What is the distance formula?

The distance between two points (x1, y1) and (x2, y2) is the square root of (x2 minus x1) squared plus (y2 minus y1) squared. This is a direct application of Pythagoras's theorem: the horizontal and vertical differences form the two legs of a right triangle and the straight-line distance is the hypotenuse.

How do you find the midpoint between two coordinates?

The midpoint is the average of the two x-coordinates paired with the average of the two y-coordinates: midpoint = ((x1+x2)/2, (y1+y2)/2). It is the exact centre of the line segment connecting the two points.

What does the slope between two points represent?

The slope (also called gradient) measures how steeply the line rises or falls as you move from left to right. It is calculated as (y2 minus y1) divided by (x2 minus x1), which gives the rise over the run. A positive slope means the line goes upward; a negative slope means it goes downward. A vertical line has an undefined slope.

Distance Formula Calculator

The distance formula calculates the straight-line length between any two points on a coordinate plane. It is derived directly from Pythagoras's theorem: the horizontal difference between the two points and the vertical difference form the two legs of a right triangle, and the direct distance is the hypotenuse. Written out, the formula is d = the square root of (x2 minus x1) squared plus (y2 minus y1) squared. This calculator takes four inputs, the x and y coordinates of each point, and returns five results in one go. The primary output is the straight-line distance between the points. You also get the midpoint, which is the point exactly halfway along the line segment, found by averaging each pair of coordinates. The slope of the line through the two points is the rise divided by the run: (y2 minus y1) divided by (x2 minus x1). From the slope and one point the calculator derives the y-intercept and writes out the full equation of the line in slope-intercept form, y = mx + b. Vertical lines, where x1 equals x2, have an undefined slope and no y-intercept form, and the calculator flags that case. The default example uses points (1, 2) and (4, 6), which give a distance of 5, a midpoint at (2.5, 4), and a slope of 1.33. This tool suits students studying coordinate geometry, map readers working with grid references, and anyone who needs to find the distance between two known locations on a scaled diagram. Results are for reference only.

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5.00

distance between the two points

Midpoint(2.5, 4)

Slope (m)1.33

Line equationy = 1.33x + 0.67

How it works

The calculator reads the four coordinate inputs and applies the distance formula: d = √((x2−x1)² + (y2−y1)²). The midpoint is ((x1+x2)/2, (y1+y2)/2). The slope is m = (y2−y1)/(x2−x1). The y-intercept is b = y1 − m×x1. If x1 equals x2, the line is vertical; the slope is undefined and no slope-intercept equation exists.

Worked example

Point 1 = (1, 2) and Point 2 = (4, 6) (the default values). Distance = √((4−1)² + (6−2)²) = √(9+16) = √25 = 5.00. Midpoint = ((1+4)/2, (2+6)/2) = (2.5, 4). Slope = (6−2)/(4−1) = 4/3 = 1.33. Y-intercept = 2 − 1.33×1 = 0.67. Line equation: y = 1.33x + 0.67.

Related calculators

Midpoint Calculator: focus on finding the exact centre of a line segment.
Slope Calculator: calculate slope, y-intercept and full line equation from two points.
Hypotenuse Calculator: use Pythagoras's theorem in right-triangle form.
Percent Error Calculator: measure how far a calculated distance differs from a true value.

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