Midpoint Calculator

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Enter the coordinates (x1,y1)\hspace{0.2em} (x_1, y_1) \hspace{0.2em}

P1=(\hspace{0.2em} P_1 = ( , )) \hspace{0.2em}

Enter the coordinates (x2,y2)\hspace{0.2em} (x_2, y_2) \hspace{0.2em}

P2=(\hspace{0.2em} P_2 = ( , )) \hspace{0.2em}
midpoint illustration

Hello there!

Please provide your input and click the calculate button
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About the Midpoint Calculator

This midpoint calculator lets you calculate the midpoint of a line segment if you know the end points. You can also calculate one end point if you know the midpoint and the other end point.

The calculator will tell you not only the answer, but also how to calculate the midpoint (or the end point).

Usage Guide

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i. Valid Inputs

Each input can be a real number in any format — integers, decimals, fractions, or even mixed numbers. Here are a few examples.

  • Whole numbers or decimals → 2\hspace{0.2em} 2 \hspace{0.2em}, 4.25\hspace{0.2em} -4.25 \hspace{0.2em}, 0\hspace{0.2em} 0 \hspace{0.2em}, 0.33\hspace{0.2em} 0.33 \hspace{0.2em}
  • Fractions → 2/3\hspace{0.2em} 2/3 \hspace{0.2em}, 1/5\hspace{0.2em} -1/5 \hspace{0.2em}
  • Mixed numbers → 51/4\hspace{0.2em} 5 \hspace{0.5em} 1/4 \hspace{0.2em}

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what we mean by midpoint and how to calculate it.

What Is the Midpoint?

The midpoint of a line segment is the point on the line segment that is equidistant from its end points (lies at its center).

Midpoint Calculation

For a line segment with endpoints P1(x1,y1)\hspace{0.2em} P_1\hspace{0.05em}(x_1, \hspace{0.2em} y_1) \hspace{0.2em} and P2(x2,y2)\hspace{0.2em} P_2\hspace{0.05em}(x_2, \hspace{0.2em} y_2) \hspace{0.2em}, the midpoint M(xm,ym)\hspace{0.2em} M\hspace{0.05em}(x_m, \hspace{0.2em} y_m) \hspace{0.2em} is given by the formula —

(xm,ym)=(x1+x22,y1+y22)\left ( x_m, \hspace{0.2em} y_m \right) \hspace{0.25em} = \hspace{0.25em} \left ( \frac{x_1 + x_2}{2}, \hspace{0.2em} \frac{y_1 + y_2}{2} \right )

The formula above is known as the midpoint formula.

As an example, let's calculate the midpoint of a line segment whose endpoints are (2,3)\hspace{0.2em} (-2, \hspace{0.2em} 3) \hspace{0.2em} and (1,4)\hspace{0.2em} (1, \hspace{0.2em} 4) \hspace{0.2em}.

Well, all we need to do is plug the values into the formula. so, the coordinated of the midpoint would be —

(xm,ym)=(2+12,3+42)=(12,72)\begin{align*} \left ( x_m, \hspace{0.2em} y_m \right) \hspace{0.25em} &= \hspace{0.25em} \left ( \frac{-2 + 1}{2}, \hspace{0.2em} \frac{3 + 4}{2} \right ) \\[1.5em] &= \hspace{0.25em} \left ( -\frac{1}{2}, \hspace{0.2em} \frac{7}{2} \right ) \end{align*}

Note — The same formula can be used to to calculate an end point if the midpoint and the other endpoint are known.

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