Whether you are cooking or sewing, there are functional reasons why you might decide to cut something on the bias, and I've outlined them here for you.
When you cut a food on the bias, you are cutting it against its natural grain, or direction of fibers. The primary reason for cutting certain foods, especially tougher foods, against these fibers is that doing so helps to make them more tender, and less stringy or tough. Another reason may be for visual aesthetic.
There are two types of steak that immediately come to mind when I think of cutting on the bias: flank steaks and skirt steaks. They're both naturally flat, relatively chewy steaks, with an easy-to-spot grain, or direction of muscle fibers.
If you slice these steaks along their grain, your teeth will have to do a lot of work to break down several long strands of muscle fibers at a time. However, if you slice these steaks against their grain, your knife will do most of the work of breaking down those long strands for you, and your teeth can enjoy a more pleasant chewing experience.
Small cuts that come from larger cuts
The image below shows a 5-pound beef tenderloin that we served for Easter this year. We reverse seared* the entire loin then sliced it into ~.5 inch slices so that everyone could take as much or as little as they wanted. This tenderloin is sliced thinly on the bias.
Large loins like this one, whose muscle fibers run longways are often cut into 1-2 inch pieces and sold as filet mignons rather than as a full loin. If you buy a 6oz filet mignon, you're buying the cross section of a bigger tenderloin, which means the muscle fibers of the filet actually run up and down the 1-inch side rather than across the wide part that you sear. So when you sear a filet mignon, you will not cut it on the bias. The butcher has already done that.
Other cuts that are taken from larger pieces, and therefore are already cut on the bias, include ribeyes, strip steaks, and T-bones, among many others.
Celery is another food that I find more pleasant when cut at some kind of angle, rather than when served in strips. Though there are other ways to improve the chewing experience of celery sticks so that you can dip them or serve them alongside buffalo wings, cutting celery against its grain can help reduce its stringy texture.
The Right Angle
In cooking, on the bias is a rather general term that, when used on its own, doesn't specify an angle at which you should cut your food.
When slicing a flank or skirt steak on the bias, I first break down the meat into 2-3 smaller steaks, which just makes them more manageable to slice, then I cut at a 90 degree angle, or perpendicular to the grain.
When slicing celery on the bias, I might use a steep angle to make it look fancy, such as when using it in a soup or salad, or I might make thin slices perpendicular to the stalk, such as when making chicken or tuna salad- so it adds some crunch without taking over the dish.
Since I cannot do so much as thread a needle, I'll keep this section short. In researching bias cuts in sewing, I came across the blog Cucicucicoo, whose author, Lisa, writes about various sewing techniques. She explains that to cut fabric on the bias actually does refer to cutting at a specific angle, unlike in cooking.
Cutting woven fabric on its bias means to cut it at a 45 degree angle to its natural grain. This creates a stretchy, more elastic edge that has many uses in sewing, such as making neck ties and preventing garments from fraying. Her artice What is Bias? Fabric Bias vs. Grain can be found here, and it offers more detailed explanations and techniques.
*Reverse Sear: To cook meat slowly at a low temperature until it reaches a desired internal temperature, and then sear it on all sides until it's brown and crispy.
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