The IRS treats a bonus as "supplemental wages," and gives employers two legal ways to withhold federal tax from it. Almost all employers use the "percentage method": a flat 22% is withheld from the bonus, rising to a mandatory 37% on any amount that pushes your cumulative supplemental wages for the year above $1,000,000. This is separate and different from the graduated withholding tables used on your regular salary paychecks.
That 22%/37% figure is a withholding rate, not your actual tax rate. Your real federal income tax liability on the bonus is determined when you file: the bonus gets added to your salary and taxed at your marginal bracket, the same 10%-37% progressive brackets that apply to every other dollar of income. If your marginal bracket is below 22%, you were over-withheld and get the difference back as part of your refund. If it's above 22%, whether because the bonus itself pushed you into a higher bracket, you were under-withheld and owe the gap.
On top of federal tax, FICA (Social Security and Medicare) applies to a bonus exactly like regular wages, no special treatment, and state income tax applies too in every state that has one. On a large bonus, this calculator's "true net bonus" figure, which nets out the actual federal liability rather than the flat withholding, is the number that best represents what a bonus is really worth to you.