Use this rise over run calculator to find slope from two points or from a direct rise and run, then compare the ratio, decimal slope, percent grade, angle.
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Rise over run calculator Calculate slope from either two points or a direct rise and run. The result explains the ratio, decimal slope, percent grade, angle, and the line equation behind the answer.
Choose a mode
Point 1
Point 2
Helpful presets
Try a graph-based example, an ADA-style ramp ratio, a negative slope, or a vertical line to see how the outputs change.
What rise and run mean
Rise is the change in y. Run is the horizontal change in x. The slope is rise divided by run, so using horizontal distance matters.
Start with points or a ratio Enter two graph points or a direct rise and run to see the slope, percent grade, angle, and line equation.
Rise over run calculator: slope, percent grade, angle, and line equation from two points
A rise over run calculator finds the slope of a line by dividing the vertical change by the horizontal change. This version works both as a slope calculator from two points and as a direct rise and run calculator, then explains the decimal slope, percent grade, angle of inclination, and line equation so the result is useful on a graph, a worksheet, or a practical grade check.
How a rise over run calculator works
Rise over run is the core slope formula used in algebra: the rise is the change in y, the run is the horizontal change in x, and slope is rise divided by run. When two points are known, the calculator first subtracts the coordinates to find rise and run, then uses that same ratio to derive the decimal slope, percent grade, and angle.
That matters because many searchers do not only want a bare slope number. They also want to know whether the line is ascending or descending, whether the slope is undefined, and how the same result would look as a percent grade or line equation. A stronger rise over run calculator should answer all of those intent questions in one pass.
rise = y2 - y1
Find the vertical change between the two points.
run = x2 - x1
Find the horizontal change between the same points.
slope = rise / run
The slope is the rise over run ratio. This is the specific relationship the calculator applies when building the result.
From slope ratio to percent grade and angle
A rise over run calculator is also useful as a slope percentage calculator because percent grade comes from the same ratio multiplied by 100. If the rise is 3 and the run is 4, the slope is 0.75 and the percent grade is 75%. This is why the same line can be described with several equivalent labels depending on whether the user is working in school math, road grade, ramps, or roof pitch.
The angle of inclination uses inverse tangent. That conversion helps when a user searches for rise over run to angle or wants to compare a graph slope with a geometric angle. In practice, the ratio form is often easier for algebra work, while percent grade and angle are easier for field measurements and design conversations.
percent grade = (rise / run) x 100
Shows the same slope as a percentage of horizontal run.
angle = arctan(rise / run)
Converts the slope ratio into degrees. This is the specific relationship the calculator applies when building the result.
Why two modes help real users
Competitor pages often force the user into only one workflow: either coordinate points or a direct rise and run entry. In practice, both are common. Students and teachers often start with two graph points, while builders, surveyors, and ramp planners often already know the rise and horizontal run. A useful online rise over run calculator should support both without making the reader translate the problem into a different format first.
That is also why this page shows the line equation, midpoint, and line type after the ratio is calculated. Those extra outputs help a user sense-check the result instead of accepting a number with no context. If the line is vertical, the page surfaces that explicitly rather than pretending there is a finite slope.
Vertical, horizontal, and sign edge cases
When the run is zero, the line is vertical. The slope is undefined because division by zero is not allowed, but the geometry still has a real rise and a real segment length. Good calculator behavior here is to explain the edge case instead of silently returning zero or some placeholder value.
When the rise is zero, the line is horizontal and the slope is exactly zero. Negative slopes simply mean the line falls from left to right. If two identical points are entered, there is no unique line at all, so the page should stop and ask for distinct points rather than displaying a misleading slope.
Worked example: slope from two points
Suppose the points are (1, 2) and (5, 5). The rise is 5 - 2 = 3, the run is 5 - 1 = 4, and the slope is 3/4 or 0.75. That same result can also be read as a 75% grade and an angle of about 36.87 degrees.
This kind of worked example helps in classrooms because it shows the slope formula, the direction of the line, and the equivalent grade interpretation all at once. It also helps in practical planning because a 3:4 ratio is much easier to inspect visually than a raw decimal alone.
When this calculator is useful and when it is not
Use this rise over run calculator when you need to find slope from two points, compare rise and run directly, or translate the same line into percent grade and angle. It is appropriate for algebra homework, graph interpretation, quick geometry checks, and practical slope comparisons.
It does not replace a full design check. Real construction or accessibility decisions may depend on code definitions, tolerances, cross slope, and measured horizontal distance. The calculator reports the geometry implied by the numbers you enter; it does not decide whether a project is compliant or safe.
Rise over run means the change in y divided by the change in x. It is the standard slope formula for a line on a coordinate plane.
How do you calculate slope from two points?
Subtract the y-values to find rise, subtract the x-values to find run, then divide rise by run. For points (x1, y1) and (x2, y2), the slope is (y2 - y1) / (x2 - x1).
Is rise over run the same as slope?
Yes. Rise over run is another way of stating the slope of a line. In algebra, slope, gradient, and rise over run all refer to the same ratio.
What if the run is zero?
A zero run means the line is vertical. The slope is undefined because dividing by zero is not valid, but the line still has a real rise and segment length.
Can rise over run be negative?
Yes. A negative rise over run means the line descends from left to right. The percent grade and angle become negative as well.
How do you turn rise over run into a percent?
Multiply the slope by 100. A rise over run of 0.08 becomes an 8% grade, while a rise over run of 3/4 becomes 75%.
How do you convert rise over run to degrees?
Use the inverse tangent of the slope ratio. In symbols, angle = arctan(rise / run).
Why does the calculator ask for horizontal run instead of slope length?
Because slope is defined with horizontal distance, not the distance along the line itself. Using slope length instead of horizontal run changes the ratio and produces the wrong slope.
What does a slope of zero mean?
A slope of zero means the rise is zero, so the line is horizontal. The y-value stays constant as x changes.
Can this calculator also give the line equation?
Yes. When you enter two points, the page also shows the line equation so you can connect the rise over run result to the graph of the same line.
