Enter two points using X₁, Y₁, X₂, and Y₂ — or switch your Calculation Method to use Rise and Run directly — and the Slope Calculator gives you the Slope (m) alongside the Grade Percentage, Angle, Distance, and Y-Intercept.
Slope (m)
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Grade Percentage
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Angle
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Distance
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Y-Intercept
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X-Intercept
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The slope of a line is a measure of its steepness, calculated as the ratio of vertical change (rise) to horizontal change (run). It's also known as the gradient and indicates how much y increases for each unit increase in x.
To calculate slope from two points (x₁,y₁) and (x₂,y₂), use the formula: m = (y₂ - y₁) / (x₂ - x₁). This gives you the rate of change between the two points.
A negative slope means the line is decreasing - as you move from left to right, the line goes downward. The steeper the negative slope, the more rapidly the line descends.
To convert slope to percentage grade, multiply the slope by 100. For example, a slope of 0.25 equals a 25% grade. This is commonly used for roads, ramps, and construction.
Slope is the ratio of rise over run, while angle is measured in degrees from horizontal. The angle θ relates to slope by: θ = arctan(slope). A 45° angle corresponds to a slope of 1.
Yes, vertical lines have undefined slope because the run (horizontal change) is zero, making the slope calculation involve division by zero. Vertical lines are described as having infinite slope.
Use the point-slope form: y - y₁ = m(x - x₁). Rearrange to slope-intercept form y = mx + b, where b is the y-intercept. Substitute the known point and slope to solve for b.
For driveways, a slope of 10-15% (about 6-8.5 degrees) is ideal. For wheelchair accessibility, ramps should have a maximum slope of 8.33% (1:12 ratio). Steeper slopes can be unsafe or difficult to navigate.