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What is a cut-off grade

The cut-off grade (COG) is the lowest grade of the valuable component in ore at which mining and processing it still pays. A tonne of ore graded below the cut-off makes a loss, above it a profit. It is the line that separates ore from waste.

In the break-even model the cut-off grade follows from the condition “revenue = cost”:

COG = C × KP × R × (1 − L)

• C — cost of mining and processing 1 t of ore;
• P — price per unit of product (concentrate or metal);
• R — recovery of the valuable component, %;
• L — processing losses, %;
• K — conversion factor to the chosen unit of measure.

Why it is calculated

• Outlining ore bodies. The cut-off grade is the first of the economic cut-off criteria: it decides which blocks go into the reserve estimate and which stay out.
• Estimating reserves and resources. Tonnage, average grade and, in the end, the economics of the project depend on it directly.
• Justifying the cut-off criteria in a feasibility study. Together with a sensitivity analysis it shows how robust the criteria are to swings in prices, costs and processing performance.
• Mine planning. It separates ore from overburden and drives the extraction schedule.

Where it is used

The calculation is needed at every stage, from exploration to production: in the geological and economic assessment of a deposit, in the feasibility study for cut-off criteria, in the annual reserve update, in audits of resource estimates under the international codes, and in operational planning whenever price or cost has moved noticeably.

Types of cut-off

• Break-even. The most common: the grade at which revenue equals cost. This is the one this calculator computes.
• Marginal. Counts only the costs that can be avoided by not mining the block (processing, haulage) — used when stripping is already paid for.
• Internal and external. The first separates ore from waste inside the pit outline; the second decides whether an area should be mined at all.
• Optimised (Lane). Maximises net present value (NPV) under mining, processing and market constraints; it changes over time.

Formulas and units of measure

The calculator supports six units. Only the factor K differs — the formula itself stays the same. The concentrate grade (G_conc) is entered in percent and is not divided by 100.

For kg/m³ the bulk density of the ore ρ (t/m³) is required — it is what turns a mass fraction into a volume one.

Metal equivalent (equivalent grade)

When a deposit is polymetallic, reserves are estimated on a single measure — the metal equivalent. Each co-product is brought to the main component by a conversion coefficient:

k_i = Price_i × Recovery_iPrice_main × Recovery_main

The equivalent grade is then G_eq = G_main + Σ Gᵢ × kᵢ. The coefficients are rounded to four decimal places. An example for titanium-zirconium ore:

TiO₂Eq(%) = TiO₂(%) + Rutile(%) × 5.0615 + Zircon(%) × 7.0678

The conversion coefficients follow the SCMR methodological guidelines (items 102–106); the same approach is described by Rendu and in JORC 2012 Table 1, Section 4.

Reporting codes and the Ukrainian classification

The CRIRSCO-family codes — JORC (Australia), NI 43-101 (Canada), CIM (definition standards), SAMREC (South Africa), S-K 1300 (USA) — require Mineral Resource and Mineral Reserve estimates to rest on a justified cut-off and “reasonable prospects for eventual economic extraction”.

Ukraine uses the Classification of reserves and resources of the state subsoil fund: the cut-off criteria (including the cut-off grade) are approved by Ukraine's State Commission on Mineral Reserves (SCMR) on the basis of a feasibility study. The calculation logic is the same in both systems — the terminology, the reserve categories and the approval procedure differ.

A bridge between the two: the Ukrainian bortovyi vmist is the cut-off grade; the kondytsii (economic cut-off criteria) correspond to modifying factors; categories A/B/C₁/C₂ ↔ Measured / Indicated / Inferred (not a literal match). Further reading: Hall, Cut-off Grades and Optimising the Strategic Mine Plan; Rendu, An Introduction to Cut-off Grade Estimation.

Common mistakes

• Incomplete cost. Only mining is counted and processing, haulage or overheads are forgotten — the cut-off grade comes out too low.
• Mixed-up units. A price per tonne of concentrate with a grade in g/t, or ppm instead of %, is off by a factor of thousands.
• Ignoring processing losses. Leaving out the (1 − L) term systematically understates the result.
• An optimistic price. A calculation at the peak price gives criteria that do not survive a market downturn — which is why a sensitivity analysis is needed.
• One cut-off for the whole deposit. Different areas, mining methods and ore types may need different values.

What affects it and how often to review it

The cut-off grade is not a constant. It depends on:

• metal and concentrate prices, the exchange rate;
• the cost of energy, fuel, reagents and labour;
• processing performance: recovery, concentrate grade, losses;
• the mining method (open pit or underground) and depth;
• taxes, royalties and environmental requirements.

Practice: review it at least once a year, and whenever a key parameter changes materially (as a guide, by more than 10–15 %) or the processing technology changes.

Examples from real data

One worked example for each unit of measure: the inputs, the result of the formula and the figure printed in the report itself. The “Open in the calculator” button puts the example into the form — then you can change the sensitivity step or any field and recalculate your own way.

Unit: %

Unit: g/t

Unit: kg/t

Unit: kg/m³

Unit: ppm

Unit: oz/t

Sources: Ukrainian geological and economic assessment reports from the project archive, public SEC filings (S-K 1300), JORC reports from the ASX. The full catalogue of checked cases (several dozen) is kept internally — it is for verifying the formulas, not for everyday work.