Gradient Calculator

At its core, gradient represents the steepness of a line or surface, calculated as the vertical change divided by the horizontal change. The fundamental equation is gradient = linerise / linerun, where linerise equals y2 - y1 and linerun equals x2 - x1. To find the inclination angle, the calculator uses the inverse tangent function: angle = atan(linerise / linerun). Finally, the direct linear distance between two points is computed using the Pythagorean theorem, expressed as distance = sqrt(linerise^2 + linerun^2), giving you a complete geometric profile.

Imagine you are designing a wheelchair ramp and need to evaluate its steepness. Your starting coordinate is point (0, 0) and your ending coordinate is point (10, 2), meaning x1 = 0, y1 = 0, x2 = 10, and y2 = 2. First, calculate the rise: linerise = 2 - 0 = 2. Next, calculate the run: linerun = 10 - 0 = 10. Divide the rise by the run to find the gradient: 2 / 10 = 0.2, or a 20 percent slope. Using the arctangent of 0.2 yields an inclination angle of approximately 11.31 degrees. Finally, determine the ramp length using the distance formula: sqrt(2^2 + 10^2) = sqrt(4 + 100) = sqrt(104) approximately 10.20 units.

Always ensure your coordinate units match consistently before performing calculations to avoid scaling errors. When working with percentage gradients, remember that a 100 percent gradient equals a 45-degree angle, not a vertical wall. Double-check whether your application requires the slope expressed as a ratio, a percentage, or an absolute degree measurement to select the correct output format.