Slope Calculator
Slope, equation, angle & distance from two points
How to Use
- 1Enter the x and y coordinates of your first point.
- 2Enter the coordinates of the second point.
- 3Read the slope, the full line equation and the angle instantly.
- 4The tiles also give rise, run, distance and both intercepts.
Slope Formulas
- Slopem = (y₂ − y₁) ÷ (x₂ − x₁)
- Line equationy = mx + b
- y-interceptb = y₁ − m·x₁
- Angleθ = atan(m)
- Distanced = √(Δx² + Δy²)
Quick Examples
Tap an example to load it above.
Everything about the Slope Calculator
Rise over run, the slope formula, and what positive, negative and zero slopes mean.
Slope measures how steep a line is, or how much it rises (or falls) for every step to the right. This slope calculator takes two points and returns the slope m, the equation of the line in slope-intercept form, the angle of incline, the distance between the points and both intercepts, all with the working shown.
The formula is m = (y₂ − y₁) ÷ (x₂ − x₁), or "rise over run". For the points (1, 2) and (5, 10): rise = 8, run = 4, so m = 2. The line climbs 2 units for every 1 unit right.
Reading slopes: positive m rises left-to-right, negative m falls, m = 0 is horizontal, and a vertical line has an undefined slope because the run is zero.
From slope to the line equation
Once you have m, the y-intercept is b = y₁ − m·x₁. With m = 2 and point (1, 2): b = 2 − 2×1 = 0, so the line is y = 2x. Every straight line (except vertical ones) can be written this way.
What else the calculator gives you
- 1Angle of incline
θ = atan(m). A slope of 1 is 45°; a slope of 2 is about 63.4°. Useful for ramps, roofs and roads.
- 2Distance between the points
The Pythagorean theorem on rise and run: d = √(Δx² + Δy²). For (1,2)→(5,10): √(16+64) ≈ 8.944.
- 3Intercepts
Where the line crosses the axes: y-intercept at (0, b) and x-intercept at (−b/m, 0) when m ≠ 0.
- 4Special cases handled
Identical points, horizontal lines (m = 0) and vertical lines (undefined m, equation x = c) are all reported clearly instead of erroring.
Frequently Asked Questions
What is the slope formula?
m = (y₂ − y₁) ÷ (x₂ − x₁), the change in y divided by the change in x, often called "rise over run". Pick any two points on a line and the formula gives the same slope.
How do I find slope from two points?
Subtract the y-values, subtract the x-values (in the same order), then divide. For (3, 4) and (7, 12): rise = 12 − 4 = 8, run = 7 − 3 = 4, slope = 8 ÷ 4 = 2.
What does a negative slope mean?
The line falls as you move right, so y decreases while x increases. A slope of −3 drops 3 units for every unit right. Positive slopes rise, zero slopes are flat.
Why is the slope of a vertical line undefined?
Because the run (x₂ − x₁) is zero, and dividing by zero is undefined. A vertical line cannot be written as y = mx + b; instead it is written x = c. This calculator detects that case and tells you.
How do I turn a slope into an angle?
Take the inverse tangent: θ = atan(m). A slope of 1 gives 45°, slope 0.5 gives about 26.6°, and slope 2 gives about 63.4°. The calculator reports the angle automatically.
Is this slope calculator free and does it work on mobile?
Yes. It is completely free with no sign-up, works in any modern browser on any device, and shows every step so it is safe to use for checking homework.