Find one median or all three with ease. Use side lengths, points, and exact formulas. Download neat summaries for study, teaching, and verification today.
For side lengths, the median formulas are:
ma = 1/2 √(2b2 + 2c2 - a2)
mb = 1/2 √(2a2 + 2c2 - b2)
mc = 1/2 √(2a2 + 2b2 - c2)
For coordinates, first find the midpoint of the opposite side:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Then measure the median with the distance formula:
d = √((x2 - x1)2 + (y2 - y1)2)
The centroid divides each median in a 2:1 ratio from the vertex.
| Triangle | Input | m_a | m_b | m_c |
|---|---|---|---|---|
| Scalene Example 1 | a = 5, b = 6, c = 7 | 6.0208 | 5.2915 | 4.2720 |
| Scalene Example 2 | a = 7, b = 8, c = 9 | 7.7621 | 7.0000 | 6.0208 |
| Isosceles Example | a = 10, b = 10, c = 12 | 9.8489 | 9.8489 | 8.0000 |
A triangle median is a line segment from a vertex to the midpoint of the opposite side. It is a core idea in geometry. It also appears in mensuration, construction, and coordinate analysis. This calculator helps students, teachers, and problem solvers find one median or all three medians with speed and accuracy.
You can solve by side lengths or by coordinates. That makes the tool useful in pure geometry and analytic geometry. If you already know the three sides, the calculator applies the standard median formula directly. If you know the vertex points, it first finds the midpoint, then measures the median length with the distance formula.
Every triangle has three medians. They meet at one point called the centroid. The centroid divides each median in a two to one ratio. The longer part lies between the vertex and the centroid. This relation is important in proofs, balance problems, and design work. The calculator shows these values clearly, so the structure of the triangle becomes easier to understand.
The result area is placed above the input form. That improves review and comparison. You can inspect the chosen mode, input values, midpoint details, median lengths, and centroid distances without searching through the page. Export options are also included. You can download a CSV file for records or a PDF file for sharing and printing.
This page is also useful for practice. The example table shows sample triangles and ready answers. The formula section explains the symbols. The usage steps guide new users. The FAQ section answers common questions in plain language. Together, these sections make the page helpful for homework, classroom revision, engineering preparation, and fast self study. A clear median calculator saves time, reduces manual errors, and supports confident geometry work.
Median calculations are often tested with scalene, isosceles, and coordinate based questions. This tool handles each case in one place. It also checks triangle validity before solving. That prevents impossible inputs from producing misleading outputs. Because the page keeps the layout simple, users can focus on numbers, formulas, and interpretation. The result is a practical geometry resource for accurate daily problem solving across school tasks and exam revision sessions.
A median is a segment joining one vertex to the midpoint of the opposite side. Every triangle has exactly three medians.
Yes. The three medians always intersect at the centroid. The centroid is inside the triangle for every valid triangle.
Yes. Choose the single median mode, enter the three sides, and select the target side. The page returns the requested median and centroid split values.
Yes. Enter the coordinates of A, B, and C. The calculator finds the opposite midpoint and then measures the median with the distance formula.
The page checks triangle validity before solving. Invalid side sets or collinear coordinates produce an error message instead of a false answer.
The centroid divides each median in a 2:1 ratio. The longer segment runs from the vertex to the centroid.
They export the currently displayed result. The file includes the result title, generated time, and the metric value pairs shown in the table.
Yes. It helps with geometry drills, classroom checks, coordinate problems, and quick verification during homework or revision sessions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.