Why the ratio isn't always 1:1
Cornstarch is nearly pure starch, which makes it an efficient, powerful thickener — a little goes a long way, and it turns clear (not cloudy) as it thickens, which is why it's the go-to for glossy pie fillings and stir-fry sauces. All-purpose flour is only about 75% starch, with the rest being protein and other components that don't thicken, so it takes roughly twice as much flour to match the same thickening power — and flour also thickens a mixture cloudy rather than clear. Arrowroot and potato starch are both nearly pure starch like cornstarch, so they swap in at the same 1:1 ratio and keep the same clear, glossy result.
When to add each one
Cornstarch and flour both hold up fine to a few minutes of simmering once mixed in. Arrowroot and potato starch are more delicate — both break back down and lose their thickening power if boiled too long, so stir them in near the very end of cooking rather than early. Arrowroot has the added advantage of working well in acidic mixtures (citrus-based fillings, for example), where cornstarch can thicken less reliably.
FAQ
Do I need to make a slurry with these substitutes too? Yes — mix any of them with a small amount of cold water first before adding to a hot liquid, exactly like you would with cornstarch, to avoid clumping.
Can I use these for baking, not just sauces? Flour is a natural fit since it's already a baking ingredient. Arrowroot and potato starch work in baking too — often used in small amounts in gluten-free flour blends — but check a recipe's cornstarch role first, since baking uses (like in shortbread or a pan-coating) sometimes rely on cornstarch specifically for its fine, ultra-smooth texture.