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Metallurgical Accounting

Ratio of Concentration Calculator

The ratio of concentration K is the tonnes of feed that must be treated to make one tonne of concentrate. It is derived from the same two-product mass balance as recovery and yield: K = (c − t)/(f − t), the reciprocal of the mass yield. This calculator returns K from the measured feed, concentrate, and tailings assays, with the reciprocal mass yield, recovery, and enrichment ratio shown for context. It accounts for measured streams, calculates accounting metrics, and reconciles assay relationships. It does NOT predict future plant performance, predict recovery or grade, predict flotation or leaching response, guarantee recovery, optimise a plant, or replace metallurgical testwork. Inputs must satisfy c > f > t.

TypeInteractive engineering calculator

Calculator

% or g/t

assay of the feed stream

% or g/t

must be higher than the feed

% or g/t

must be lower than the feed

Result
Ratio of concentration12.25 : 1
Concentrate yield (mass pull)8.16327 %
Recovery81.6327 %
Enrichment ratio10 ×
  • !Accounting estimate only — the ratio of concentration is an assay mass-balance relationship derived from the two-product formula. It does NOT predict recovery or grade, model the process, or guarantee performance.
  • !Use the same metal and the same assay units for all three streams. Results assume c > f > t.

Formulas

Ratio of concentration
K = (c − t) / (f − t)
Reciprocal mass yield
Y = 1 / K
Metal recovery
R = Y × (c / f)
Enrichment ratio
ER = c / f

Diagram

Ratio of concentration — tonnes of feed per tonne of concentratefeed fconc cK = (c − t)/(f − t) = 1/Yan assay mass-balance ratio — not a performance claim

Worked example

A circuit assays feed 1.0%, concentrate 10.0%, and tailings 0.2%. How many tonnes of feed are treated per tonne of concentrate?

  1. 01Ratio of concentration: K = (10.0 − 0.2) / (1.0 − 0.2) = 9.8 / 0.8 = 12.25
  2. 02Reciprocal mass yield: Y = 1 / 12.25 = 0.08163 = 8.163%
  3. 03Recovery (for context): R = 0.08163 × (10.0 / 1.0) = 81.63%
  4. 04Enrichment ratio (for context): ER = 10.0 / 1.0 = 10.0
Result

Ratio of concentration 12.25 — about 12.25 tonnes of feed per tonne of concentrate. An assay mass-balance relationship, not a performance claim.

FAQ

What does the ratio of concentration mean?
It is the weight of feed that must be treated to produce one unit weight of concentrate — for example K = 12.25 means roughly 12.25 tonnes of feed per tonne of concentrate. It is a mass-balance ratio of measured assays, not a throughput, recovery, or performance guarantee.
How is the ratio of concentration related to the two-product formula?
It is the reciprocal of the two-product mass yield: K = 1/Y = (c − t)/(f − t). This dedicated calculator gives K (and Y) directly; the two-product formula calculator additionally returns recovery and enrichment ratio as primary outputs. Both use the same measured feed/concentrate/tailings assays.
Does a higher ratio of concentration mean better recovery?
No. A higher K means more feed per tonne of concentrate (a higher-grade, lower-mass-pull concentrate). Recovery depends on K and on the grades together (R = (c/f)/K). The ratio of concentration is an accounting ratio, not a recovery indicator on its own.
Why must c > f > t?
For an upgrade to be physical the concentrate must be richer than the feed and the feed richer than the tailings. If the inputs violate c > f > t the ratio is meaningless, so the calculator shows an input error.

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