Ball Mill Critical Speed Calculator
Work out the critical speed of your ball mill and the recommended operating range in rpm Get In ContactHow fast should your ball mill turn? This free calculator works out your mill’s critical speed – the speed at which the grinding media would be pinned to the shell and stop tumbling – along with the operating speed range for efficient grinding.
Enter the mill’s inside diameter and the size of the largest grinding media in millimetres or inches. Results update instantly in revolutions per minute (rpm). To check an existing mill, enter its current speed and the gauge will show where it sits.
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What is ball mill critical speed?
As a ball mill turns, the shell and liners carry the grinding media up the side of the mill until gravity pulls it back down, so it cascades and tumbles onto the material being ground. Critical speed is the speed at which the centrifugal force on the outer layer of media exactly balances gravity at the top of the mill. At that point the media is held against the liners and travels round with the shell instead of falling, so almost no grinding takes place.
Critical speed depends only on the mill’s inside diameter and the size of the grinding media. It doesn’t change with the length of the mill, the weight of the charge or the material being ground.
The critical speed formula
Nc = 42.3 ÷ √(D − d)
- Nc – critical speed in revolutions per minute (rpm)
- D – inside diameter of the mill, measured inside the liners, in metres
- d – diameter of the largest grinding media, in metres
The constant 42.3 comes from balancing centrifugal force against gravity for a ball travelling around the inside of the shell. If you work in feet, the same formula uses 76.6 instead: Nc = 76.6 ÷ √(D − d), with D and d in feet. Because the media is small compared with the mill, the formula is often simplified to Nc = 42.3 ÷ √D. The calculator above includes the media size for a slightly more accurate figure.
Worked example
A mill with an inside diameter of 1,800 mm (1.8 m), charged with 50 mm (0.05 m) balls:
- D − d = 1.8 − 0.05 = 1.75 m
- √1.75 = 1.323
- Nc = 42.3 ÷ 1.323 = 32.0 rpm
At 75% of critical speed, this mill would run at about 24 rpm. Its 65–80% operating range is roughly 20.8 to 25.6 rpm.
What speed should a ball mill run at?
Ball mills run below critical speed so the media keeps tumbling. Most operate at around 65–80% of critical speed, and 70–75% is a common starting point. Where your mill sits in that range changes how the charge moves and how it grinds.
How mill speed affects grinding
| Speed (% of critical) | What the charge does | Effect on grinding |
|---|---|---|
| Below about 65% | Media rolls gently down the face of the charge (cascading) | Grinding mainly by attrition. Gentler and slower – at very low speeds the charge slides and wastes energy |
| 65–80% | A mix of rolling and falling media | The efficient range for most ball mills, balancing impact and attrition |
| 80–100% | Media is thrown clear and lands on the charge or liners (cataracting) | More impact energy, but higher liner and media wear. Efficiency drops as speed nears critical |
| 100% and above | Media is held against the shell (centrifuging) | Almost no grinding |
The best speed for your mill also depends on the liner and lifter design, the size and type of media, how full the mill is and whether you’re grinding wet or dry. For a very fine product, a cascading charge towards the lower end of the range usually works better than a cataracting one.
Choosing media for your mill? See our range of grinding media, or read more about ball mill grinding.
Ball mill critical speed FAQs
What is the critical speed of a ball mill?
It’s the speed at which the grinding media would be held against the shell by centrifugal force and stop tumbling. For a mill with inside diameter D and largest media diameter d, both in metres, critical speed Nc = 42.3 ÷ √(D − d) rpm.
What percentage of critical speed should a ball mill run at?
Most ball mills run at about 65–80% of critical speed, with 70–75% a common starting point. The best figure depends on your liners, your media and the grind you need.
What happens if a ball mill runs above critical speed?
The media centrifuges: it’s carried round with the shell instead of falling, so grinding almost stops. Running close to critical speed also increases liner and media wear.
Does the length of the mill affect critical speed?
No. Critical speed depends only on the inside diameter and the media size. Length affects capacity and how long material stays in the mill, not critical speed.
Should I measure the diameter inside or outside the liners?
Inside the liners. That’s the diameter the media actually travels around, so using the outer shell diameter would underestimate the critical speed.
How do I work out my mill speed as a percentage of critical speed?
Divide the mill’s actual speed by its critical speed and multiply by 100. For example, a mill turning at 24 rpm with a critical speed of 32 rpm runs at 75% of critical. Enter your current speed in the calculator to check yours, or contact us for advice on your mill.