Resources, Reserves & Cut-off Grade
Not all mineralised rock is ore. Learn the difference between mineral resources (inferred, indicated, measured) and ore reserves (probable, proved) under JORC / NI 43-101, how the breakeven cut-off grade is calculated from price, recovery and costs, and how grade–tonnage curves show the effect of changing cut-off.
Ore is rock that can be mined, processed and sold at a profit. Whether a block of rock is ore or waste depends on metal price, costs and recovery — so the same deposit can grow or shrink as markets change.
Public reporting codes (JORC in Australia, NI 43-101 in Canada, SAMREC, S-K 1300) protect investors by requiring a Competent/Qualified Person to sign off estimates.
An analogy
Cut-off grade is like the minimum tip that makes a delivery trip worthwhile: below it, the effort costs more than you earn.
Resources vs reserves
A Mineral Resource has reasonable prospects of eventual economic extraction: Inferred (low confidence), Indicated and Measured (highest). An Ore Reserve is the part of Indicated/Measured resources that is economically mineable after applying 'modifying factors' — mining, processing, economic, legal, environmental, social: Probable and Proved.
Cut-off grade
Blocks above cut-off go to the mill; below go to waste or low-grade stockpiles. The marginal cut-off (for rock that must be mined anyway) uses only processing costs; the breakeven cut-off includes mining cost. Higher prices or recoveries lower the cut-off and increase reserves.
Grade–tonnage curves
Plot tonnage above cut-off and average grade above cut-off versus cut-off. Raising cut-off reduces tonnage but raises average grade — a trade-off between mine life and early cash flow.
Lane's theory and dilution
Kenneth Lane's method finds cut-offs that maximise NPV considering mine, mill and market constraints — often higher early in life. Real mining also includes dilution (waste mixed in) and ore loss, which must be applied when converting resources to reserves.
Formulas
- Mill (marginal) cut-off:
c = C_p / (P × R) - Breakeven (pit-limit) cut-off:
c = (C_m + C_p) / (P × R) - Value per tonne:
NSR = g × R × P − costs - Exponential grade model:
T(c) = T₀ e^(−c/μ), ḡ(c) = c + μ
Worked example: Copper cut-off grade
Given: Cu price $9.0/kg, selling cost $0.5/kg; Recovery 88 %; Processing $12/t, G&A $3/t, mining $2.5/t
Find: Mill and breakeven cut-offs.
- Value of 1 % Cu per tonne = 10 kg × 0.88 × 8.5 = $74.8/t
- Mill cut-off = 15/74.8 = 0.20 % Cu
- Breakeven = 17.5/74.8 = 0.23 % Cu
Answer: 0.20 % (mill) and 0.23 % (breakeven)
Worked example: Effect on tonnage
Given: Exponential deposit: T₀ = 200 Mt, μ = 0.5 %
Find: Tonnage and grade above 0.20 % and 0.40 %.
- 0.20 %: T = 200 e^(−0.4) = 134 Mt at 0.70 %
- 0.40 %: T = 200 e^(−0.8) = 90 Mt at 0.90 %
Answer: Doubling cut-off cuts tonnage by one-third but raises grade 29 %
Common mistakes
- Wrong: Calling inferred resources 'reserves'. — Right: Only indicated/measured resources can convert to reserves.
- Wrong: Ignoring recovery in the cut-off. — Right: Only recovered metal earns revenue.
Applications
- Public reporting: Annual reserve statements for stock exchanges.
- Grade control: Daily ore/waste decisions at the pit face.
- Price scenarios: Reserves re-estimated when prices move.
Key takeaways
- Resources (inferred/indicated/measured) → reserves (probable/proved).
- c = costs / (price × recovery).
- Grade–tonnage curves show the cut-off trade-off.
- Competent Persons sign public estimates.
Going further
- Lane's cut-off theory: Balances mine, mill and market capacities for maximum NPV.
- NSR cut-off: Polymetallic ores use net smelter return in $/t instead of grade.
- Reconciliation: Compare model, grade control and mill results to calibrate estimates.