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For a lack of a better title and phrasing of my question, I am asking: do units have to make sense in physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

Which has units of Coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the physics field? Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?

For a lack of a better title and phrasing of my question, I am asking: do units have to make sense in physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

Which has units of Coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the physics field? (EDIT: I may have misunderstood this part and it is probably not true).

Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?

For a lack of a better title and phrasing of my question, I am asking do units have to make sense in Physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

Which has units of coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in Physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the Physics field? Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?

For a lack of a better title and phrasing of my question, I am asking: do units have to make sense in physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

Which has units of Coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the physics field? Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?

For a lack of a better title and phrasing of my question, I am asking do units have to make sense in Physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{meters^{2} \cdot seconds \cdot henry}{coulomb^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{meters^{2} \cdot seconds \cdot henry}{coulomb^{3}}$$

Which has units of coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in Physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the Physics field? Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?

For a lack of a better title and phrasing of my question, I am asking do units have to make sense in Physics?

Let me give an example of what I mean. Let's say that I have some arbitrary units (for argument's sake):

$$\frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

And I want this to be equal to charge let's say,

$$C = \frac{\mathrm{meters}^{2} \cdot \mathrm{seconds} \cdot \mathrm{henry}}{\mathrm{coulomb}^{3}}$$

Which has units of coulombs. But the units don't add up to equal one coulomb as you can see.

So my real question is that do you have to do some manipulation with the units in order for them to equal one coulomb? What are the rules and conventions in Physics for this?

I have seen in EE (electrical engineering) that if you can cancel out all units, then you can give it any units you want in the end. It is the same for the Physics field? Or can you set the units to whatever you want even if they are not equal to one coulomb?

I have heard that the constant in the EFE's is a conversion factor to get the right units:

$$\frac{8\pi G}{c^4} T_{\mu \nu }$$

Where $\frac{8\pi G}{c^4}$ is the conversion factor. This is a real example that I found that I want to understand as well.

In summary:

• Can you set the units to whatever you want even if they are not equal to one coulomb?
• If you can cancel out all units, then can you give it any units you want in the end?
• Do you have to do some kind of manipulation of units to get the right units?