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Surface Finish (Ra) Calculator — Feed Rate, Nose Radius & Material Correction

Calculate Theoretical Surface Roughness for Turning and Milling Operations

Free surface finish calculator for machinists and CNC programmers. Enter your feed rate and tool nose radius to calculate theoretical Ra using Ra = f² / (32 × r). Includes material-specific correction factors for BUE effects and a reverse calculator to find maximum feed for a target Ra.

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Goes beyond basic formula with corrections for aluminum, stainless, titanium, cast iron, and more. A finish scale bar shows where your result falls on the standard roughness scale from 500 to 2 microinches.

Pro Tip: The theoretical Ra formula assumes a perfectly sharp tool with zero vibration. In practice, expect actual finish to be 1.5 to 3 times worse. If the print calls for 63 microinch Ra, calculate feeds that produce 32 microinch theoretical — that gives you a reasonable margin for real-world conditions.

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Surface Finish (Ra) Calculator
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How It Works

  1. Enter Feed Rate

    Input feed per revolution (IPR or mm/rev). For turning, this is carriage feed. For milling, use feed per tooth times number of teeth.

  2. Enter Tool Nose Radius

    Input insert nose radius in inches or mm. Common values: 1/64" (0.016"), 1/32" (0.031"), 0.8mm, 1.2mm.

  3. Select Material

    Choose workpiece material for BUE correction: Aluminum (0.8x), Steel (1.0x), Stainless (1.5x), Titanium (1.8x), etc.

  4. Review Theoretical and Corrected Ra

    See both values and the finish scale bar showing standard roughness ranges from 500 to 2 microinches.

  5. Use Reverse Calculator

    Enter a target Ra and the calculator solves for maximum allowable feed rate at your current nose radius.

Built For

  • CNC programmers setting finish pass feed rates to meet surface roughness callouts
  • Turning operators selecting nose radius inserts based on required finish and feed rate
  • Manufacturing engineers specifying achievable surface finish targets
  • Quality inspectors verifying programmed feeds can theoretically produce specified finish
  • Tool selection decisions between different insert nose radii
  • Students learning the math between feed, nose radius, and surface roughness

Features & Capabilities

Standard Ra Formula

Ra(μin) = f² / (32 × r) × 1,000,000. The textbook formula for single-point tool marks.

Material Correction Factors

BUE corrections for 8 materials: Aluminum (0.8x) through Titanium (1.8x).

Finish Scale Bar

Log scale from 500 to 2 μin with standard finish categories labeled and your result plotted.

Reverse Feed Calculator

Enter target Ra and solve for maximum feed per revolution.

Unit Flexibility

Works in both inch and metric units with automatic conversion.

PDF Export

Export calculations as a branded PDF for CNC program documentation or quality records.

Frequently Asked Questions

The formula calculates the theoretical minimum based on geometry alone. Vibration, BUE, tool wear, workpiece deflection, and coolant all degrade real-world finish. Expect 1.5 to 3x worse under normal conditions.
Theoretically yes, but larger radii increase cutting forces and chatter risk. If the setup lacks rigidity, a larger radius can actually worsen finish by inducing vibration.
Turning: 16-32 μin Ra on steel, 8-16 μin on aluminum. Face milling with wipers: 16-32 μin. Below 16 μin typically requires grinding, honing, or lapping.
Approximately: Rz ≈ 4-6 × Ra for machined surfaces. RMS ≈ 1.11 × Ra. These are estimates — always specify the parameter explicitly for contractual purposes.
Disclaimer: Surface finish calculations are theoretical estimates. Actual results depend on machine rigidity, tool condition, material properties, and cutting fluid. Always verify critical finishes with calibrated profilometer measurement.

Learn More

Machinist

Surface Finish (Ra) — How Feed Rate and Tool Radius Control Your Part Quality

How feed rate, tool nose radius, and cutting conditions determine surface finish. Ra vs Rz, common callouts, and when to machine vs grind.

Read Guide →

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