O-Ring Calculator.

How it’s calculated

The design follows the order recommended by the handbook: the fluid and the temperature range choose the compound first, because the compound sets the hardness, expansion and swell that the gland then has to accommodate (Parker Hannifin, 2021, Secs. 2.3.1 and 3.0). Every dimension is entered as a nominal size with a tolerance. Housing diameters use ISO 286 fits (for example H8 bores, f7 pistons, h9 grooves), whose limits follow from the standard tolerance grade IT and the fundamental deviation for the size range (ISO 286-2, 2010). O-ring tolerances follow ISO 3601-1: cross-section tolerances of ±0.08 to ±0.15 mm, and inner-diameter tolerances from (ISO 3601-1, 2012)

The AS568 and ISO 3601-1 size tables list the standard combinations of inner diameter and cross-section (SAE AS568, 2020; ISO 3601-1, 2012). All results are computed at both tolerance limits, so the design works for every combination of parts that can come off the production line.

Materials and temperature

The material list has twenty entries: the fourteen elastomer families described in the handbook (nitrile, carboxylated and hydrogenated nitrile, ethylene acrylate, polyacrylate, EPDM, butyl, chloroprene, fluorocarbon, TFE/propylene, perfluoroelastomer, silicone, fluorosilicone and polyurethane), plus the low- and high-temperature nitrile grades and SBR of its temperature chart, a 90 Shore nitrile, a low-temperature fluorocarbon and a low-temperature silicone (Parker Hannifin, 2021, Secs. 2.2 and 3.10.2 and Fig. 2-3). Their continuous service ranges come from the elastomer descriptions and the temperature chart; above the continuous limit a compound survives only short excursions, and below the low limit it hardens and loses the resilience a seal needs (Parker Hannifin, 2021, Sec. 2.2 and Fig. 2-3). The fluids each family resists or should avoid are summarised under the material field from the same section; for a specific fluid the compatibility tables of the handbook remain the reference (Parker Hannifin, 2021, Sec. 7).

Temperature changes are applied through the linear expansion of the O-ring and the housing relative to 23 °C. The coefficients are taken from the handbook table, converted from in/in/°F by 1.8: 112·10⁻⁶/K for nitrile, 137 for chloroprene, 160 for EPDM, 162 for fluorocarbon, 180 for silicone, 198 for low-temperature silicone, 270 for fluorosilicone and 324 for perfluoroelastomer, against 12.1 for mild steel, 17.3 for 302 stainless steel and 23.4 for aluminium (Parker Hannifin, 2021, Table 2-5). Elastomers expand roughly ten times more than steel, perfluoroelastomer about 27 times, which is why a gland that is right at room temperature can overfill when hot or lose its squeeze when cold (Parker Hannifin, 2021, Secs. 2.4.20 and 3.1.2). The table gives one value for general-purpose nitrile, which is also used for the other nitrile grades. Where it has no value at all (HNBR, XNBR, ACM, AEM, butyl, SBR, TFE/propylene, polyurethane, and the low-temperature fluorocarbon grade) the closest family is used and the material note says so; replace it with the datasheet value when one is available.

Stretch and cross-section reduction

A piston O-ring is stretched onto the groove root, stretch = (d₃ − d₁)/d₁. Stretching thins and flattens the cross-section. The calculator uses the empirical “observed” curve of the handbook, a statistical fit of General Motors test data, where X is the stretch and Y the loss of cross-section, both in percent (Parker Hannifin, 2021, Fig. 3-3):

The installed stretch should not exceed 5 %; more ages the rubber faster, nitrile most of all, so EPDM, fluorocarbon, polyurethane or chloroprene are preferred where high stretch cannot be avoided (Parker Hannifin, 2021, Secs. 3.3 and 3.5). To pass over the piston the inner diameter must expand to the piston diameter; this is ordinarily 25–50 % and should not exceed half of the ultimate elongation of the compound, which is checked when the elongation is entered (Parker Hannifin, 2021, Sec. 3.3). A rod O-ring should not be stretched noticeably by the rod; its outer diameter is held by the groove, as the handbook asks for rotary seals (Parker Hannifin, 2021, Sec. 2.4.17). The 5 % installed-stretch limit is applied to the rod as well; the handbook's own rod glands stretch the ring slightly onto the rod, about 1–3 % for most sizes and more for the smallest, which limits the compression of the outer diameter (Parker Hannifin, 2021, Design Table 5-2). The limits of 5 % mean OD compression for a rod ring and 3 % circumferential compression for piston and face rings, beyond which a ring can buckle, are common design practice rather than handbook values; the tolerance of the ring itself is added to them at the extremes. A ring confined in a gland shrinks linearly by only about half of its volume shrinkage (6 % by volume gives about 3 % in the cross-section), and this reduction is applied to the squeeze (Parker Hannifin, 2021, Fig. 3-6). Swell is not added to the compression, because a ring confined in a gland swells much less than a free one, but it is added to the groove fill (Parker Hannifin, 2021, Sec. 2.3).

Gland depth, eccentricity and squeeze

For a piston seal the gland depth is t = (d₄ − d₃)/2, for a rod seal t = (d₆ − d₅)/2, and for a face seal t is the groove depth h. The concentric results assume the parts are centred. In the eccentric case the piston or rod is pushed fully to one side: on one side the gap closes, giving the maximum compression; on the other the depth grows by the maximum radial clearance, half the diametral clearance. Half of the groove eccentricity (TIR) is added on top, exactly as in the handbook's tolerance build-up example for a 2-012 piston seal, where 0.007 in of nominal minimum squeeze falls to 0.0035 in with the piston tangent to the bore and 0.002 in TIR (Parker Hannifin, 2021, Sec. 5.9). Bore breathing under pressure enlarges the clearance and is added to the extrusion gap (Parker Hannifin, 2021, Sec. 3.1.4).

The recommended compression depends on the cross-section and the service and is interpolated from the handbook design charts, for example 16–23 % for a 3.53 mm static radial seal, 9–16 % for the same ring in a reciprocating seal, 20–30 % in a face seal and 0–7 % in a rotary seal (Parker Hannifin, 2021, Design Charts 4-2, 4-3, 5-2 and 5-4). The charts derive these ranges from the inch tolerances of AS568 rings and glands, without the stretch correction; ISO tolerances, fits and the stretch spread are wider, so the check asks for the mean compression to lie in the chart range and lets the tolerance extremes exceed it by up to two percentage points. Independently of the cross-section, the squeeze should not fall below about 0.2 mm (0.007 in), because below 0.1 mm almost every compound takes a full compression set (Parker Hannifin, 2021, Fig. 3-5 and Sec. 3.6). In the worst eccentric position the ring must still touch both surfaces, and if the compound shrinks in the fluid the squeeze there must be at least 0.076 mm (0.003 in) (Parker Hannifin, 2021, Sec. 5.9). The ceiling is 30 % for static seals; for dynamic seals the handbook gives about 16 %, and up to 25 % for small cross-sections (Parker Hannifin, 2021, Sec. 3.6). In the eccentric position the calculator uses 30 % (static) or 25 % (dynamic) as the ceiling, or the chart maximum plus the two-point allowance where that is higher, so for larger dynamic rings the chart range is the check that matters.

Groove fill and fluid swell

The O-ring area, enlarged by volume swell, must fit in the groove area left after any back-up rings. Most glands are designed for 60–85 % fill, 75 % being the optimum, and at least 10 % void is essential (Parker Hannifin, 2021, Sec. 3.7):

A groove width or radius left empty is set to the middle of the handbook design-chart range, scaled to the cross-section, and the chart ranges for the chosen ring are listed under the results (Parker Hannifin, 2021, Design Charts 4-2, 4-3 and 5-4). Metric housing dimensions for general applications are also standardised in ISO 3601-2 (ISO 3601-2, 2016); the calculator itself uses the handbook charts. For face seals the groove diameter on the low-pressure side is primary: with internal pressure the groove OD equals the mean O-ring OD with a minus tolerance of 1 %, with external pressure the groove ID equals the mean O-ring ID with a plus tolerance, so the default fits are h11 on the groove OD and H11 on the groove ID (Parker Hannifin, 2021, Sec. 4.3 and Design Chart 4-3). A static seal tolerates up to about 30 % volume swell and a dynamic one 10–20 % (15 % is used as the limit). Shrinkage is far more critical than swell, because it adds to compression set; more than 3–4 % is serious for dynamic seals (Parker Hannifin, 2021, Secs. 2.3, 2.4.10 and 5.1). Only the upper limit is a pass/fail check; a fill below 60 % is reported as a note. Vacuum glands are the exception to the fill limit: a nearly full gland, heavy squeeze and vacuum grease give the lowest leak rate (Parker Hannifin, 2021, Sec. 3.11.3).

Extrusion and back-up rings

The allowable total diametral clearance is read from the handbook's extrusion-limit curves for 70, 80 and 90 Shore A compounds, measured over 100 000 pressure cycles from zero to the test pressure at 71 °C without back-up rings; between the curves the calculator interpolates linearly in hardness and in the logarithm of pressure (Parker Hannifin, 2021, Fig. 3-2). The clearance must include any expansion of the bore under pressure, and for silicone and fluorosilicone it is reduced by 60 % (the design charts halve it) (Parker Hannifin, 2021, Fig. 3-2 and Design Chart 4-2). Back-up rings should be considered for all seals above 103.5 bar (Parker Hannifin, 2021, Sec. 4.2). With elastomer back-up rings the 90 Shore curve is used as the limit, valid to 74 °C (Parker Hannifin, 2021, Secs. 3.1.4 and 6.1); PTFE back-up rings have no curve in the handbook. With a single back-up ring the O-ring belongs between the ring and the pressure (Parker Hannifin, 2021, Sec. 6.2). If the friction of the moving part drags the ring in the direction of the pressure, extrusion starts at only 30–40 % of the normal pressure, so the groove should be placed in the part where friction opposes the pressure (Parker Hannifin, 2021, Sec. 5.6).

Rotary shafts

A stretched elastomer contracts when heated (the Gow-Joule effect). In a rotary seal the friction heat would make a stretched ring grip the shaft harder, so the O-ring inner diameter is chosen 1–3 % larger than the shaft and the ring is compressed only by the groove, in a groove slightly narrower than the cross-section (Parker Hannifin, 2021, Secs. 2.4.17 and 5.27). The rotary design chart is less strict and sizes the shaft at the O-ring ID plus 0.05 mm; either way the ring must not be stretched (Parker Hannifin, 2021, Design Chart 5-4). The surface speed v = π d n limits the cross-section: up to 1.02 m/s (200 ft/min) any reciprocating gland may be used, above that at most 3.53 mm to 2.03 m/s, 2.62 mm to 3.05 m/s and 1.78 mm to 7.62 m/s. Rotary glands are rated to 55.2 bar with an 80 Shore minimum compound, between −40 and 121 °C, and the shaft should run within 0.013 mm TIR (Parker Hannifin, 2021, Table 5-5, Design Chart 5-4 and Sec. 5.27). Because the shaft is located by its bearings and must not touch the housing, the eccentric case uses only the run-out, and the extrusion check uses the radial clearance, as the extrusion chart allows when concentricity is rigidly maintained (Parker Hannifin, 2021, Fig. 3-2).

Sealing force

The Young's modulus of the compound is estimated from its Shore A hardness with Gent's relation, which gives about 5.5 MPa for 70 Shore A, 9.4 MPa for 80 and 21 MPa for 90 (Gent, 1958):

The force needed to squeeze the ring, per unit length of seal, follows Lindley's relation for laterally unrestrained O-rings, where ε is the fractional compression (Lindley, 1967). Multiplied by the length of the sealing line it gives the minimum bolt load of a face seal before pressure is applied:

Friction of reciprocating seals

Running friction is estimated with the handbook method, as a squeeze part proportional to the rubbing length and a pressure part proportional to the projected area of the gland (Parker Hannifin, 2021, Sec. 5.11.2):

f_c rises linearly with the percent compression, about 0.067, 0.12 and 0.16 lb per inch per percent for 70, 80 and 90 Shore A, and f_h rises from about 10 to 72 lb/in² between 0 and 3000 psi; both were read from the handbook curves, measured on chrome-plated surfaces of 15 µin finish in MIL-H-5606 hydraulic oil at speeds above 1 ft/min, for 70 to 90 Shore A (Parker Hannifin, 2021, Figs. 5-9 and 5-10). Break-out friction after a long rest can reach about three times the running friction for a 70 Shore ring on an 8 µin surface (Parker Hannifin, 2021, Sec. 5.11.1).

Gas permeation leak rate

Every elastomer lets gas diffuse through it. Treating the squeezed ring as a rectangle of the same area as the free section, height t = d₂(1 − S) and width w = π d₂ / [4(1 − S)], the permeation through a ring of inner diameter D gives

with F the permeability in std cm³·cm/(cm²·s·bar), Δp in bar and D in cm. In the handbook the same relation appears in mixed US units as L = 0.7 F D P Q (1 − S)², and 4 × 2.54/14.504 = 0.70 reproduces its constant exactly (Parker Hannifin, 2021, Sec. 3.12.1). The factor Q corrects the idealised geometry for real seals and depends on the squeeze and on whether the ring is dry or greased; it is read from the handbook curve between 15 and 50 % squeeze (Parker Hannifin, 2021, Fig. 3-11). Permeabilities come from the handbook table for helium, hydrogen, nitrogen, oxygen, air, carbon dioxide, argon and methane, taking the upper end where the table lists a range; compounds without a row (HNBR, XNBR, AEM, TFE/propylene, perfluoroelastomer, the special grades) use their family's value, which the result says (Parker Hannifin, 2021, Table 3-24). Where values are listed at several temperatures the calculator interpolates ln F linearly in 1/T. This Arrhenius form is our assumption: the handbook only says that permeability rises with temperature without an easily defined relationship (Parker Hannifin, 2021, Sec. 3.12). The result is an order-of-magnitude estimate: the handbook itself expects ±50 % for helium, permeability differs between compounds of the same polymer, and it rises steeply with temperature (Parker Hannifin, 2021, Secs. 3.12 and 3.12.1). Above 27.6 bar gas absorbed in the rubber can blister it when the pressure is released quickly (explosive decompression); smaller cross-sections suffer less (Parker Hannifin, 2021, Sec. 3.13).

Theory checked against the handbook

Each model above was compared with the measured data or worked examples of the handbook. The first two rows also show what changed from the previous version of this calculator.

The Lindley estimate falls inside the handbook bands, in their lower half for a 70 Shore compound; the handbook reads a ring in the middle third or lower half of the band when its hardness is below nominal and in the upper third or upper half when it is above, depending on whether the ring is under or over 25.4 mm in diameter, so real forces can be up to about twice the estimate (Parker Hannifin, 2021, Table 2-3). The digitised curves (extrusion, friction, Q) were read from the handbook figures and are accurate to a few percent of their scale.

The drawing

The gland drawing is to scale. The squeezed ring is drawn as a rounded rectangle with the same area as the free cross-section, which is how an elastomer deforms: it is nearly incompressible, so squeezing it in one direction widens it in the other (Parker Hannifin, 2021, Sec. 1.4). When that shape no longer fits, the excess area is drawn as rubber forced into the clearance gap. For face seals the radial position of the ring follows from its real inner diameter and stretch, and under pressure from the balance between the pressure load and the hoop tension of the ring, p·t·r = E·ε·A (Young et al., 2012, Ch. 9). The animation is a qualitative picture; the numbers in the results table are the design check. Always confirm a final design with the O-ring supplier's data for the chosen compound, fluid and temperature range.