Calculator Form
Formula Used
For a triangle with side lengths a, b, and c, the medians are:
mₐ = 1/2 × √(2b² + 2c² − a²)
mᵦ = 1/2 × √(2a² + 2c² − b²)
m𝒸 = 1/2 × √(2a² + 2b² − c²)
The calculator also finds area with Heron’s formula:
s = (a + b + c) / 2
Area = √(s(s − a)(s − b)(s − c))
The centroid lies where the three medians meet. It divides every median in a 2:1 ratio from the vertex.
How to Use This Calculator
- Enter the three side lengths of a valid triangle.
- Add an optional unit label such as cm, m, or in.
- Select how many decimal places you want in the output.
- Click Calculate Triangle Medians.
- Review all median values, centroid position, area, perimeter, and triangle type.
- Use the chart to inspect the triangle, midpoints, medians, and centroid visually.
- Download the current result as CSV or PDF when needed.
Example Data Table
| Example | Side a | Side b | Side c | Median mₐ | Median mᵦ | Median m𝒸 | Triangle Type |
|---|---|---|---|---|---|---|---|
| Example 1 | 3 | 4 | 5 | 4.2720 | 3.6056 | 2.5000 | Scalene Right |
| Example 2 | 5 | 5 | 6 | 4.9244 | 4.9244 | 4.0000 | Isosceles Acute |
| Example 3 | 7 | 8 | 9 | 7.7621 | 7.0000 | 6.0208 | Scalene Acute |
Frequently Asked Questions
1) What is a triangle median?
A triangle median is a line segment from one vertex to the midpoint of the opposite side. Every triangle has exactly three medians, and they always intersect at the centroid.
2) Can I calculate medians from only the side lengths?
Yes. The median formulas use the three side lengths directly. You do not need angles or coordinates as long as the three sides form a valid triangle.
3) What happens if my sides do not form a triangle?
The calculator checks the triangle inequality. If one side is greater than or equal to the sum of the other two, it stops and shows a validation message.
4) What is the centroid?
The centroid is the common intersection point of the three medians. It divides each median into two parts, with the vertex-to-centroid segment twice the centroid-to-midpoint segment.
5) Are medians equal in every triangle?
No. In an equilateral triangle, all three medians are equal. In isosceles and scalene triangles, one or more medians can differ in length.
6) Are the output units the same as the side units?
Yes. Median lengths and perimeter use the same length unit as the input sides. Area uses squared units, such as cm² or m².
7) Does the chart show the exact triangle?
Yes. The graph builds a coordinate model from the entered side lengths, then plots the triangle, the three midpoint targets, the medians, and the centroid.
8) Why should I export the result?
Exports help when you need records for homework, reports, design notes, or comparison tables. CSV works well for spreadsheets, while PDF is useful for clean sharing and printing.