Use the millimetre size as your starting point
First identify whether the pattern specifies knitting needles, a regular crochet hook or a steel crochet hook. A number or letter from one system is not a dependable conversion into another. Check the millimetre size printed on the tool and packaging.
The Craft Yarn Council notes that letter and number labels vary between manufacturers. Its separate needle and hook charts are a better reference than a single combined conversion formula. When a vintage or regional label is ambiguous, identify the brand and system before buying a replacement.
A few useful reference points
In the Council’s charts, a 5 mm knitting needle corresponds to US 8, while a 5 mm regular crochet hook corresponds to H-8. A 3.5 mm knitting needle is US 4, while the crochet hook is E-4. These are two different labels for two different tools, not evidence that needle and hook numbers are interchangeable.
Some US labels cover more than one millimetre entry. Do not round an unlisted metric size to the nearest numbered tool without checking the manufacturer. Use an appropriate gauge for an unmarked tool; measuring a tapered tip does not establish the working shaft diameter.
Match the finished fabric, not just the label
Make a swatch in the actual yarn and stitch pattern, finish it as the project will be finished, and measure over a representative area. Compare stitches and rows with the pattern before calculating the project count.
If your stitch count is too low over the specified width, your stitches are too large; try a smaller tool and make another swatch. If the count is too high, try a larger tool. Row gauge may respond differently, so remeasure both directions rather than assuming that one adjustment solves everything.