Triangle median calculator
A median joins a vertex to the midpoint of the opposite side. This works out all three from the sides alone, for geometry students and drafting work.
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How to use it
- Enter side a, side b and side c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
The median to side a is m_a = ½ × √(2b² + 2c² - a²), and likewise m_b and m_c. The centroid splits each median 2 : 1, so its distance from the vertex is ⅔ of the median.
Example
Inputs: Side a = 13, Side b = 14, Side c = 15. Result: Median to side a: 12.9711; Median to side b: 12.1655; Median to side c: 11.2361.
Limits and caveats
- Use one length unit for all sides; the medians come out in the same unit.
- Each median is named by the side it bisects, so the median to side a starts at the opposite vertex A.
Questions about this tool
How is a median different from an altitude?
A median runs to the midpoint of the opposite side, an altitude meets that side at a right angle. They coincide only on the base of an isosceles triangle.
Why is the median to the hypotenuse half the hypotenuse?
In a right triangle the midpoint of the hypotenuse is the center of the circle through all three vertices, so it sits half the hypotenuse from each one.
What is the centroid?
The point where the three medians meet. It lies two thirds of the way along each median from the vertex and is the balance point of a uniform triangular plate.