Gauge In the Round vs Flat
Knitting in the round and knitting flat use the identical knit stitch, but for a real share of knitters, the two produce measurably different gauge — a genuinely common and frequently misunderstood source of a hat or sweater yoke that doesn't match a swatch that was worked the "wrong" way relative to the finished project.
Where the difference actually comes from
Working flat stockinette alternates a knit row (right side) with a purl row (wrong side); working in the round for the same fabric is knit stitch every round, no purling at all. For most knitters, the knit stitch and the purl stitch aren't produced with perfectly identical tension — purling involves a different hand motion, and it's common for one or the other to come out very slightly tighter or looser. Since flat stockinette relies on both, while circular stockinette relies on knit stitches alone, a knitter whose purl tension differs from their knit tension will genuinely measure a different overall gauge between the two methods, even using the same yarn, needles, and nominal stitch pattern.
Who this actually affects
Not everyone — some knitters' knit and purl tension are close enough that the difference is negligible in practice. It matters most for knitters who already know (from experience or from a previous mismatched project) that their purl runs noticeably tighter or looser than their knit. If you've never specifically compared the two, it's worth checking once with a small in-the-round swatch (using double-pointed needles or the magic loop technique for a small circumference) alongside your usual flat swatch.
The practical rule
Swatch the way you'll actually work the project. A hat, sweater body worked in the round, or any other circular project deserves an in-the-round swatch, not a flat one used as a stand-in — even though it's more fiddly to produce a small circular test piece than a flat rectangle. If your gauge does differ meaningfully between the two methods, a flat swatch will give you a number that simply doesn't apply to the actual in-the-round project you're about to cast on.
Garter stitch is a partial exception
Garter stitch worked flat is knit every row; garter stitch worked in the round requires alternating a knit round with a purl round to produce the same ridged structure (since knitting every round in the round produces stockinette, not garter). This means garter's own flat-versus-round gauge comparison is a genuinely different situation than stockinette's — the round version of garter reintroduces the same knit/purl tension-mismatch risk that flat stockinette has, while flat garter has none of it (no purling involved at all).
What this means for crochet
Crochet doesn't have an equivalent knit/purl asymmetry — most crochet stitches are worked identically whether you're turning rows or continuing in a spiral or joined round, so a flat-versus-round gauge difference is far less common in crochet, and not a standard thing to check for the way it is in knitting. See turned rows vs continuous rounds for the real construction differences crochet does have between the two.
FAQ
How do I swatch in the round for a small circumference without wasting yarn on a full test hat? Cast on a modest number of stitches (enough to exceed roughly 4 inches of circumference) onto double-pointed needles or a magic loop setup, and work several inches in the round before measuring — you don't need to knit a full-sized test piece, just enough fabric away from the cast-on edge to measure honestly.
If my in-the-round gauge and flat gauge match, do I still need to swatch both ways? Once you've confirmed they match for a given yarn and needle combination, you can reasonably trust that relationship for future projects in similar yarns — though it's worth re-checking if you switch to a noticeably different fibre or yarn structure, since the tension relationship isn't guaranteed to be identical yarn to yarn.
Does needle type (circular versus double-pointed) affect in-the-round gauge on its own? For most knitters, not meaningfully, though a few people do notice a small tension difference between needle types — if you suspect this applies to you, swatch on the actual needle format you plan to use for the full project.