Which expression represents the rpm formula?

• A. 4 x CS divided by diameter
• B. CS divided by (4 x diameter)
• C. Diameter divided by (4 x CS)
• D. CS x diameter x 4

Answer: (A)

The rpm value is set so the edge of the rotating workpiece moves at the chosen cutting speed. The distance a point on the edge travels each minute is the circumference times the revolutions per minute, which is (π × D) × rpm. To compare with cutting speed, which is given in feet per minute, convert that distance from inches to feet: (π × D) inches per revolution becomes (π × D) / 12 feet per revolution. Multiplying by rpm gives the surface speed: rpm × (π × D) / 12 = CS. Solve for rpm: rpm = CS × 12 / (π × D). Approximating π as 3.14 and 12/π as about 3.82, you get rpm ≈ (4 × CS) / D. Since D is in inches and CS in feet per minute, this simple form gives a practical, quick estimate. That’s why the expression 4 × CS divided by diameter is the best representation of the rpm formula in this context.