Rise Over Run Calculator - Slope From Two Points

A rise over run calculator turns the coordinates of two points on a line into the slope, percentage grade, and angle of that line. Enter x1, y1 and x2, y2 and the tool returns the rise (y2 minus y1), the run (x2 minus x1), the slope m equal to rise divided by run, the same slope expressed as a percentage grade, the inclination angle in degrees, and the straight-line distance between the two points.

• • Coordinate geometry homework: Check the slope of a line through two plotted points before you turn in a worksheet.
• • Stair, ramp, or road grade: Translate a measured rise and run into the same percentage grade and angle that building codes use.
• • Roof pitch or terrain cross-section: Convert two surveyed elevation points into slope, percentage, and angle for a sketch or a quote.
• • Quick data sanity check: Drop two (x, y) points from a chart and confirm the trend you see matches the calculated slope.

Rise and run is the everyday name for slope, and the two terms mean exactly the same thing on a straight line. Once you have a rise and a run, you can read the steepness as a ratio, a percentage, or an angle, which is why so many engineering and surveying workflows start by computing this ratio from two points.

If you already know your rise and run as plain numbers and only need the percentage, the dedicated slope percentage tool gives you a one-step answer; if you need to flip that percentage back into an angle or back into a ratio, the other calculators below cover those conversions.

If you already have a rise and a run as plain numbers, the Slope Percentage Calculator gives you a one-step percentage grade without retyping the coordinates.

The calculator applies the standard two-point slope formula and then converts the same number into the other units you might need.

• x1, y1: Coordinates of the first point on the line. The order does not matter as long as you keep both points consistent.
• x2, y2: Coordinates of the second point on the line. Subtract the second point's y from the first point's y to get the rise.
• m: Slope of the line, equal to the rise divided by the run. A positive m means the line rises from left to right; a negative m means it falls.
• Percent grade: Slope scaled by 100, so a slope of 1 becomes 100 percent and a 45-degree line is exactly 100 percent.

The same computation also gives you the straight-line distance between the two points because rise and run form the legs of a right triangle whose hypotenuse is the distance. We compute that distance with the Pythagorean theorem, so the tool doubles as a quick line-segment check.

When the run is exactly zero the line is vertical, the formula would divide by zero, and the calculator instead reports an undefined slope with a 90-degree angle. When the rise is zero the line is horizontal, the slope is exactly zero, and the angle reads 0°.

According to Wolfram MathWorld, the slope of a line making an angle theta with the x-axis is the constant m = Delta y / Delta x = tan(theta), which is the identity behind the percentage and angle readouts below the slope.

According to Wolfram MathWorld, Slope, the slope of a line making an angle theta with the x-axis is the constant m = Delta y / Delta x = tan(theta), which is the identity behind the percentage and angle readouts below the slope.

According to Wikipedia, Slope, the slope of a line is m = (y2 - y1) / (x2 - x1), and the angle of inclination with the x-axis is related to the slope by m = tan(θ).

When you want to flip a slope back into an angle without going through the full slope workflow, the Arctan Calculator applies the inverse tangent to a single number.

Four ideas appear in every slope problem, whether you are working a textbook example or grading a real-world surface.

In road and ramp specifications, the percentage grade is usually the more useful number because codes and signage already speak in percent, while graphs and angle measurements tend to use degrees or a unitless ratio. Keeping all three views of the same slope side by side is what makes this tool quick to use across contexts.

If percentage grade is the form you need most often, the Percentage Calculator lets you skip the slope and convert a rise and run straight into percent.

Four steps cover every slope problem, from a textbook example to a survey point.

1. 1 Enter the first point: Type the x and y coordinates of the first point into the Point 1 row.
2. 2 Enter the second point: Type the x and y coordinates of the second point into the Point 2 row. The order matters for the sign of the result.
3. 3 Read rise, run, and slope: The calculator updates the rise, run, and slope as soon as you finish typing either row.
4. 4 Pick the unit that fits: Switch your attention to percentage grade, angle, or distance depending on whether you are reading a chart, a road sign, or a survey note.

If a stair rises 7 inches over a tread of 11 inches, type (0, 0) and (11, 7) to read a slope of about 0.636, a percentage grade of 63.64%, and an angle of about 32.5°; the same numbers also confirm the Pythagorean distance of about 13.04 inches between those two corner points.

For problems that focus on the segment between two points rather than the slope of the line through them, the 2D Distance Calculator returns the Pythagorean distance without the slope outputs.

The calculator gives you every common reading of the same slope in one place, so you rarely have to convert anything by hand.

• • Multiple readings of one number: Slope, percentage grade, and angle are computed from the same inputs, so the values cannot drift out of agreement.
• • Real-time updates: Results recompute as you type, which makes it convenient to nudge a coordinate and see the steepness change immediately.
• • Edge case handling: Vertical, horizontal, and identical-point inputs are recognised and reported with the right labels instead of NaN.
• • Distance as a bonus: The Pythagorean distance between the two points shows up alongside the slope, which is useful for chord and segment problems.
• • Signed results: Negative rise or run produces a negative slope, so the tool reflects the actual direction of the line, not just its absolute steepness.

The value of having slope, percentage, and angle together is that you rarely have to choose a single unit up front. You can describe the same stair in inches of rise per inch of run, in percent for code compliance, and in degrees for a quick sketch, and the calculator will keep all three numbers consistent.

Once you have more than two points, a single two-point slope stops being representative and the Linear Regression Calculator fits a least-squares line through the full data set.

A few simple factors decide whether the answer feels steep, gentle, or undefined.

• • When the two points are identical, the slope is mathematically undefined and the calculator reports the line as undefined, but the rise, run, and distance values will all be zero because there is no line to measure.
• • The percentage and angle outputs are formatted to two decimal places, so very small slopes below 0.005 will round to 0.00%; if you need more precision, read the unitless slope output, which is shown to four decimal places.

The numbers are only as good as the points you put in, so always confirm that the two coordinates really do belong to the same physical line or data series before interpreting the result. For data with many points, a least-squares fit is more honest than a single two-point slope, and our linear regression tool is the right next step in that case.

According to Wikipedia, Grade (slope), the percentage grade of a line is 100 multiplied by rise divided by run, so a 45-degree line, where the rise equals the run, corresponds to a 100 percent grade.

When the distance output is what you actually need, the Length of a Line Segment Calculator focuses the same two inputs on the hypotenuse of the rise over run triangle.