale tickets. If optical throughput says 8.7 t/h but the baler only sees 6 t/h of that commodity, either your occupancy or recovery assumption is wrong. Two supporting calculations round out the toolkit: the Air Separator Energy calculator sizes fan power for film and light fraction removal, typically 15 to 30 kW per separation point, and the Pick Line Labor calculator converts manual sort stations into picks per minute so you can decide where a machine beats a person.

Published 2026-07-02.