This slope calculator finds the slope between two coordinate points, along with the angle of inclination, percent grade, straight-line distance between the points, and the full equation of the line connecting them.
Slope measures how steeply a line rises or falls: the change in y divided by the change in x between the two points. A positive slope rises left to right, a negative slope falls, a slope of zero is a horizontal line, and an undefined slope (division by zero) means the line is vertical.
The slope value m is a plain ratio (rise over run). The angle of inclination converts that ratio into degrees using the arctangent function, which is more intuitive for describing steepness in everyday terms. Percent grade expresses the same rise-over-run ratio as a percentage, which is the convention used for road and ramp steepness — a 100% grade corresponds to a slope of exactly 1.
Once the slope m is known, the y-intercept b is found by plugging one of the two points back into the line equation and solving for b. Together, m and b fully describe the straight line passing through both points.
An undefined slope occurs when both points share the same x-coordinate, making the line vertical. Since the slope formula would require dividing by zero (x₂ − x₁ = 0), the slope is undefined rather than a specific number.
Both describe steepness, but percent grade is the rise-over-run ratio expressed as a percentage (common for roads and ramps), while angle of inclination converts that same ratio into degrees using the arctangent function — a 100% grade equals a 45° angle.
No — the line equation y = mx + b depends directly on the slope m, which is calculated first from the two points, and then used to solve for the y-intercept b.