# Is Time Always On The X-Axis (And Can It Be On The Y-Axis)?

In physics, different quantities are often represented on graphs and very commonly time is represented on the horizontal x-axis. But does time always have to go on the x-axis?

**Generally, time is always on the x-axis, because it allows for other quantities to be represented as functions of time, which is useful in physics. Time is also, in most cases, independent of other variables, which conventionally means that it should be on the x-axis.**

You’ll often hear the answer to this question being that “time is the independent variable” or something similar.

While that is absolutely true from a common sense perspective, for example position being dependent on time rather than time depending on position, it just isn’t really quite a satisfying enough answer.

This whole concept of the independent variable going on the x-axis is actually quite an arbitrary rule and doesn’t really have any deeper meaning. **It is simply a convention to write the independent variable on the horizontal axis.**

Besides, **time is not necessarily always the independent variable** (I explain it in this article). In most cases it will be, but not always.

You could place time on the y-axis also and there are indeed some cases where that is done.

That being said, you should always ask yourself this when making a graph; **on which axis is it more useful to represent time on?** What are the benefits of placing time on the x-axis?

First of all, the main benefit of this is that having time on the x-axis let’s us calculate new quantities more easily.

For example, when having time on the x-axis and position on the y-axis, we can then calculate **the velocity more easily from the slope of this graph**:

Compare this to having the variables the other way around:

So from this at least, it would seem more useful to just be able to calculate the velocity, rather than the inverse of the velocity. The same goes for derivatives of graphs that aren’t just straight lines.

If we were to have an accelerating frame, the position-time graph would look like some kind of a curve. Then we could get the velocity at each point from the derivative of the function.

Anyway, here is what the derivative would look like in a **(t, x) -graph**:

But if we had the variables the other way around, i.e. an **(x, t) -graph**, it would go something like this:

Again, we would get the inverse of the velocity, which in most cases, is kind of stupid, because why would we care about the inverse? I think you get the point of why time is usually more useful to represent on the x-axis.

To summarize, the bottom line for why time is usually on the horizontal axis, is because **it makes more sense mathematically in terms of calculating quantities** **from the graph**.

## Can time be on the y-axis?

Sometimes you may encounter situations where time is placed on the y-axis and in some cases this might even be useful to do.

**In principle, time can be placed on the y-axis. This is, however, not very common when making graphs and it is primarily only done in special relativity when making Minkowski diagrams or spacetime diagrams.**

In special relativity, a common way of visualizing spacetime is by drawing a spacetime diagram (also called a Minkowski diagram as it was first introduced by the physicist Hermann Minkowski).

Actually, in special relativity, instead of a time axis, we use an x^{0}-axis, which is defined as x^{0}=ct (it’s still almost a time axis!). I explain this idea in my introductory article on special relativity, which you can check out here.

Now, in spacetime diagrams, time is commonly placed on the vertical axis. But why exactly is this the case?

In short, **it is a convention to place time on the y-axis in spacetime diagrams, which presumably comes from Minkowski himself. In fact, Minkowski was the first to introduce the concept of spacetime in his paper “Space & Time” and in that paper he has time represented on the y-axis** (source: English version of Minkowski’s papers).

This notion of time on the y-axis still doesn’t have any very significant meaning, it is simply a convention that has stayed in place for some reason. Besides, time is generally never placed on the y-axis anywhere other than in special relativity.

Now, if you’re interested in Minkowski’s papers, I would highly recommend checking them out as they really have some profound insights about special relativity and spacetime. You can find the translated version here.

Also, consider checking out some of my other articles, such as the introduction to Lagrangian mechanics or the introduction to Hamiltonian mechanics. You’ll also find my **recommended resources for self-studying** these topics on this page.