How this calculator works
The slope measures how steeply a line rises or falls: it is the change in y divided by the change in x between any two points on the line. Positive slopes rise to the right, negative slopes fall, and a horizontal line has slope 0. The associated angle comes from the arctangent of the slope and always lands between -90° and 90°.
Formula
m = (y₂ - y₁) / (x₂ - x₁) and θ = arctan(m) in degrees, with θ in (-90°, 90°).
Worked example
For the points (1, 2) and (5, 10), m = (10 - 2)/(5 - 1) = 2, and θ = arctan(2) ≈ 63.4349°. For (0, 0) and (2, 5), m = 2.5 and θ ≈ 68.1986°.
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Frequently asked questions
Why is a vertical line an error?
When both points share an x value the denominator x₂ - x₁ is zero, and division by zero has no defined result. Geometrically the line is vertical and its slope is undefined.
Can the slope be negative?
Yes. When y decreases as x increases, the slope is negative and the angle is reported between -90° and 0°.
Does the order of the points matter?
No. Swapping the two points reverses both differences, so the slope and angle are unchanged.