Three systems, one object
A knitting needle has exactly one property that affects your knitting, and that is the diameter of its shaft. Millimetres state that diameter directly. The US and old UK numbering systems state a position in a list instead, and the two lists run in opposite directions, which is the source of nearly every mix-up.
US numbers increase as the needle gets thicker: US 0 is 2 mm, US 6 is 4 mm, US 15 is 10 mm. Old UK and Canadian numbers decrease as the needle gets thicker: UK 14 is 2 mm, UK 8 is 4 mm, UK 000 is 10 mm. Both systems then run out of numbers and start improvising, which is why the UK scale ends in a run of zeros and the US scale jumps from 15 to 17 to 19 to 35 with nothing in between.
Neither list is complete. Several common metric sizes have no US equivalent at all, including 3.0, 7.0 and 7.5 mm, which is why a European pattern occasionally calls for a needle that a US-labelled set simply does not contain. The chart shows those gaps rather than papering over them with a nearest match, because a nearest match is a decision you should make knowing you are making it.
Crochet hooks are a fourth system, and a messier one
US crochet hooks are lettered, sometimes numbered, and frequently both at once, which is how a 5 mm hook comes to be labelled H/8. The lettering is consistent enough up to about K, and above that it stops being consistent between manufacturers: hooks marked M, N, P and Q can be found at several different diameters depending on who made them. Steel hooks used for thread work are a separate numbering system entirely, running from about 0.6 to 1.75 mm with numbers that increase as the hook gets finer, and they are not in this chart.
The practical consequence is that a lettered hook is a weaker identifier than a lettered needle. If a pattern specifies a hook by letter and your hook is unmarked or from a different maker, measure it. A hook gauge costs very little and settles the question in a second.
Using needle size to chase a gauge
Stitch width tracks needle diameter closely enough that a proportional estimate is useful. If you are getting 5.5 stitches per inch on a 4.5 mm needle and the pattern wants 5, you need a needle bigger by the ratio of those two numbers: 4.5 times 5.5 divided by 5 is 4.95 mm, which is a 5 mm needle, one size up. That result matches the old workshop rule that one size changes gauge by roughly half a stitch per inch in worsted-weight territory, and it has the advantage of scaling correctly at other yarn weights, where half a stitch per inch is the wrong constant.
The estimate degrades over larger jumps. Beyond about two sizes the fabric itself has changed character, and a swatch that finally hits the stitch count may be too loose to hold its shape or too dense to drape. At that distance the honest conclusion is usually that the yarn is not the one the pattern was written for. Compare it on grist with the substitution calculator before buying more needles.
What the size cannot tell you
Two needles of the same stated diameter can produce different gauges in the same hands, because the surface and the taper differ. Slick metal lets stitches sit looser than grabby wood or bamboo for most knitters, and a long gradual tip forms a stitch differently from a blunt one. Cable joins on circulars, cord memory and even needle length all show up in the fabric at the margins.
Add to that the plain fact that tension is personal, that it changes with mood and speed and how tightly you are gripping, and that many knitters purl at a different tension from the way they knit. The number stamped on the needle is a way to find the needle again. Everything about the fabric comes from the swatch, and if it disagrees with the number, the swatch is right.
Questions people ask
What is a US 8 needle in mm?
Five millimetres. The nearby conversions are worth having in your head as well, because they come up constantly: US 6 is 4 mm, US 7 is 4.5 mm, US 8 is 5 mm, US 9 is 5.5 mm and US 10 is 6 mm. Above that the US scale stops being regular, with US 10.5 at 6.5 mm, US 11 at 8 mm and nothing at all at 7 mm or 7.5 mm. If a pattern calls for 7 mm and your set is US-labelled, you do not have that needle and the substitution is a real decision rather than a rounding.
Why do UK needle numbers go the wrong way?
They go the way the wire gauge went. Old UK needle numbers descend from a wire gauge system in which the number counted the drawing operations used to reduce the wire, so more passes made thinner wire and a higher number. US sizing was set up later as a straightforward ordinal list from fine to thick. Neither is wrong and neither is a measurement. Britain switched to metric labelling in the 1970s, so needles bought new in the UK today are marked in millimetres, and the old numbers survive mainly in vintage patterns and inherited needle rolls.
How many needle sizes should I change to fix my gauge?
Use the estimator on this page rather than a fixed rule, because the right answer scales with the yarn. The proportional model says the needed diameter equals your current diameter times your gauge divided by the target gauge. At worsted weight that usually works out to about one size per half stitch per inch, which is the rule of thumb most people carry, but at fingering weight one size is worth considerably less than half a stitch per inch and at bulky it is worth more. Change one size, swatch again, and only then extrapolate.
Does the needle material change the gauge?
Frequently, and by enough to matter. Most knitters get a slightly looser gauge on slick metal than on wood or bamboo of the same diameter, because the stitches slide rather than grip and end up sitting a little larger. Tip shape matters too: a long tapered tip forms a stitch further down the shaft than a blunt one. The difference is usually under half a stitch per four inches, which is small, but it is not zero, and it is enough to invalidate a swatch. Swatch on the needles you will knit the project with, not the ones nearest the sofa.
Are crochet hook letters reliable?
Up to about K, yes. Beyond that the letters diverge between manufacturers and you can find hooks marked N at 9 mm and at 10 mm, or P at anything from 10 to 15 mm. Below the lettered range, steel hooks for thread crochet use a separate numeric scale that runs the other way, with higher numbers meaning finer hooks, and they overlap confusingly with the aluminium numbers. The safe habit is to read a hook by its millimetre marking where it has one and to measure it where it does not.