Slope Calculator

To calculate slope, pick two points on the line, (x1, y1) and (x2, y2), and divide the change in y by the change in x: m = (y2 − y1) / (x2 − x1). This is often remembered as 'rise over run' — rise is the vertical change, run is the horizontal change. For example, with points (1, 2) and (4, 8), the slope is (8 − 2) / (4 − 1) = 6 / 3 = 2, meaning the line rises 2 units for every 1 unit it runs to the right.

A slope of 0 means the line is perfectly horizontal — y stays the same no matter how x changes, because the numerator (y2 − y1) is zero. An undefined slope means the line is perfectly vertical — x stays the same as y changes, so the denominator (x2 − x1) is zero and division by zero is undefined. Vertical lines cannot be written in the form y = mx + b; they are instead expressed as x = constant.

To convert a slope to a percent grade, multiply the slope (rise/run) by 100. A slope of 0.06 becomes a 6% grade, and a slope of 0.02 becomes a 2% grade. Percent grade is the standard way road signs, trail maps, and construction plans express steepness, since it directly states how many units of vertical rise occur per 100 units of horizontal distance.

To convert a slope to an angle, take the arctangent (inverse tangent) of the slope value: θ = atan(m), then convert the result from radians to degrees. For example, a slope of 2 corresponds to atan(2) ≈ 63.43°. This angle measures how steeply the line tilts relative to the horizontal x-axis, with 0° being flat and 90° being vertical.

A positive slope means the line rises as it moves from left to right — as x increases, y also increases. A negative slope means the line falls from left to right — as x increases, y decreases. The steeper the absolute value of the slope, the more dramatic the rise or fall; a slope near zero indicates a nearly flat line in either direction.

A 6% slope (or 6% grade) rises 6 feet for every 100 feet of horizontal distance, which corresponds to an angle of about 3.43° — noticeable but still fairly gentle, similar to many highway grades. Road engineers use percent grade to design safe inclines, drainage plans use slope to ensure water flows away from structures, and roofers use a rise-over-run ratio (like 4:12) to describe roof pitch. This calculator converts between all of these formats — decimal slope, percent grade, ratio, and angle — automatically.