Slope & Line Calculator

Give it two points and it works out everything the line through them implies: the slope as Δy over Δx, the equation in slope-intercept form, the angle of inclination, the straight-line distance, the midpoint, and the rise and run separately. A vertical line is handled rather than divided by zero — the slope comes back undefined and the equation as x equals a constant, which is correct and is the case most implementations forget.

Slope gets expressed three different ways in practice, and they are easy to confuse because all three sound like percentages of something. As a ratio it is rise over run. As an angle it is the arctangent of that ratio. As a grade it is the ratio times a hundred, and that last one is where the confusion lives: a 100 percent grade is not vertical, it is 45 degrees, because it means rising one unit for every unit travelled horizontally. A 10 percent road sign is 5.7 degrees, and an 8 percent grade is 4.6 — numbers that feel much smaller than the signs suggest.

Roofing uses a fourth convention, rise in inches per twelve inches of run. A 4:12 pitch is 18.4 degrees and a 6:12 is 26.6, which is why a roofer's "six twelve" and a surveyor's "twenty-six and a half degrees" describe the same roof without either of them converting.

The midpoint and distance are worth a note about what they assume. Both treat the plane as flat and the axes as having the same units, which is true on graph paper and not true of latitude and longitude — a degree of longitude is a different distance from a degree of latitude everywhere except the equator, so the distance between two coordinates is not the distance this returns. For geographic work the answer comes from a haversine or a geodesic calculation, not from Pythagoras on the raw degrees.