Midpoint Calculator to Find the Distance and Midpoint Between Two Points

This distance and midpoint formula calculator will find the midpoint and distance of a line segment given the line's two endpoint coordinates.

Plus, the calculator also shows the step-by-step midpoint solution using the midpoint formula and the step-by-step distance solution using the distance formula.

Finally, the calculator will attempt to plot the two endpoints, graph the line, and plot its midpoint.

Midpoint Calculator

Calculate the midpoint and distance of a line segment, and see the step-by-step midpoint formula solution, complete with the plotted Cartesian coordinates.

Special Instructions

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
ExamplesMidpoint examplesMidpoint formula examplesMidpoint formula examples:

Example midpoint calculations:

To see an example of how the midpoint calculator works and what types of entries it can handle, select a midpoint problem example from the drop-down menu. Note that the fraction example converts each fraction to a decimal before entering the coordinates into their respective fields. To clear the entry field to enter your endpoints, select "Choose" or click the "Reset" button at the bottom of the calculator.

Point 1:Point 1 (X1,Y1):Point 1 (X1,Y1):Point 1 (X1,Y1):
X1:
 Fraction X1 Whole number
-
 Fraction X1 numerator number
/
 Fraction X1 denominator
X1 decimal:
Y1:
 Fraction Y1 Whole number
-
 Fraction Y1 numerator number
/
 Fraction Y1 denominator
Y1 decimal:

Point 1 (X1,Y1):

Enter the X and Y values of the first point. The values can be in the form of a decimal or a whole number.

If you need to convert mixed numbers and fractions to decimals, expand the description to reveal a mini fraction-to-decimal calculator. Enter the whole number (if none, leave blank), the numerator, and the denominator, and the calculator will make the conversion and enter the decimal into the corresponding calculator field.

x1:
 Point X1
y1:
 Point Y1
Point 2:Point 2 (X2,Y2):Point 2 (X2,Y2):Point 2 (X2,Y2):
X2:
 Fraction X2 Whole number
-
 Fraction X2 numerator number
/
 Fraction X2 denominator
X2 decimal:
Y2:
 Fraction Y2 Whole number
-
 Fraction Y2 numerator number
/
 Fraction Y2 denominator
Y2 decimal:

Point 2 (X2,Y2):

Enter the X and Y values of the second point. The values can be in the form of a decimal or a whole number.

If you need to convert mixed numbers and fractions to decimals, expand the description to reveal a mini fraction-to-decimal calculator. Enter the whole number (if none, leave blank), the numerator, and the denominator, and the calculator will make the conversion and enter the decimal into the corresponding calculator field.

x2:
 Point X2
y2:
 Point Y2
X midpoint:

X midpoint:

This is the midpoint of the X values.

Y midpoint:

Y midpoint:

This is the midpoint of the Y values.

Midpoint:

Midpoint:

This is the midpoint of the line segment established by the entered coordinates (x1,y1) (x2,y2).

Distance:

Distance:

This is the distance between the entered coordinates (x1,y1) (x2,y2).

Midpoint distance:

Midpoint distance:

This is the distance between the midpoint and either of the endpoints (1/2 of the distance between the two endpoints).

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Learn

How to find the midpoint and distance of a line segment, and examples of both.

How to Find Midpoint Between Two Points

To find the midpoint of a line segment, you calculate the two x coordinates' average to get the x-midpoint coordinate and the two y coordinates' average to get the y-midpoint coordinate.

Midpoint Formula
(xm,ym) =(x1 + x2,y1 + y2)
22

So given the endpoints (-3, 3) and (5, 3), you would solve for the midpoint like this:

 Midpoint Formula Solution x1 = -3 y1 = 3 x2 = 5 y2 = 3 (xm,ym) = ( x1 + x2 , y1 + y2 ) 2 2 (xm,ym) = ( -3 + 5 , 3 + 3 ) 2 2 (xm,ym) = ( 2 , 6 ) 2 2 (xm,ym) = ( 1 , 3 )

How to Find the Length of a Segment with Endpoints

To find the length of a line segment, you add the squared x difference to the squared y difference and calculate the result's square root.

Distance Formula
d=(x2 - x1)2 + (y2 - y1)2

So given the endpoints (-3, 3) and (5, 3), you would solve for the distance like this:

 x1 = -3 y1 = 3 x2 = 5 y2 = 3
Distance Formula Solution
d=(x2 - x1)2 + (y2 - y1)2
d=(5 - -3)2 + (3 - 3)2
d=(8)2 + (0)2
d=64 + 0
d=64
d=8

Distance and Midpoint Formula Examples

The following are three examples showing how to find the midpoint between two points and the length of a segment with endpoints (actual results from the Distance and Midpoint Calculator on this page).

Example #1: (0, 4) and (5, 6)

Find the midpoint and length of the line formed by the endpoint coordinates (0, 4) and (5, 6).

 Midpoint Formula Solution x1 = 0 y1 = 4 x2 = 5 y2 = 6 (xm,ym) = ( x1 + x2 , y1 + y2 ) 2 2 (xm,ym) = ( 0 + 5 , 4 + 6 ) 2 2 (xm,ym) = ( 5 , 10 ) 2 2 (xm,ym) = ( 2.5 , 5 )
Distance Formula Solution
d=(x2 - x1)2 + (y2 - y1)2
d=(5 - 0)2 + (6 - 4)2
d=(5)2 + (2)2
d=25 + 4
d=29
d=5.385164807134504

Based on the above calculations, the midpoint of the line formed by the endpoint coordinates (0, 4) and (5, 6) is (2.5, 5), and the distance between the two endpoints is 5.385164807134504.

Example #2: (-4, -9) and (3, 5)

Find the midpoint and length of the line formed by the endpoint coordinates (-4, -9) and (3, 5).

 Midpoint Formula Solution x1 = -4 y1 = -9 x2 = 3 y2 = 5 (xm,ym) = ( x1 + x2 , y1 + y2 ) 2 2 (xm,ym) = ( -4 + 3 , -9 + 5 ) 2 2 (xm,ym) = ( -1 , -4 ) 2 2 (xm,ym) = ( -0.5 , -2 )
Distance Formula Solution
d=(x2 - x1)2 + (y2 - y1)2
d=(3 - -4)2 + (5 - -9)2
d=(7)2 + (14)2
d=49 + 196
d=245
d=15.652475842498529

Based on the above calculations, the midpoint of the line formed by the endpoint coordinates (-4, -9) and (3, 5) is (-0.5, -2), and the distance between the two endpoints is 15.652475842498529.

Example #3: (-3, 7) and (5, -9)

Find the midpoint and length of the line formed by the endpoint coordinates (-3, 7) and (5, -9).

 Midpoint Formula Solution x1 = -3 y1 = 7 x2 = 5 y2 = -9 (xm,ym) = ( x1 + x2 , y1 + y2 ) 2 2 (xm,ym) = ( -3 + 5 , 7 + -9 ) 2 2 (xm,ym) = ( 2 , -2 ) 2 2 (xm,ym) = ( 1 , -1 )
Distance Formula Solution
d=(x2 - x1)2 + (y2 - y1)2
d=(5 - -3)2 + (-9 - 7)2
d=(8)2 + (-16)2
d=64 + 256
d=320
d=17.88854381999832

Based on the above calculations, the midpoint of the line formed by the endpoint coordinates (-3, 7) and (5, -9) is (1, -1), and the distance between the two endpoints is 17.88854381999832.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.