Free calculators for mining and mineral processing
17 mine and mill calculations: slurry, metallurgical balance, grinding, cyclones, thickeners and tailings. Formula shown, with practice problems.
Slurry and reagents
Percent solids from slurry density
Assumes water of SG 1.0 (correct it if the process water is very saline). With a pulp density scale, cut the full stream and weigh before the solids settle.
Slurry SG from percent solids
Handy to set grinding dilution or check a density gauge. Ball mill discharge: often 65 to 75 % solids; flotation feed: 25 to 40 %.
Dry tonnage in a slurry line
This is the basis of a mass balance from a magnetic flowmeter and a nuclear density gauge. Check now and then against a sample weighing and the belt scale.
Dilution ratio and make-up water
Dilution ratios (water/solids) add up; percent solids do not. A negative result means water must be removed (thickener, cyclone).
Reagent dose: g/t to solution flow
Flocculant: 10 to 40 g/t, stock solution often 0.25 to 0.5 % (2.5 to 5 g/L), then diluted in line. Collectors: a few g/t up to 100 g/t. Confirm the pump rate with a graduated-cylinder drawdown test.
Metallurgical balance and production
Two-product formula: recovery and ratio of concentration
Valid at steady state with samples taken at the same time. Works in % or g/t as long as all three grades use the same unit. Very sensitive to assay error when f is close to t.
Metal produced and concentrate tonnage
For base metals (grades in %), in dry tonnes. For gold and silver in g/t, use the next calculator.
Gold or silver production (g/t)
Troy ounce = 31.1035 g. Use the reconciled grade of the ore actually milled, not the resource model grade.
Stripping ratio (waste to ore)
Can also be done in volume (bank m³): do not mix tonnes and m³. Compare with the break-even ratio of the mine plan.
Haul truck productivity
Round n up to the next whole truck. Time the cycles in the field or take them from the dispatch system; 45 to 50 working minutes per hour is common.
Grinding and classification
Bond's law: grinding energy and power
Wi from a laboratory grindability test (ball mill). Rowland's efficiency factors (diameter, fineness, dry grinding…) are not applied: a first-order estimate.
Mill critical speed
Ball mills: about 65 to 80 %; AG and SAG mills: 70 to 80 %. Above about 85 % the charge starts to centrifuge and does less work. Set d = 0 for the simplified formula.
Circulating load from percent solids (cyclones)
Direct closed circuit: overflow equals new feed. Take the three samples at the same time; typical: 200 to 400 %.
Circulating load from a size fraction
Pick a size where the three products differ clearly (e.g. % retained on 150 µm). More reliable than percent solids when dilution water varies.
Thickening, tailings and water
Thickener: underflow and recovered water
Assumes a clear overflow (no solids) and water of SG 1.0. Watch overflow clarity: solids that report to overflow reduce the usable water.
Thickener: area, diameter and rise rate
Solids loading comes from settling tests: about 0.05 to 0.3 t/m²·h for a conventional thickener, 0.5 to 1.5 for a high-rate thickener. Too high a rise rate gives a dirty overflow.
Tailings: storage volume and life
Dry density depends on the deposition method and consolidation (often 1.2 to 1.6 t/m³ for slurry tailings, more for filtered tailings). Does not replace the deposition plan or the required freeboard.
Learning and checking tools. The ranges shown are general guidance: always follow your plant's procedures, permits and set points. Nothing is sent anywhere: the calculations run in your browser.