Recovery Math

How to Calculate Black Mass Yield, Recovered Metal Value, and Line Throughput in Battery Recycling

The core battery recycling formulas worked end to end: black mass yield, recovered metal value per ton, sorting throughput, and shredding line capacity with real inputs and units.

Start with black mass recovery yield, the ratio that governs everything downstream. Yield equals recovered black mass mass divided by input active-material mass. If a batch feeds 1,000 kg of packs and the active material fraction is 42 percent, your theoretical active mass is 420 kg. Recover 357 kg of black mass through shredding, screening, and separation and yield is 357 divided by 420, or 85 percent. Note the denominator: you divide by active material, not gross pack weight, because casings, wiring, and modules never become black mass. The Black Mass Recovery Yield calculator handles this split so you do not accidentally benchmark against total feedstock.

Recovered metal value converts that black mass into dollars. For each metal, value equals assayed grade times black mass mass times realized recovery rate times market price. Take 357 kg of NMC black mass assaying 6 percent lithium, 18 percent nickel, and 12 percent cobalt. Lithium mass is 357 times 0.06 times a 90 percent recovery, or 19.3 kg. Nickel at 18 percent and 95 percent recovery gives 61.1 kg; cobalt gives 40.7 kg. Multiply each by price, roughly 15 dollars per kg lithium (LCE-adjusted), 16 dollars nickel, 33 dollars cobalt, and sum. The Recovered Metal Value calculator carries the four metals and your price inputs together.

Watch the two recovery rates that stack here. Black mass yield (mechanical) and hydrometallurgical metal recovery (chemical) are different numbers, and multiplying them gives your true wall-to-wall recovery. An 85 percent black mass yield feeding a 92 percent lithium recovery step means only 78 percent of the lithium entering as feedstock leaves as product. If you quote against the 92 percent figure alone you overstate output by 14 points. Always chain the ratios: overall recovery equals mechanical yield times chemical recovery, computed metal by metal because lithium, nickel, and cobalt each behave differently in leaching.

Cell sorting throughput sizes the front of the line. Throughput equals cells per hour per station times station count times uptime fraction, converted to a shift basis. Six stations running 220 cells per hour at 82 percent uptime yield 6 times 220 times 0.82, or 1,082 cells per hour, and across a 7.5 hour productive shift about 8,120 cells. Mixed-chemistry incoming streams cut the per-station rate because operators must identify formats before segregating, so use a measured rate, not a spec sheet number. The Cell Sorting Throughput Capacity calculator turns station rate, count, and uptime into sortable cells per shift.

Shredding line capacity must exceed or match sorting output or you strand capacity. Capacity in kg per hour equals nameplate feed rate times availability times a feed-density factor. A line rated at 1,500 kg per hour at 78 percent availability delivers 1,170 kg per hour effective. Convert cells to mass to compare stages: if sorted cells average 0.045 kg each, 1,082 cells per hour is only 49 kg per hour of cell mass, so sorting, not shredding, is the constraint on a small-format line. The Battery Shredding Line Capacity calculator gives effective kg per hour so you can balance stages in the same units.

Material assay workload sets how much lab time each ton demands. Workload equals number of lots times samples per lot times minutes per assay, divided by available analyst minutes. Twenty lots per week at 3 samples each and 40 minutes per assay is 2,400 analyst-minutes, or 40 hours, roughly one full-time analyst before rechecks. Undersampling wrecks the value calculation upstream because a single assay point on a heterogeneous lot can miss a 2 point grade swing worth thousands per ton. The Material Assay Workload calculator ties lot count and sampling depth to staffing so assay never becomes the silent bottleneck.

Tie the chain together with a single ton of NMC feedstock. Gross 1,000 kg, active fraction 42 percent, mechanical yield 85 percent, chemical recovery 92 percent lithium and 95 percent nickel and cobalt. Recovered metal value from the assay above lands near 5,000 to 6,500 dollars per ton depending on price inputs. Every input has a source: active fraction from teardown data, assay grade from the lab, recovery rates from your own reconciliation, and prices from a daily commodity feed. Keeping units consistent, kilograms and dollars per kilogram throughout, is what separates a defensible number from a guess.

Reconcile the math against actual output monthly, because assumed rates drift. Take metal shipped in kilograms, divide by metal received as feedstock in kilograms, and compare that measured overall recovery to the product of your assumed mechanical and chemical rates. A gap wider than 3 points means one input is stale, usually the mechanical yield after screen wear or the assay grade after a feedstock mix change. Feed the corrected numbers back into Black Mass Recovery Yield and Recovered Metal Value so next quarter's quotes rest on reconciled data rather than nameplate assumptions that quietly erode as the line ages.

Published 2026-07-01.