Bond Work Index Explained

Definition

The Bond Work Index (Wi) is a material property — the energy, in kilowatt-hours per tonne, that characterises how resistant an ore is to comminution under Bond's Third Theory of Comminution (Bond, 1952). Bond's Third Theory states that the specific grinding energy W required to reduce a feed from an 80%-passing size F80 to an 80%-passing product size P80 follows W = 10 · Wi · (1/√P80 − 1/√F80), with the sizes in micrometres and W and Wi in kWh/t. F80 and P80 are the sieve sizes through which 80% of the feed and product pass respectively — the standard single-number descriptors of a size distribution. The ProcessConvert Bond calculator works this equation two ways: forward, it computes the specific energy W from a work index you supply 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. In both cases the work index is something you bring to the calculation — from a grindability test or the literature — not something the calculator predicts.

Why it matters

The reason this page exists is to police one boundary: calculating with the Bond equation is not the same as determining a work index. A true Bond Work Index comes from a standardised Bond locked-cycle ball-mill (or rod-mill) grindability test run on your ore — a laboratory procedure this calculator describes but does not replicate. Supplying a Wi and computing W gives a preliminary, uncorrected energy estimate; measuring W and back-calculating Wi,op gives an operating work index that bundles in real-circuit inefficiencies. Neither is an ore-specific guarantee, and neither sizes a mill. Bond's classical method also uses Rowland's EF1–EF8 efficiency factors to correct the energy for dry grinding, mill diameter, oversize feed, fineness, and so on — this calculator names those factors but deliberately does not apply them, so its output is the raw equation value only. That matters because the gap between a textbook energy estimate and a mill specification is exactly where testwork, vendor methods, and qualified engineering belong. Getting the supplied-Wi-versus-measured-W distinction right, and not mistaking either for a grindability test or a mill-sizing result, is the whole point.

Formula

Units involved

• •Wi — Bond work index, kWh/t (supplied from a test or the literature)
• •W — specific grinding energy, kWh/t
• •F80 — 80% passing feed size, micrometres (µm)
• •P80 — 80% passing product size, micrometres (µm); must be smaller than F80
• •Wi,op — operating / apparent work index, kWh/t (back-calculated from measured W)

Concept diagram

Worked example

Common mistakes

• •Believing the calculator determines your ore’s work index — Wi is an input you supply, not an output it predicts.
• •Mistaking the calculation for a Bond locked-cycle grindability test (the lab procedure that yields a true Wi).
• •Using the raw W to size or select a mill — no Rowland EF1–EF8 efficiency factors are applied.
• •Putting F80 or P80 in millimetres — the equation as written needs micrometres.
• •Applying the equation far outside Bond’s conventional rod/ball-mill size range and trusting the number.
• •Treating an operating work index back-calculated from one measurement as a fixed ore property.

When to use the calculator

Use the Bond Work Index calculator in the forward direction when you have a work index (from a Bond test or the literature) and want a preliminary specific-energy estimate for an F80→P80 reduction. Use the reverse direction when you have a measured specific energy and the two sizes and want the operating (apparent) work index of a running circuit. Pair it with the reduction ratio calculator, which shares F80/P80. For a true ore work index use a Bond grindability test; for a mill specification use vendor methods, efficiency-factor corrections, and qualified review.

FAQ