# Rise Over Run Calculator

Created by Álvaro Díez
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 05, 2023

This is Omni's rise over run calculator – the easiest, fastest, and most entertaining way to calculate the rise over run (slope) on the web. Simply choose two points, and we will use the rise over run formula to tell you all you need to know about them. Alternatively, if you want to do it by hand, we will also teach you how!

## What is rise over run – is it a slope?

As gentlewomen and gentlemen do, let's start from the beginning. You might be asking yourself, what is rise over run? (If you don't, the next section welcomes you.) So rise over run is a simple way to describe a straight line or function's slope.

As the name implies, it is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run, or slope, is the term used in many non-technical environments as it is self-explanatory

Don't be intimidated by it. Rise over run, slope (and even gradient) are terms that describe the same concepts when referring to a straight line. It only differs when we talk about other, more complicated functions, but that's for another day. Or you can simply check our average rate of change calculator.

## Rise over run formula, calculating by hand

The rise-over-run formula is quite literally that, "rise over run", as that is how you would calculate the slope of a straight line joining any two points. All you need to do is calculate the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run).

It does not seem complicated because (hopefully) it is not complicated. If you are still in doubt, let's take a look at an example. Imagine we have two points: $(1, 2)$ and $(4, 8)$. Let's calculate the rise over run (slope) of the line that goes through both of the example points.

You can very well use the Omni calculator to your left, but we will do it by hand just to prove how easy it is to find. The first step is calculating the rise, which is the difference between y coordinates. If we assume that the points are given in Cartesian coordinates, that means we need to calculate the difference between the second coordinate of each point: $y_2 - y_1 = 8 - 2 = 6$.

Now the next step is to take the difference between the horizontal points, in our case that is the x variables, or the first coordinate of each point: $x_2 - x_1 = 4 - 1 = 3$. Remember that we are not using absolute value here, so this can be negative.

Now, all that's left to do is divide the rise over the run to get our slope. $6 / 3 = 2$. It's just a simple division of two numbers, similar to the calculation of vertical exaggeration, used for the creation of 3D maps or animations. That wasn't too painful, was it?

You might find more complicated situations where the numbers aren't as easy to work with as in the example. And you might not be able to happily apply the rise over run formula and calculate it by hand in an instant. It is for those situations that we here at Omni have created the Rise Over Run calculator.

## How to use Omni's rise over run calculator?

If you thought that using the run over rise formula by hand was easy, get ready for things to be even easier now because we are going to teach you how to calculate the rise over run slope using our calculator!

The first steps you need to do are:

• Fill in the $x$ coordinate for the first point
• Fill in the $y$ coordinate for the first point
• Fill in the $x$ coordinate for the second point
• Fill in the $y$ coordinate for the second point
• Enjoy the results!!

Yes, I know that a bullet list for something as easy as filling in 4 fields is overkill, but that only proves my previous point, doesn't it?

You might be a bit confused with the results, though. This calculator has many more output values than the slope, but they are all related and will help you to better understand the concept of the rise over run slope.

## Extra perks free with rise over run calculator

This is by far the most complicated part of the whole calculator, and it's really easy. Let's make a list of the output variables that calculator computes for you, with a brief explanation of each.

The first results are Rise, Run, and Slope, which should be clear by now. Then the calculator shows a graphical representation of the line you've input. And then the weird numbers appear:

• Angle: The angle the line makes with the x axis. The calculation is shown below the Angle field.
• Percentage grade: Rise over run slope expressed as a percentage.
• Distance: 2D distance between the points. The calculation is shown below, where means the square root. You can read more about the different ways to calculate distance in our distance calculator.

## Every error is a lesson, so let's see what we can learn

It might look simple, but the rise over run formula is a little rascal that will create havoc whenever you stop looking. In this case, havoc means mathematical problems with the calculation, so don't worry, your house isn't going to burn down (Omni Calculator is not responsible if your house burns down due to your CPU setting alight).

The first error you might encounter is if, by mistake, you introduce the same point twice, instead of introducing two different points. Simple to solve: simply change one of the coordinates.

More mathematically complex problems arise when either the x coordinates or the y coordinates for both points are the same. In the latter case, we have ourselves a constant function in which the value of y is always the same, independent of x. Here the value of the slope, as calculated with the rise over run formula, is $0$ (zero); check it if you don't trust us.

A more mathematically complicated problem arises when both the x coordinates are the same. This is a vertical line. This line does not represent a function anymore. In this case, the slope is not shown because, mathematically speaking, it is undetermined.

In this situation, what we have is division by zero, which is a mathematical indetermination, a.k.a. it does not have a defined value. You will hear people say it is equal to infinity, but don't listen to them unless you know how to . In that case, go ahead.

For us, that's way off-topic, so we will end this explanation here. Feel free to use and share this calculator with anyone that might need it. And if it was useful for you, send us an email, we love hearing from users like you!

## FAQ

### What is the rise over run for points (2,3) and (4,7)?

It's 2. This is because the difference in x-coordinates is 4-2 = 2 and that in y-coordinates is 7-3 = 4. Hence, the rise over run formula gives 4/2 = 2.

### How do I find rise over run on a graph?

If you have to determine rise over run from a graph, follow these steps:

1. Determine the coordinates of any two points (x₁, y₁) and (x₂, y₂) that lie on the line. The points on the axes may be a good choice.
2. Compute the difference in x-coordinates of these two points: x₂ - x₁. This result is run.
3. Compute also the difference in y-coordinates for these two points: y₂ - y₁. This outcome is rise.
4. Divide rise by run (y₂ - y₁)/(x₂ - x₁) and... you're done!

### How do I find slope using rise over run?

Rise over run is just a different name for slope. So if you know the rise over run of a line/function, then you automatically know its slope – it's exactly the same number!

### How do I calculate rise over run for stairs?

1. Measure the length of the tread, including the nosing if present. This is run.
2. Measure the height of a step (riser), i.e., the distance between the tops of two consecutive treads. This is rise.
3. Divide rise by run. This is the result you've been looking for.
4. Master carpenters came up with two rules for the perfect stairs:
• The run plus the rise should equal 18 inches; or
• The run plus twice the rise should equal 25 inches.
Álvaro Díez
First point coordinates
x₁
y₁
Second point coordinates
x₂
y₂
Result
Rise (Δy)
Run (Δx)
Slope (m)
Related numbers
Y - intercept
Angle (θ)
deg
%
Distance (d)
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