Find the midpoint, distance, and slope between any two coordinate points. Enter x and y values for both points and get instant results with a full step-by-step breakdown.
✓ Midpoint coordinates to 4 decimal places
✓ Euclidean distance between the two points
✓ Slope with vertical line detection
✓ Step-by-step solution shown automatically
Enter Two Coordinate PointsFree · Instant
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Midpoint
(5, 5)
Distance
7.2111
Slope
0.6667
Step-by-step
Midpoint:((2+8)/2, (3+7)/2)
= (5, 5)
Distance:√((8−2)²+(7−3)²)
= 7.2111
Slope:(7−3)/(8−2)
= 0.6667
How the Formulas Work
Three formulas work together: midpoint, distance, and slope. Each uses the same two input points.
Midpoint M = ((x1+x2)/2, (y1+y2)/2) Distance d = √((x2-x1)² + (y2-y1)²) Slope m = (y2-y1) / (x2-x1)
The distance formula comes from the Pythagorean theorem. Treating the horizontal difference as one leg and the vertical difference as the other, the segment itself becomes the hypotenuse. Slope measures the rate of vertical change per unit of horizontal change.
Who Uses This Calculator?
Algebra and geometry students
Check homework answers or verify test prep work on midpoint and distance problems.
Calculus students
Use midpoints for Riemann sum approximations and midpoint rule integration problems.
Game developers
Find the center point between two positions or calculate movement distances on a 2D grid.
GIS and mapping analysts
Calculate the midpoint between two coordinate pairs for route planning and spatial analysis.
How to Use the Calculator
1
Enter x₁ and y₁ for the first point
Type positive or negative numbers including decimals. There is no restriction on value range.
2
Enter x₂ and y₂ for the second point
These can be any real numbers. If both x values are the same, the slope will show as Undefined.
3
Read the midpoint
The midpoint coordinates appear in the highlighted purple box at the top of the results.
4
Check distance and slope
Distance is the straight-line length between the two points. Slope is rise over run, shown to 4 decimal places.
Example Calculation
Sofia's geometry homework asks for the midpoint, distance, and slope between A(−3, 5) and B(7, −1).
The midpoint formula averages the coordinates. A common error is subtracting x1 from x2 and dividing by 2 instead of adding them first. Always use (x1 + x2) / 2, not (x2 - x1) / 2.
!
Forgetting to square both differences in distance
The distance formula requires squaring the x-difference and the y-difference separately before adding. Forgetting to square one of them produces an incorrect result.
!
Confusing slope as undefined versus zero
A horizontal line (same y, different x) has a slope of 0. A vertical line (same x, different y) has an undefined slope. These are not the same thing.
!
Using coordinates in the wrong order for slope
Slope = (y2 - y1) / (x2 - x1). Switching the numerator to (y1 - y2) gives the same result in magnitude but the wrong sign if the line is not symmetric.
Primary reference for the geometric definitions and derivations of the midpoint and distance formulas used on this page.
2
NCTM (National Council of Teachers of Mathematics): Coordinate Geometry Standards
Curriculum standard source for coordinate geometry concepts including midpoint, slope, and the Pythagorean distance formula at the Algebra 1 and Geometry levels.
P
Dr. Patricia Nguyen
Mathematics educator, MS Mathematics, 14 years teaching Algebra and Geometry at secondary and community college level
Patricia reviewed the formula accuracy, step-by-step derivations, and common student misconceptions described on this page. She teaches coordinate geometry at both the high school and introductory college level.
Formula Reference
Midpoint
((x1+x2)/2, (y1+y2)/2)
Distance
√((x2-x1)² + (y2-y1)²)
Slope
(y2-y1) / (x2-x1)
Perp. Slope
-1 / m
Point-Slope
y - y1 = m(x - x1)
Slope Types
PositiveGoes up left to right
NegativeGoes down left to right
Zero (0)Horizontal line
UndefinedVertical line (x1 = x2)
Pro Tip
To find the perpendicular bisector of a line segment, use the midpoint as your point and negate the reciprocal of the slope. If slope = 2, perpendicular slope = -1/2. Then write the line equation using point-slope form.