# Why is the Km of an enzyme half of Vmax? [closed]

Why is the Km of an enzyme half of Vmax?

• We welcome new users to SE Biology, but we expect them to read the help on asking questions before posting, and to look at examples of well-presented questions. Your question, I am afraid does not come up to the mark. You have put half your question in the title, and the rest as a single line. The premise is incorrect in actual fact — Km is the substrate concentration at Vmax/2, and I have no idea what you mean by "any other specific reason". This is why your question has been downvoted. Commented Dec 14, 2018 at 16:25

## 1 Answer

$$K_M$$ is a constant and is not $$V_{\mathrm{max}}/2$$ as they have different dimensions. But by the Michaelis Menten equation, $$V=\frac{V_{\mathrm{max}}[S]}{K_M+[S]}$$. So, when $$[S]=K_M$$, we have $$V=\frac{V_{\mathrm{max}}[S]}{[S]+[S]}=\frac{V_{\mathrm{max}}}{2}$$. Hence, $$K_M$$ is the substrate concentration, at which we would have $$V=V_{\mathrm{max}}/2$$.

Reference: Worthington Biochemical Corporation

• We can also see that $K_M$ can't be identically $V_{\mathrm{max}}/2$ since $V_{\mathrm{max}}$ is dependent on the initial enzyme concentration while $K_M$ isnt.
– Jam
Commented Dec 14, 2018 at 15:23
• Km is never Vmax/2. It is the substrate concentration at Vmax/2. I would sort out the question before giving an answer. In this case I would not answer the question because it is so badly presented and shows so little effort on the poster's part. See "Answer well-asked questions" in the Help on answering questions. And the suggestion that a naive user reads a "credible textbook on enzyme kinetics" is, well, incredible. Again, point him to a page online. And if you answer take the trouble to set it out in a readable manner. Commented Dec 14, 2018 at 16:20
• [Edited] I believe your comment and my answer say the exact same thing. I've told the OP that what they've said is false. In my opinion, even if it's a low effort question, the OP deserves to know that they're wrong. If you would like the OP's question to be deleted, then please vote for that. If you take any particular issue with my formatting that suggests my answer isn't readable, please point it out.
– Jam
Commented Dec 14, 2018 at 17:11