sumivo

Sumivo · Manufacturing

Cutting Speed Calculator

Convert tool diameter and spindle speed to surface speed, a common CNC machining conversion.

01 / INPUTS

mm
rpm

02 / RESULT

SURFACE SPEED

31.41592654 m/min

Surface speed
31.41592654 m/min

Calculation trace

  1. π × 10 mm × 1,000 rpm ÷ 1000 = 31.415927 m/min
    31.41592654 m/min
    Surface speed

WORKED EXAMPLES

  • 50 mm end mill at 1,000 rpm

    π × 50 × 1000 ÷ 1000 ≈ 157.1 m/min. Larger diameters reach a higher cutting speed at the same rpm.

  • 10 mm drill at 2,000 rpm

    π × 10 × 2000 ÷ 1000 ≈ 62.8 m/min. A small drill needs high rpm to reach a usable cutting speed.

  • 100 mm turned bar at 800 rpm

    π × 100 × 800 ÷ 1000 ≈ 251.3 m/min. On a lathe the diameter is the workpiece diameter, not the tool.

Maintained by Jack Shi

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How it works

Cutting speed (surface speed) vc is how fast the workpiece surface passes the cutting edge. For a tool or workpiece of diameter D (mm) rotating at n revolutions per minute, the edge travels one circumference (π·D) per revolution, so vc = π·D·n / 1000 metres per minute — the divide by 1000 converts millimetres to metres. This is the standard turning and milling relationship published in machining references such as Sandvik Coromant’s formulas.

Assumptions & limits

  • D is the effective cutting diameter in millimetres and n is the spindle speed in revolutions per minute.
  • The result is the theoretical surface speed; real machining also depends on workpiece material, tool grade, coolant and feed, which this calculator does not model.
  • Uses the exact geometric relation vc = π·D·n/1000 with no material-specific derating.

Verified runs

Synthetic examples executed at build revision 24533ff on . Cards round decimal results to 6 significant figures; matching uses full precision and the tolerance below. Matches cover the displayed fields, not every possible input or clinical or engineering validation.

  • Inputs: Diameter: 10 mm; Spindle speed: 1000 rpm

    Result: Surface speed: 31.4159 m/min (expected Surface speed: 31.4159 m/min) ✓

  • Inputs: Diameter: 0.001 mm; Spindle speed: 0.001 rpm

    Result: Surface speed: 3.14159e-9 m/min (expected Surface speed: 3.14159e-9 m/min) ✓

  • Inputs: Diameter: 50 mm; Spindle speed: 2000 rpm

    Result: Surface speed: 314.159 m/min (expected Surface speed: 314.159 m/min) ✓

How these runs were checked

Method: cutting-speed@1.0.0. Expectations come from the listed test fixtures or hand arithmetic; they are not copied from these executions. Omitted optional inputs use the method defaults. Run dates record execution, not expert review or fresh measurements.

Download all verified runs (JSON) — full inputs, returned values, expectations, timestamps and buildRevision.

  • normal: . Absolute tolerance: 5e-7. Text and booleans match exactly. Full-precision result: Surface speed: 31.41592653589793 m/min. Expected: Surface speed: 31.415926536 m/min. Expectation: packages/calculator-core/tests/cutting-speed.test.ts
  • boundary: . Absolute tolerance: 5e-16. Text and booleans match exactly. Full-precision result: Surface speed: 3.141592653589793e-9 m/min. Expected: Surface speed: 3.141592653589793e-9 m/min. Expectation: packages/calculator-core/tests/cutting-speed.test.ts
  • sensitivity: . Absolute tolerance: 5e-7. Text and booleans match exactly. Full-precision result: Surface speed: 314.1592653589793 m/min. Expected: Surface speed: 314.159265 m/min. Expectation: packages/calculator-core/tests/cutting-speed.test.ts

Reproduce from the source checkout with pnpm --filter @sumivo/web gen:verified-runs. A rebuild changes execution times; the revision identifies its Git starting point, including any uncommitted changes made for that build.

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FAQ

How do you calculate cutting speed?
Multiply π by the diameter in millimetres and the spindle speed in rpm, then divide by 1000: vc = π·D·n/1000 in metres per minute. For example, a 50 mm diameter at 1000 rpm gives π×50×1000/1000 ≈ 157 m/min.
What is the difference between cutting speed and spindle speed?
Spindle speed (n) is how many revolutions per minute the machine turns. Cutting speed (vc) is the surface speed at the cutting edge. They are linked by the diameter: vc = π·D·n/1000, so the same rpm gives a higher cutting speed on a larger diameter.
How do I convert cutting speed back to RPM?
Rearrange the formula to n = vc·1000 / (π·D). Given a target cutting speed and a diameter, this gives the spindle speed to set on the machine.
What units does this calculator use?
Diameter in millimetres, spindle speed in revolutions per minute, and cutting speed output in metres per minute — the metric convention used in most machining data tables.
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SOURCES