# Surface Finish Ra to RMS Converter > Source: https://netray.co/tools/surface-finish-ra-to-rms-converter > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Convert Ra to RMS in microinches or micrometers and estimate the theoretical Ra a turning insert leaves from feed and nose radius. ## Category manufacturing ## Industry Machine Shops ## Audience - CNC machinist - Quality engineer - Manufacturing engineer ## Tool **Kind:** calculator **Inputs:** #### Ra value **Key:** ra **Type:** number **Default:** 32 **Min:** 0 **Step:** 1 **Help:** Enter the Ra callout from the drawing in the unit chosen below. #### Unit of the Ra value **Key:** unit **Type:** select **Default:** 1 **Options:** ##### Microinches (uin) **Value:** 1 ##### Micrometers (um) **Value:** 2 #### Turning feed per revolution **Key:** feed_rev **Type:** number **Default:** 0.008 **Min:** 0 **Step:** 0.001 **Unit:** in/rev **Help:** Used only for the theoretical finish estimate. #### Insert nose radius **Key:** nose_r **Type:** number **Default:** 0.031 **Min:** 0.001 **Step:** 0.001 **Unit:** in **Help:** For example 1/32 inch is 0.031 and 1/64 inch is 0.016. **Outputs:** #### Ra in microinches **Key:** ra_uin **Expr:** ra * if(eq(unit, 2), 39.3701, 1) **Format:** decimal #### Ra in micrometers **Key:** ra_um **Expr:** ra_uin / 39.3701 **Format:** decimal #### RMS in microinches **Key:** rms_uin **Expr:** ra_uin * 1.11 **Format:** decimal **Primary:** true **Description:** RMS is about 1.11 x Ra for a sinusoidal profile. #### RMS in micrometers **Key:** rms_um **Expr:** rms_uin / 39.3701 **Format:** decimal #### Theoretical turned Ra (uin) **Key:** th_ra_uin **Expr:** feed_rev * feed_rev / (32 * nose_r) * 1000000 **Format:** decimal **Primary:** true **Description:** Ra is about f squared / (32 x nose radius). #### Theoretical turned Ra (um) **Key:** th_ra_um **Expr:** th_ra_uin / 39.3701 **Format:** decimal **Disclaimer:** The 1.11 factor assumes a sinusoidal profile; real machined surfaces differ. The turned Ra estimate is geometric only and ignores tool wear, vibration and built-up edge. Measure with a profilometer for acceptance. ## Content **Intro:** Older drawings call out RMS, newer ones call out Ra, and your profilometer may report either. This converter handles the conversion in both unit systems and also estimates what finish a turning insert should leave at a given feed. **Sections:** #### How to use the converter **Body:** Enter the roughness value, choose microinches or micrometers, and read the equivalent Ra and RMS in both units. To check whether a turning setup can reach a callout, enter the feed per revolution and the insert nose radius as well; the tool returns the theoretical Ra the geometry produces. If the theoretical value is already near or above the drawing requirement, lower the feed or move to a larger nose radius before looking at anything else. #### Ra, RMS and the conversion factor **Body:** Ra is the arithmetic mean of the absolute profile deviations from the mean line. RMS, now called Rq in ISO terms, is the root mean square of the same deviations. For a sine wave profile Rq is about 1.11 times Ra, which is the factor used widely in shop practice. One micrometer equals 39.37 microinches, so 0.8 um Ra is about 32 uin Ra. Treat the factor as a rule of thumb: random or sharply peaked surfaces give different ratios. **Bullets:** - RMS (uin) = 1.11 x Ra (uin) - uin = um x 39.3701 - ISO uses Ra and Rq; older ASA drawings used RMS #### Theoretical finish from feed and nose radius **Body:** For a round-nosed turning tool the feed marks form scallops, and Ra is approximately feed squared divided by 32 times the nose radius. At 0.008 in/rev and a 1/32 inch radius that is about 65 uin. Halving the feed to 0.004 drops it to about 16 uin, because feed is squared. The formula gives the best case; real surfaces are rougher because of tool wear, vibration, material tearing and a poor edge, so aim a notch below the callout. #### Common mistakes **Body:** Do not assume Ra and RMS are interchangeable on an inspection report; a 32 RMS callout is about 29 Ra. Also avoid comparing readings taken with different cutoff lengths or filters, since they change the result. For milling, finish depends on stepover, runout and cutter geometry rather than the turning formula, and a ball nose scallop height needs its own calculation. Always state the unit when you write a callout on a drawing. **Cta:** If finish requirements and inspection results are scattered across drawings, spreadsheets and your ERP quality module, Netray can help bring them together for review. **Faq:** #### How do I convert Ra to RMS? **Answer:** Multiply Ra by about 1.11 to get RMS (Rq) for a typical sinusoidal profile. For example 32 uin Ra is roughly 35.5 uin RMS. The factor is a rule of thumb and varies with the actual surface profile. #### How many microinches are in a micrometer? **Answer:** One micrometer equals about 39.37 microinches. So 1.6 um Ra is about 63 uin Ra, and 0.8 um is about 32 uin. The converter does this automatically in both directions. #### What does a 32 Ra finish mean? **Answer:** It means an average roughness of 32 microinches, about 0.8 micrometers. It is a common machined finish for general precision surfaces and is typically reachable by finish turning or milling with a sharp tool and a modest feed. #### Is the theoretical turned Ra reliable? **Answer:** It is a good lower bound for a sharp tool in a stable setup, because it only considers feed marks. Vibration, wear, soft or gummy materials and coolant conditions raise the real Ra, sometimes by a factor of two or more. ## Search terms ra to rms converter, surface finish converter, ra to rms conversion, microinch to micrometer ra, surface roughness calculator, theoretical surface finish turning, ra rms formula, 32 ra surface finish --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json