Slope Calculator
From two points: slope, y-intercept, line equation, angle of inclination, and distance.
Written by Golam Rabbani, Founder & Lead Engineer
How to use this slope calculator
- Enter the coordinates of the first point as x₁ and y₁.
- Enter the coordinates of the second point as x₂ and y₂.
- Press Calculate. The tool returns the slope, y-intercept, slope-intercept form, point-slope form, angle of inclination, and the distance between the points.
- Use Copy to save the full breakdown to your clipboard.
- Press Reset to clear all four coordinates.
About this slope calculator
The slope calculator finds the slope of the line through two points using m = (y₂ − y₁) / (x₂ − x₁), then derives the rest of the line’s identity: the y-intercept b = y₁ − m·x₁, the slope-intercept equation y = mx + b, the point-slope form y − y₁ = m(x − x₁), the angle of inclination θ = arctan(m), and the distance between the points using the Pythagorean theorem √((x₂ − x₁)² + (y₂ − y₁)²).
As a worked example, enter (1, 2) and (4, 8). Then Δx = 3, Δy = 6, so the slope m = 6 / 3 = 2. The y-intercept is b = 2 − 2·1 = 0, the slope-intercept form is y = 2x, the point-slope form is y − 2 = 2(x − 1), the angle of inclination is arctan(2) ≈ 63.43°, and the distance between the two points is √(3² + 6²) = √45 ≈ 6.708.
Vertical lines (where x₁ = x₂) produce an undefined slope; the tool handles this case explicitly and returns the line equation as x = x₁ rather than crashing or printing Infinity.
FAQ
- What does a negative slope mean?
- A negative slope means the line goes down from left to right. As x increases by 1, y decreases by |m|.
- What does the angle of inclination tell me?
- It is the angle the line makes with the positive x-axis, measured counter-clockwise. The tool reports it in degrees with the equivalent in radians shown next to it.
- How do you handle a vertical line?
- When x₁ = x₂ the slope is undefined. Instead of returning Infinity, the tool reports the line as x = x₁ and flags the slope as undefined.
- What if both points are the same?
- Two identical points do not define a unique line. The calculator detects this and asks you to enter two distinct points.
- How is distance computed?
- The distance is the straight-line (Euclidean) distance: √((x₂ − x₁)² + (y₂ − y₁)²). Units match whatever units you used for the coordinates.
- Is the calculator free?
- Yes. All arithmetic happens in your browser with no signup and no upload.