1. What is the Cutting Speed to RPM Formula?

Definition: This calculator converts cutting speed in feet per minute (fpm) to revolutions per minute (RPM) for rotating tools.

Purpose: Essential for machinists and CNC operators to determine the correct spindle speed for cutting operations.

2. How Does the Formula Work?

The formula used is:

Where:

• \( RPM \) — Revolutions per minute
• \( CS \) — Cutting speed (feet per minute)
• \( D \) — Diameter of the cutting tool (inches)
• \( \pi \) — Pi (approximately 3.1416)

Explanation: The formula converts cutting speed from feet to inches (×12), then divides by the tool's circumference to determine rotations per minute.

3. Importance of RPM Calculation

Details: Correct RPM ensures optimal cutting conditions, tool life, and surface finish while preventing damage to the workpiece or tool.

4. Using the Calculator

Tips: Enter the cutting speed in fpm and tool diameter in inches. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's a typical cutting speed for steel?
A: For high-speed steel tools, 80-100 fpm for mild steel; carbide tools can run 300-500 fpm.

Q2: Why multiply by 12 in the formula?
A: It converts feet to inches since diameter is in inches and we need consistent units.

Q3: How does diameter affect RPM?
A: Larger diameters require lower RPM to maintain the same cutting speed at the tool's edge.

Q4: What if I know RPM and need cutting speed?
A: Rearrange the formula: \( CS = \frac{RPM \times \pi \times D}{12} \)

Q5: Does material affect the calculation?
A: No, but material determines the appropriate cutting speed (CS) to input.