Ball Mill Power Calculator
This tool applies Bond's Law of comminution.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the ore's Bond ball-mill work index Wi in kWh/t (from testwork — typically 8–20 kWh/t for most ores).
- Enter the 80%-passing feed size F80 and product size P80, both in micrometres (µm); P80 must be finer than F80.
- Enter the dry ore throughput in t/h and read the estimated net mill power in kW (and hp) plus the specific energy in kWh/t.
How it works
This tool applies Bond's Law of comminution. The specific grinding energy is W = 10 × Wi × (1/√P80 − 1/√F80), where Wi is the Bond work index in kWh/t and the sizes are the 80%-passing feed (F80) and product (P80) apertures in micrometres. Multiplying the specific energy by the mass throughput gives the net power: Power (kW) = W (kWh/t) × throughput (t/h), because kWh/t × t/h = kW.
The result is the theoretical net power required at the mill shell to achieve the stated size reduction. Real installed motor power is higher: divide by the drive/motor efficiency and apply Bond's efficiency factors (EF1–EF8) for dry grinding, mill diameter, oversize feed, fineness and open/closed circuit. The tool reports hp as a convenience (1 hp = 0.7457 kW). It is an order-of-magnitude sizing aid, not a substitute for a full comminution circuit design.
Worked example
Rod-mill feed ground to 100 µm at 50 t/h. A ball mill treats ore with a Bond work index of 15 kWh/t, feeding at F80 = 2,000 µm and producing P80 = 100 µm at a throughput of 50 t/h. Specific energy W = 10 × 15 × (1/√100 − 1/√2000) = 11.65 kWh/t. Mill power = 11.65 × 50 = 582.3 kW (about 780.9 hp) of net grinding power at the shell.
Common mistakes
- Entering feed and product sizes in millimetres instead of micrometres — Bond's equation requires µm (2 mm = 2,000 µm), and mixing units gives a power that is off by orders of magnitude.
- Treating the result as installed motor power. It is net power at the shell; you must still divide by drive/motor efficiency and apply Bond correction factors EF1–EF8 to size the actual motor.
- Setting P80 equal to or larger than F80. A mill grinds finer, so P80 must be smaller than F80 or the specific energy is zero/negative and the calculation is meaningless.
Frequently asked questions
Is this the installed motor power?
No. Bond's equation gives the net grinding power at the mill shell. Installed motor power is larger — you divide by the drive and motor efficiency and apply Bond's efficiency factors (EF1–EF8) for dry grinding, mill diameter, oversize feed and circuit type. Treat this as a first-pass estimate only.
What units do F80 and P80 use?
Micrometres (µm). F80 and P80 are the 80%-passing sizes of the feed and product. For example 2 mm = 2,000 µm and 0.1 mm = 100 µm. Using millimetres by mistake will throw the answer out by orders of magnitude.
Where do I get the Bond work index?
From a standard Bond ball-mill grindability test on a representative sample, reported in kWh/t. It typically ranges from about 8 kWh/t (soft ores) to 20+ kWh/t (very hard/competent ores). Use your site's testwork value rather than a textbook figure.
Does this include no-load power or liner/media effects?
No. It is purely the size-reduction energy from Bond's Law. It excludes no-load (empty-mill) power, liner and grinding-media condition, slurry density and classification. Use it for scoping, then confirm with a full comminution model and vendor sizing.
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