Surface Roughness Calculator
Convert between Ra, Rz, RMS, and other surface roughness parameters. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Rz = 4 x Ra | RMS = 1.11 x Ra | Ra = f^2 / (32 x r)
Approximate conversion ratios between roughness parameters. Ra is arithmetic average, Rz is mean peak-to-valley height, RMS is root mean square. The theoretical turning formula uses f = feed rate (mm/rev) and r = tool nose radius (mm).
Worked Examples
Example 1: Converting Ra to Other Parameters
Problem:A drawing specifies Ra 1.6 micrometers. What are the equivalent Rz, RMS, and N-grade values?
Solution:Ra = 1.6 micrometers\nRz = Ra x 4.0 = 1.6 x 4.0 = 6.4 micrometers\nRMS (Rq) = Ra x 1.11 = 1.6 x 1.11 = 1.776 micrometers\nMicroinches = 1.6 x 39.37 = 63 microinches\nN-grade = N7 (Ra 1.6)
Result:Ra 1.6 = Rz 6.4 = RMS 1.776 = 63 microinches = N7
Example 2: Theoretical Roughness from Turning Parameters
Problem:A finish turning operation uses 0.15 mm/rev feed rate with a 0.4mm nose radius insert. What is the theoretical Ra?
Solution:Ra (theoretical) = f^2 / (32 x r) = 0.15^2 / (32 x 0.4) = 0.0225 / 12.8 = 0.001758 mm = 1.758 micrometers\nThis corresponds to approximately N7 grade\nActual Ra will be 1.5-3x higher due to tool wear and vibration = 2.6 to 5.3 micrometers
Result:Theoretical Ra: 1.758 micrometers (N7) | Actual expected: 2.6-5.3 micrometers
Frequently Asked Questions
What is surface roughness and how is it measured?
Surface roughness is a measure of the texture of a machined surface, quantified by the small-scale deviations from the ideal smooth surface. It is typically measured using a stylus profilometer that drags a diamond-tipped probe across the surface and records the vertical displacements. The most common parameter is Ra (Arithmetic Average Roughness) which calculates the average absolute deviation from the mean line over a sampling length. Other measurement methods include optical profilometry using laser or white light interferometry, and atomic force microscopy for extremely fine surfaces. Surface roughness directly affects part function including friction, wear, sealing capability, and fatigue life.
What is the difference between Ra, Rz, and RMS roughness values?
Ra is the arithmetic average of the absolute deviations from the mean line and is the most widely used roughness parameter worldwide. Rz measures the average distance between the highest peak and lowest valley in each of five sampling lengths, making it more sensitive to occasional deep scratches or high peaks. RMS (Root Mean Square or Rq) squares each deviation before averaging, giving more weight to extreme values. Typical conversion ratios are Rz equals approximately 4 times Ra and RMS equals approximately 1.11 times Ra, though these ratios vary with the surface profile shape. Different industries and countries historically preferred different parameters.
What surface roughness is achievable with different machining processes?
Different machining processes produce characteristic roughness ranges. Rough turning and milling typically achieve Ra 3.2 to 12.5 micrometers. Finish turning and milling produce Ra 0.8 to 3.2 micrometers. Grinding achieves Ra 0.1 to 1.6 micrometers. Lapping and honing produce Ra 0.025 to 0.4 micrometers. Superfinishing and polishing can achieve Ra below 0.025 micrometers. These ranges assume proper tool condition, machine rigidity, and cutting parameters. The achievable roughness is influenced by cutting speed, feed rate, tool nose radius, and material properties. Each step to finer roughness typically doubles or triples the manufacturing cost.
How does feed rate affect surface roughness in turning?
In turning operations the theoretical surface roughness is primarily determined by the feed rate and the tool nose radius according to the formula Ra equals f squared divided by 32 times r, where f is the feed rate in mm/rev and r is the tool nose radius in mm. This means surface roughness increases with the square of the feed rate, so doubling the feed rate quadruples the theoretical roughness. For example, with a 0.8mm nose radius, a feed of 0.2mm/rev gives Ra approximately 0.0156mm or 15.6 micrometers, while reducing to 0.1mm/rev gives Ra 3.9 micrometers. This formula provides the theoretical minimum; actual roughness is typically 1.5 to 3 times worse due to tool wear and vibration.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy