TAHA Engineering Toolsby TAHA Knowledge Lab

Machining & Workshop

Turning Material Removal Rate Calculator

Metal removal rate (cm³/min) of a turning cut from diameter, depth of cut, feed and speed.

Inputs

Calculate from
Side view of a bar being turned: the uncut part has diameter D, the cut part diameter d, the depth of cut ap is the radial step.fDdaₚ
The tool removes a ring of depth aₚ from the diameter D, leaving d = D − 2aₚ. Volume removed per minute Q = π × (D − aₚ) × aₚ × f × n. Diagram not to scale.

How far the tool cuts into the radius. The diameter reduces by twice this amount.

Result

Material removal rate
87
Quick estimate Vc × ap × f
90
Diameter after the cut
56
Spindle speed
954.93rpm
Working
n = 1000 × 180 ÷ (π × 60) = 954.93 rpm Q = π × (D − ap) × ap × f × n = π × (60 − 2) × 2 × 0.25 × 954.93 = 87,000 mm³/min = 87 cm³/min Quick estimate: Vc × ap × f = 180 × 2 × 0.25 = 90 cm³/min

The cut removes about 87 cm³/min of metal, reducing the diameter to 56 mm.

Educational estimate — check the assumptions below.

About this calculator

The material removal rate (MRR, often written Q) is the volume of metal a cut removes each minute. It is the main measure of how productive a roughing operation is, and — together with the material’s specific cutting force from your tooling supplier — it is used to estimate the cutting power needed. This calculator works out the exact volume of the ring of metal removed, and also the common quick estimate Vc × ap × f used in tool catalogues.

Formula

Q = π × (D − ap) × ap × f × n

Quick estimate: Q ≈ Vc × ap × f   (cm³/min with Vc in m/min, ap and f in mm)

D = diameter before the cut, ap = radial depth of cut, f = feed per revolution, n = spindle speed, Vc = cutting speed. The exact form uses the mean diameter of the removed ring, D − ap; the quick estimate uses the starting diameter, so it is slightly higher.

Worked example

Roughing a 60 mm bar with a 2 mm depth of cut, 0.25 mm/rev feed, at 180 m/min:

  • n = 1000 × 180 ÷ (π × 60) = 954.9 rpm
  • Q = π × (60 − 2) × 2 × 0.25 × 954.9 = 87 000 mm³/min = 87.0 cm³/min
  • Quick estimate = 180 × 2 × 0.25 = 90 cm³/min
  • Diameter after the cut = 60 − 2 × 2 = 56 mm

Assumptions and limitations

  • A straight longitudinal turning cut at constant depth, feed and speed.
  • The rate is while the tool is cutting. Average removal over a whole cycle is lower.
  • Cutting power also depends on the material and tool geometry (specific cutting force kc); it is not calculated here because it requires material data from your tooling supplier.

References

  • Volume of the removed annulus per revolution: π (D − aₚ) aₚ f; catalogue approximation Q = Vc · aₚ · f.