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Comminution

Bond Work Index Calculator

This calculator applies the published Bond Third-Theory equation, W = 10 · Wi · (1/√P80 − 1/√F80), with F80 and P80 in micrometres and Wi and W in kWh/t. Forward, it computes the specific grinding energy W from a Bond work index Wi you supply (from a test or the literature) and your F80/P80. In reverse, it back-calculates an operating (apparent) work index Wi,op from a measured specific energy and the two sizes. It is a preliminary, formula-based, educational calculator. It is NOT a Bond grindability test, does NOT determine your ore’s work index, does NOT apply Rowland efficiency factors, and does NOT size or select a mill. The user must supply Wi or measured W. Source: Bond, F.C. (1952), “The Third Theory of Comminution,” Trans. AIME 193, 484–494; corroborated by Wills’ Mineral Processing Technology and the SME Mineral Processing & Extractive Metallurgy Handbook.

TypeInteractive engineering calculator

Calculator

kWh/t

supplied from a test or the literature — not predicted here

µm

80% passing feed size, micrometres

µm

80% passing product size, micrometres (< F80)

Result
Specific grinding energy (W)10.4675 kWh/t
  • !Preliminary formula calculator only — it applies the published Bond Third-Theory equation to a work index you supply (from a test or the literature), or back-calculates the operating work index from measured energy. It is NOT a Bond grindability test, does NOT determine your ore’s work index, does NOT apply Rowland efficiency factors, and does NOT size or select a mill.
  • !Valid only within the assumptions of Bond’s equation (conventional rod/ball-mill size range). Excludes efficiency factors, circuit configuration, classification effects, liner/media effects, motor efficiency, ore variability, and scale-up. Final mill design requires testwork, vendor methods, site data, and qualified review.

Source: Bond, F.C. (1952), “The Third Theory of Comminution,” Trans. AIME 193, 484–494 (specific-energy equation); corroborated by Wills’ Mineral Processing Technology and the SME Mineral Processing & Extractive Metallurgy Handbook. Preliminary, uncorrected estimate from a user-supplied work index or measured energy — not a grindability test, ore-Wi prediction, or mill sizing/selection.

Related: Bond Work Index Explained · Reduction Ratio · Grinding Circuit Calculations

Formulas

Specific grinding energy (forward)
W = 10 · Wi · (1/√P80 − 1/√F80)
Operating work index (reverse)
Wi,op = W / [10 · (1/√P80 − 1/√F80)]

Diagram

Bond Third-Theory specific energy — W from a supplied work index WiF80grindingP80W (kWh/t)W = 10 · Wi · (1/√P80 − 1/√F80)Wi,op = W / [10 · (1/√P80 − 1/√F80)]supplied Wi or measured W — not a grindability test

Worked example

An ore with a supplied Bond work index Wi = 14 kWh/t is ground from F80 = 2000 µm to P80 = 106 µm. Estimate the specific energy, then confirm the reverse calculation.

  1. 011/√P80 = 1/√106 = 0.097129; 1/√F80 = 1/√2000 = 0.022361; difference = 0.074769
  2. 02Forward: W = 10 × 14 × 0.074769 = 10.47 kWh/t
  3. 03Reverse check: Wi,op = 10.47 / (10 × 0.074769) = 14.00 kWh/t
Result

W ≈ 10.47 kWh/t from a supplied Wi = 14 kWh/t; the reverse recovers Wi,op = 14.00 kWh/t — the published equation only, not a grindability test or mill sizing.

FAQ

Does this calculator determine my ore’s Bond Work Index?
No. The work index is an input you supply, from a standardised Bond grindability test on your ore or from the literature. The calculator applies the published Bond equation to that supplied value; it cannot predict a work index from ore properties. The reverse mode back-calculates an apparent operating work index from a measured specific energy, which is circuit-specific, not a determined ore property.
Is this a Bond grindability test?
No. A true Bond Work Index comes from a standardised locked-cycle ball-mill (or rod-mill) grindability test in the laboratory. This calculator only evaluates the Bond Third-Theory energy equation; it does not perform or replace the test.
Why are no Rowland efficiency factors applied?
Bond’s classical mill-sizing method corrects the equation energy with Rowland’s EF1–EF8 factors (dry grinding, mill diameter, oversize feed, fineness, and so on). This calculator reports only the raw Third-Theory value so the result is transparent. Applying efficiency factors and scaling to a mill is design work needing vendor methods and qualified review.
What units do F80 and P80 use?
Micrometres (µm), as the Bond equation is written here, with F80 larger than P80. F80 is the size through which 80% of the feed passes and P80 the size through which 80% of the product passes. Do not enter them in millimetres.
Can I trust the result for any ore and size range?
Treat it as a preliminary estimate within Bond’s assumptions — conventional rod- and ball-mill grinding within a stated size range. Outside that range (very coarse crushing, very fine grinding, or unusual ores) the relationship loses accuracy and other models apply. The result is uncorrected and not a plant-energy guarantee.

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