There is no point reaching for a calculator that cannot show its working. This one starts from x₁, x₂, y₁, y₂ and atan and reports angle (θ = arctan(m)), slope (m = δy/δx) and percentage grade, so you can see how each answer follows from the numbers you entered.
What Is the Rise Over Run Calculator?
The rise over run calculator works through x₁, x₂, y₁, y₂ and atan to give you angle (θ = arctan(m)), slope (m = δy/δx) and percentage grade.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Rise Over Run Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with x₁ set to 10, x₂ set to 5, y₁ set to 2, the calculator returns slope (m = δy/δx) of -19.6, and angle (θ = arctan(m)) of -1.51982, and distance (d) of 98.127. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out angle (θ = arctan(m))?
Enter x₁, x₂, y₁, y₂ and atan. The calculator then works through the relationship and reports angle (θ = arctan(m)), slope (m = δy/δx) and percentage grade.
What does the rise over run actually calculate?
It takes x₁, x₂, y₁, y₂ and atan and converts them into angle (θ = arctan(m)), slope (m = δy/δx) and percentage grade using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter x₁?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.