Grinding Circuit Calculations Explained
The concept anchor for comminution calculations — circulating load, screen (undersize-recovery) efficiency, reduction ratio, and Bond Work Index, all from measured operating data. Carries the operating-checks-vs-design boundary: these check and estimate; they do not size equipment, predict grindability, or simulate a circuit.
Definition
Grinding circuit calculations are the preliminary, formula-based checks a mineral-processing engineer uses to turn measured operating data into circuit metrics: the circulating load of a closed grinding circuit (the recycle tonnage relative to fresh feed), the screen efficiency or undersize recovery of a classifying screen, the comminution reduction ratio (how much coarser the feed is than the product), and the Bond specific grinding energy or operating work index. Each one is an accounting or textbook-equation calculation on numbers you already have — tonnages, undersize masses, F80/P80 sizes, or a supplied work index. None of them designs equipment, predicts how an ore will grind, or simulates a circuit. They are the everyday arithmetic of running and understanding a grinding circuit, scoped strictly to checks, teaching, and early-stage screening.
Why it matters
The sharpest line in this whole topic is operating checks versus design and prediction. Circulating load tells you the recycle tonnage relative to fresh feed — it is not cyclone classification efficiency, mill power, or grinding efficiency. Screen efficiency here is specifically undersize recovery (the fraction of true undersize in the feed that actually reports to the undersize product) — it is not a screen sizing or deck-selection method, and it says nothing about aperture, blinding, moisture, or capacity. Reduction ratio is same-unit sizing arithmetic, F80/P80 — it is not equipment selection and carries no energy, work index, throughput, or capacity information. Bond Work Index calculation applies a published energy equation to a work index you supply — it is not a Bond grindability test and does not determine your ore's work index. Confusing any of these for the design or prediction version is the classic error: a circulating-load number does not size a cyclone, a reduction ratio does not pick a crusher, and a Bond energy estimate does not size a mill. Getting the boundary right is what keeps these calculations honest and useful.
Formula
Units involved
- •fresh feed, recycle, total mill feed — tonnage rates (t/h)
- •undersize in feed, undersize product — tonnage rates (t/h)
- •CLR — circulating load ratio, dimensionless (×100 for %)
- •E — screen efficiency / undersize recovery, %
- •F80, P80 — 80% passing sizes in the same unit (µm or mm); reduction ratio is dimensionless
- •Wi, W — Bond work index and specific grinding energy (kWh/t), with F80/P80 in micrometres (µm)
Concept diagram
Worked example
A closed circuit runs 100 t/h fresh feed with 250 t/h recycle; a screen carries 80 t/h undersize in its feed and 68 t/h passes; the mill reduces F80 2000 µm to P80 106 µm. Compute the core circuit metrics.
- 01Circulating load ratio: CLR = 250 / 100 = 2.5 → 250%
- 02Total mill feed: 100 + 250 = 350 t/h
- 03Screen efficiency: E = 68 / 80 × 100 = 85.0%, with 12 t/h undersize lost to oversize
- 04Reduction ratio: R = 2000 / 106 = 18.87, a 94.7% size reduction
- 05Read all four as operating checks for the sampled period — not a sizing or performance prediction
CLR 2.5 (250%), total mill feed 350 t/h, screen efficiency 85.0%, reduction ratio 18.87 — preliminary operating checks from measured data.
Common mistakes
- •Treating circulating load as cyclone classification efficiency — it is a recycle mass-flow ratio, not a partition curve.
- •Reading screen efficiency as a screen sizing or capacity result — it is undersize recovery only.
- •Mixing units between F80 and P80 in the reduction ratio — both must be in the same unit.
- •Using the Bond energy estimate to size or select a mill, or treating it as a grindability test.
- •Assuming any of these predicts how a specific ore will grind or how a circuit will perform.
- •Trusting the metrics when the input tonnages or sizes are not representative or reconciled.
When to use the calculator
Use the circulating load calculator for the recycle ratio and total mill feed of a closed circuit. Use the screen efficiency calculator for undersize recovery across a classifying screen. Use the reduction ratio calculator for F80/P80 and percent size reduction in the same unit. Use the Bond work index calculator for specific grinding energy from a supplied work index, or the reverse operating work index from measured energy. All four are preliminary checks — for equipment sizing, ore-specific grindability, or circuit performance, use testwork, vendor methods, and qualified review.