Alloy round bar intended for machining stock is governed by two distinct tolerance families: hot-rolled (ASTM A29/A322 family) and cold-finished (ASTM A108), with cold-finish 4140/4130 to 1.5" diameter held to ±0.004" while hot-rolled 4340 at 8.25–9.5" diameter runs +0/-0.1875" [S5].
Out-of-round (ovality) and straightness are separate contractual values: for cold-finish rounds, out-of-round is commonly limited to 50–75% of the diameter tolerance band, and standard straightness is 1/4" in any 5 feet of length, with a special 1/8" in 5 feet available for finish-machining stock [S1][S6]. Specifying all four axes (diameter, ovality, straightness, surface) on the PO is what separates a machinist-friendly order from a rejection pile.
Hot-rolled round bar tolerance bands (ASTM A29 family)
For hot-rolled carbon and alloy rounds from 1/4" up to 10" diameter, the size tolerance is symmetric ± until you cross 1.5", then the band goes one-sided plus-only because the mill cannot pull undersize on a hot bar reliably [S1]. Concrete bands: to 5/16" is ±0.005", over 5/16–7/16" is ±0.006", over 7/8–1" is ±0.009", over 1.5–2" is ±1/64" (about ±0.0156"), over 2.5–3.5" is +3/64"/-0 (about +0.0469"/-0), over 5.5–6.5" is +1/8"/-0, and over 8.25–9.5" is +3/16"/-0 [S1].
Out-of-round for hot-rolled rounds scales with diameter: 0.008" at the 1/4–5/16" range, climbing to 0.035" at 2.5–3.5", 0.058" at 4.5–5.5", and 0.100" at 8.25–9.5" [S1]. For heavy shaft stock on 4140 or 4340, the practical diameter envelope is roughly nominal plus the tolerance, so a "3" plus 3/64" bar can arrive at 3.0469" and still be in spec, which sets the facing stock you must remove. See alloy steel for the grade families these bars ship in.
Cold-finished (cold-drawn or turned, ground, polished) tolerance bands
Cold-finish 4130 normalized, 4140 annealed, and 4340 normalized rounds to 1.5" diameter are held to ±0.004"; over 1.5–2.5" to ±0.005"; over 2.5–4" to ±0.006"; and over 4–6" to ±0.007" [S5]. 8620 cold-drawn runs tighter, at ±0.003" to 1.5", ±0.004" to 2.5", and ±0.005" to 4" [S5].
For VAR (vacuum-arc-remelted) aerospace grades 4330, 4340, and 9310, the bands are tighter still at the small end: ±0.005" up to 0.3125", ±0.006" to 0.4375", ±0.007" to 0.625", and ±0.008" to 0.875" [S5]. Metric cold-drawn 4140 TGP from 6–42 mm runs +0/-0.0127 mm (about 0.0005"), and 45–60 mm runs +0/-0.0191 mm (about 0.00075") [S5]. These bands are what make cold-finish bar the default for screw-machine and shafting work where each cut costs cycle time.
Out-of-round, straightness, and the cut-tolerance layer
For stainless and nickel round bar, ovality is commonly held to 0.05–0.075 mm, or roughly 50–75% of the total diameter tolerance window [S6]. Out-of-round is the difference between max and min diameter at the same cross-section; the same definition applies to hot-rolled carbon and alloy bar under the A29 tables [S1]. On cold-finish rounds, the practical rule of thumb is to treat half the diameter tolerance as your ovality budget when the PO does not call it out separately.
Standard straightness for hot-rolled and cold-finish rounds, squares, hexes, octagons, and flats is 1/4" in any 5 feet of length (or 1/4" × number of feet / 5); a "special" 1/8" in 5 feet is available where the next operation is finish machining and a bar must feed an auto lathe without a roller straightener [S1]. Straightness tolerances cease to apply if any post-straightening heating operation is performed [S1]. Many service centers add a separate cut-tolerance layer: for example, +0.125"/-0" cut length on long products unless otherwise specified, so a 12" cut can land anywhere from 12.000" to 12.125" [S5].
Comparing the four common machining-stock conditions
For a buyer choosing a finish condition, the relevant axes are diameter tolerance, surface roughness, internal soundness, and cost-per-pound. The four workhorse conditions line up as follows on these criteria: hot-rolled (HR) rough is the cheapest with the loosest band (e.g. ±0.010" at 1–1.125" 4340); hot-rolled rough-turned (RT) tightens the band and improves surface but is still plus-only above 1.5"; cold-drawn (CD) hits the tightest symmetric band (±0.004" to 1.5" on 4140) at moderate cost; and turned, ground, and polished (TGP) delivers the best diameter, surface, and straightness for pre-machined features at the highest cost [S5].
The diameter-band comparison for 4140/4130 to 1.5" diameter is hot-rolled at roughly ±0.009" to ±0.014" depending on the size bin, cold-drawn at ±0.004", and TGP at ±0.002" or tighter as a bespoke order [S1][S5]. For more on choosing between forging and rolling for the same alloy family, the forged vs rolled alloy steel bar selection guide is the natural follow-on read. And where surface scale or decarburization is the gating defect rather than size, shot blasting versus pickling for bars and wire rod sits one step upstream of the tolerance choice.
Specifications, surface, and common pitfalls
Each alloy family carries its own product specification, and the dimensional tolerance tables are stacked on top of that: 4140 and 4130 are commonly produced to ASTM A29 or A322 for hot-rolled bar and ASTM A108 for cold-finish, while 8620 is typically delivered to A29/A322 as hot-rolled and to A108 as cold-drawn, and 4340 in the vacuum-arc-remelt condition is covered by a separate VAR product spec with its own tighter bands [S5][S9]. The 4340-Norm. hot-rolled/rough-turned column is the one most often misused: the band is one-sided +0/-X (no minus), so a nominal 3" bar can arrive at 3.0469" and you must leave that much facing stock on every face [S5].
Surface finish is a separate line item from size tolerance: cold-drawn bars carry the smooth, scale-free surface that feeds a screw machine without a grinding pass, while hot-rolled bars carry mill scale and decarburization that must be machined off or pickled away before any case-hardening step [S5][S6]. For stainless round bar, the tolerance class (h9, h10, h11) should be written into the PO, distinct from straightness, roundness, and surface roughness, because each is a separate contractual value and the mill will not give you h11 straightness unless you paid for it [S8]. Buyers who skip the surface callout on 4140QT or 4340 often find decarburization on the OD that pushes them into an extra rough-turn pass; the related machining stock definitions for carbon bar cover the lower-alloy side of that problem.
Decision rules for a machinist-friendly PO
If the part is a shaft, pin, or bushing produced on a CNC lathe or screw machine in volumes that make each 0.001" of stock matter, order cold-drawn 4140 or 4130 to ASTM A108, with diameter band ±0.004" to 1.5", out-of-round at half the diameter band, special straightness 1/8" in 5 feet, and a 125 RMS or better surface callout [S1][S5]. If the part is a heavy shaft, roll, or pin above 3" diameter where finish turning is the first operation, hot-rolled rough-turned 4340 is the right call because the mill has already removed the decarburized skin and given you a known-plus-only diameter you can trust to program around [S5].
For parts destined for case-hardening, nitriding, or through-hardening where surface integrity is non-negotiable (aerospace 4330/4340/9310 VAR landing-gear pins, for example), the VAR product specification and its tighter small-end bands are worth the premium, and the mill cert should be called out on the PO rather than left to the stockist's default [S5][S9]. Across all cases, writing diameter, ovality, straightness, and surface as four separate lines, and naming the ASTM product spec, is what makes a tolerance dispute resolvable. Track these signals: (a) service centers continuing to publish one-sided plus-only bands above 1.5" diameter for HR rounds [S1][S5]; (b) growing use of h9/h10/h11 ISO tolerance classes on imported stainless and nickel round bar [S8]; (c) demand for VAR-grade 4330/4340/9310 small-diameter bar with ±0.005"–±0.008" bands for aerospace and defense machining [S5].
For the relevant spec sheets and selection criteria, see aluminum alloy.