How this calculator works
Enter the coordinates of two points and this calculator finds the slope of the line through them, the full line equation in y = mx + b form, the straight-line distance between the points, their midpoint, and the angle the line makes with the horizontal axis.
Slope measures steepness: how much y changes for every unit change in x. A positive slope rises left to right, a negative slope falls, a slope of 0 is a flat horizontal line, and a vertical line has no defined slope at all because the change in x is zero and division by zero is undefined. This calculator reports that case explicitly rather than showing an error.
How do you calculate slope?
Slope: m = (y₂ − y₁) ÷ (x₂ − x₁)Line equation: y = mx + b, where b = y₁ − m·x₁Distance: d = √((x₂ − x₁)² + (y₂ − y₁)²)Midpoint: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)Angle from horizontal: θ = arctan(m), in degreesWorked example: (0, 5) to (5, 0)
- Slope: m = (0 − 5) ÷ (5 − 0) = −5 ÷ 5 = −1.
- Y-intercept: b = 5 − (−1 × 0) = 5, so the line is y = −1x + 5.
- Distance: √((5−0)² + (0−5)²) = √50 ≈ 7.07.
- Midpoint: (2.5, 2.5); angle from horizontal: arctan(−1) = −45°.
Frequently asked questions
Why is a vertical line's slope undefined instead of zero?
Slope is a ratio of vertical change to horizontal change. On a vertical line the horizontal change (x₂ − x₁) is zero, and dividing by zero has no defined value, so the slope is undefined rather than 0. A horizontal line, by contrast, has a defined slope of exactly 0.
How do I read the sign of the slope?
A positive slope means the line rises as x increases; a negative slope means it falls. The larger the absolute value, the steeper the line — a slope of 5 is much steeper than a slope of 0.5.
What is the angle from horizontal used for?
It converts slope into a more intuitive degree measurement using arctan(m). A 45° angle corresponds to a slope of exactly 1 (or −1), while angles approach 90° as the line gets closer to vertical.
Does the order of the two points matter?
No. Swapping (x₁, y₁) and (x₂, y₂) flips the sign of both the numerator and denominator in the slope formula, so the slope, line equation, distance and midpoint all come out the same.
How do I find the line equation from one point and the slope?
Use point-slope form: plug the known slope m and the point's coordinates into y − y₁ = m(x − x₁), then simplify. This reaches the same y = mx + b form this calculator returns from two points, just starting from one point and the slope directly instead of a second point.