Triangle Median Calculator

Work out triangle median instantly with clear inputs, formula shown and shareable results.

About Triangle Median Calculator

A median joins a vertex to the midpoint of the opposite side. Apollonius's theorem gives its length from the three sides: mₐ = ½√(2b² + 2c² − a²).

Formula

Apollonius (median length)

mₐ = ½√(2b² + 2c² − a²)

Worked example

With the default values below, Triangle Median Calculator returns Median to side a of 8.5440. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side aminimum 0: 6
Side bminimum 0: 8
Side cminimum 0: 10

Results

Median to side a: 8.5440
Median to side b: 7.2111
Median to side c: 5.0000
Sum of medians: 20.7551

Step by step

1Values used
2Apollonius (median length)
3Median to side a= 8.5440
4Median to side b= 7.2111
5Median to side c= 5.0000
6Sum of medians= 20.7551

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Do the three medians always intersect?

Yes, at the centroid, which divides each median in a 2:1 ratio measured from the vertex.

Which median is longest?

The median to the shortest side is the longest one.