Inductive Sensor Sensing Distance: Sn, Sr, Su, Sa and the 0.81 Rule

An inductive proximity sensor carries four distances, and only one is printed on the box. IEC 60947-5-2 defines the nominal (rated) operating distance Sn, the effective operating distance Sr measured on one sensor at 23 °C and rated voltage, the usable operating distance Su measured across the full temperature and voltage range, and the assured operating distance Sa, where switching is guaranteed under all of those conditions. Sr may land anywhere from 0.9 to 1.1 Sn. Su may land anywhere from 0.9 to 1.1 Sr. Multiply the two worst cases, 0.9 x 0.9, and you get 0.81. That is the 81 percent rule: you can only count on 81 percent of the number on the label.

The method for a given gap is one line: divide the gap by 0.81, divide again by the target correction factor, and pick the next larger Sn in the catalog. For 38 mm on mild steel that is 38 / 0.81 = 46.9 mm, so you need Sn of at least 47 mm.

The four distances, and where 0.81 comes from

Our selection overview already covers the standard target and the 0.9 to 1.1 Sn band for Sr. It did not show the chain.

Sr absorbs manufacturing spread. Turck's operating distance guide states 0.9 Sn ≤ Sr ≤ 1.1 Sn at constant rated voltage and 23 °C; Pepperl+Fuchs gives the temperature as 23 ± 5 °C.

Su absorbs the environment. Pepperl+Fuchs defines it as 0.9 Sr ≤ Su ≤ 1.1 Sr across the rated ambient range (its example is -25 to +70 °C) with supply between 85 and 110 percent of rated voltage. Turck uses the same voltage window and states the result relative to Sn: 0.81 Sn ≤ Su ≤ 1.21 Sn. Balluff's Basics and Installation manual gives the identical band and ties it to EN 60947-5-2.

Sa is the bottom of that band. The worst sensor out of the box is 0.9 Sn. Put it in the hottest, lowest-voltage corner of its spec and it drops another 10 percent to 0.9 x 0.9 Sn = 0.81 Sn. Turck, Balluff, Pepperl+Fuchs and Rockwell Automation all publish Sa as 0 to 0.81 Sn. ifm states the same chain in words: real range is at worst 90 percent of nominal, operating distance at worst 90 percent of real. Every Turck datasheet pulled for this article lists "secured operating distance ≤ (0.81 x Sn)" as a line item.

Worked example: a 38 mm gap on mild steel

A 40 mm nominal sensor looks like it covers 38 mm. It does not. Its assured distance is 0.81 x 40 = 32.4 mm. Between 32.4 and 40 mm the sensor may switch, on a good unit, on a good day. Across the rated temperature and voltage range the standard guarantees nothing there.

Run the method instead. Required Sn = 38 / 0.81 = 46.9 mm. Round up to the next catalog value, in practice a 50 mm part. A Turck NI50U-CK40-AP6X2-H1141, a 65 x 40 x 40 mm block housing with Sn = 50 mm, has an assured operating distance of 0.81 x 50 = 40.5 mm, so the 38 mm gap sits inside the guaranteed zone with 2.5 mm to spare. That is the answer to "I have 38 mm."

Layering the target correction factor

The 0.81 rule assumes the standard mild steel target. Other metals shrink the field, and manufacturers publish correction factors that multiply Sn (the ranges, and why they disagree, are in the selection overview). The formula becomes:

Stainless steel, 38 mm gap. Turck's standard M30 datasheets list stainless at 0.7. Required Sn = 38 / (0.81 x 0.7) = 67 mm. On Balluff's published stainless range of 0.60 to 1.00, the worst case is 38 / (0.81 x 0.60) = 78 mm. Either way, no standard M30 barrel does it.

Aluminum, 38 mm gap. Turck's standard M30 datasheets list aluminum at 0.3; Balluff publishes 0.30 to 0.45. Required Sn = 38 / (0.81 x 0.3) = 156 mm. That number says a standard inductive sensor is the wrong tool. On a factor 1 part the correction factor is 1 for all metals, so the aluminum requirement collapses back to 47 mm Sn.

Autonics: its PR series documents say sensing distance "can be changed by the shape, size or material of the target," and publish sensing-distance-versus-material curves rather than numeric factors. Ask Autonics for the curve for the exact model before putting a standard part on a non-ferrous target.

Flush vs non-flush: same thread, different Sn

Mounting style changes the nominal distance you can buy in a given housing. In Turck's standard M30 line, the flush BI10-M30-AP6X-H1141 has Sn = 10 mm and the non-flush NI15-M30-AP6X-H1141 has Sn = 15 mm. In Balluff's M30 line, BES M30MI-PSC10B-S04K is flush at 10 mm, BES M30MI-PSC15B-S04G flush at 15 mm, BES M30MI1-PSC22B-S04G quasi-flush at 22 mm, and BES M30MG1-PSC40F-S04G non-flush at 40 mm. Autonics PR30-10 is a 10 mm M30 and PR30-15 is a 15 mm M30. Going non-flush buys range, but it also buys the metal-free zone around the face described in the selection overview. If the bracket will not allow that clearance, the extra Sn is not real.

Temperature and voltage drift

The standard allows the 10 percent that builds Su; manufacturers publish how much of it they use. Turck's standard M30 datasheets list temperature drift at ≤ ±10 percent over -25 to +70 °C. Turck's uprox parts rated to -30 to +85 °C list ≤ ±10 percent in the core range and ≤ ±15 or ±20 percent beyond it, depending on the part. Balluff's manual gives the EN 60947-5-2 limit as Δsr/sr ≤ 10 percent. Autonics PR series specifies a maximum ±10 percent change versus 20 °C across -25 to +70 °C. The lesson in the uprox numbers: outside -25 to +70 °C, 0.81 is no longer conservative enough; rerun the arithmetic with the manufacturer's extended drift figure.

Hysteresis, and why slow targets care

Hysteresis is the gap between the switch-on point as the target approaches and the release point as it leaves. Turck's guide says it is factory set below 15 percent of Sr; Turck datasheets list 3 to 15 percent. Pepperl+Fuchs states a typical 5 to 10 percent of Sr, limit 0.2 Sr. Autonics specifies a maximum of 10 percent of Sn. Its purpose is to stop chatter under vibration.

At the edge of range it matters twice. If the target parks near 0.8 Sn and backs off by less than the hysteresis band, the output stays on after the target has "left." And for a slowly approaching target, the trip position is a band, not a line, moving with Sr, drift, and hysteresis together. Keep the target's on and off positions well inside Sa and separated by more than the datasheet hysteresis figure.

When the spec sheet says "minimum sensing distance 38 mm"

A specification that puts the gap in the nominal field is the most common way this goes wrong. A part with Sn = 38 or 40 mm meets the letter of that spec and may miss the target at the top of the temperature range or the bottom of the supply window, because the standard only guarantees detection to 0.81 Sn. Autonics is more conservative still, defining a "setting distance" of Sn x 0.7 (7 mm on a 10 mm sensor). Write the gap as the assured distance, or write the Sn you need, never the gap as the nominal.

The honest answer at the edge of a family

When the arithmetic lands at the top of a housing size, the right move is a larger housing, an extended-range part, or another manufacturer's family that reaches further in the same thread. Turck's uprox factor 1 line pushes an M30 flush to Sn = 15 mm (BI15U-M30-AP6X-H1141) and an M30 non-flush to Sn = 30 mm (NI30U-M30-AP6X-H1141), both factor 1 for all metals, and the CK40 block reaches 50 mm. Balluff's M30 line reaches 22 mm quasi-flush and 40 mm non-flush; its factor 1 M30 flush part is rated at 10 mm. Autonics lists a PRD long-distance cylindrical series in M30 for applications that need more reach.

Stateside Industrial Solutions is an authorized distributor for Turck, Balluff, and Autonics. Send us the gap, target metal, bracket, and ambient range, and we will run this arithmetic against the datasheet before you order. If you are replacing an existing sensor rather than specifying a new one, see our cross-reference method.