"The corporate tax rate is 40%. The marginal federal corporate income tax rate on the highest income bracket of corporations (currently USD 18,333,333 and above) is 35%. State and local governments may also impose income taxes ranging from 0% to 12%, the top marginal rates averaging approximately 7.5%. A corporation may deduct its state and local income tax expense when computing its federal taxable income, generally resulting in a net effective rate of approximately 40%. The effective rate may vary significantly depending on the locality in which a corporation conducts business. The United States also has a parallel alternative minimum tax (AMT) system, which is generally characterized by a lower tax rate (20%) but a broader tax base."
So, 40% up to $18,333,333; 35% on anything above that. State income tax is extra, and can be claimed as an expense against your Federal tax bill. In Delaware, the State income tax is zero, and that is where 90% of larger US businesses are based.
The expenses you can claim against your income are more generous than in the UK, so you will be paying 40% or 35% of a smaller number, however, you will most of the time pay more tax in the US than in the UK.