Ra · Rt · scallop · N-grade
Surface Finish Calculator
Predict theoretical surface finish before you cut: turning Ra from feed and nose radius, face milling finish from feed per tooth and insert radius, ball nose scallop height from stepover, and Ra unit conversions.
Turning — theoretical RaTurning — feed for target RaFace milling — theoretical RaBall nose scallop heightRa unit conversion & N-grade
Turning — theoretical Ra
Ra = fn² / (32·r)Turning — feed for target Ra
fn = √(32·r·Ra)Face milling — theoretical Ra
Rt = fz² / (8·R)Ball nose scallop height
h = R − √(R² − (ae/2)²)Ra unit conversion & N-grade
Ra µm ↔ µin · Rz ≈ 4–7×RaFormulas used
Turning: Ra (µm) = fn²/(32r) × 1000 (fn, r in mm); Rt = fn²/(8r) × 1000
Face milling: Rt ≈ fz²/(8R) × 1000; Ra ≈ Rt/4 for an ideal sinusoidal profile
Ball nose: scallop h = R − √(R² − (ae/2)²)
Frequently asked questions
What feed gives Ra 1.6 µm with a 0.8 mm nose radius?
fn = √(32×0.8×1.6/1000) ≈ 0.20 mm/rev. Halving the feed improves finish by roughly 4× in theory — but below ~0.05–0.1 mm/rev, tool rubbing and built-up edge make real finish worse, not better.
Why is my measured Ra worse than the theoretical value?
Theory assumes a perfect geometric imprint. Real finish adds vibration, built-up edge, tool wear, spindle runout and material tearing — typically 1.5–3× the theoretical value.
What is the difference between Ra and Rz?
Ra is the arithmetic mean deviation of the profile; Rz is the average peak-to-valley height of sampling lengths. Rz is typically 4–7 times Ra, but the ratio is not constant — never specify one from a measurement of the other.