Triangle altitude calculator
Altitudes are needed for area work and technical drawing. This finds the one on every side without measuring any angle.
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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
Area S by Heron's formula, then the altitude onto side a is h_a = 2S / a, and likewise h_b = 2S / b and h_c = 2S / c.
Example
Inputs: Side a = 13, Side b = 14, Side c = 15. Result: Altitude onto side a: 12.9231; Altitude onto side b: 12; Altitude onto side c: 11.2.
Limits and caveats
- In an obtuse triangle two altitudes fall outside it, on the extensions of the sides, but their lengths are still correct.
Questions about this tool
What is an altitude of a triangle?
The perpendicular segment from a vertex to the opposite side or its extension. Every triangle has three.
Which altitude is the longest?
The one onto the shortest side, because an altitude equals twice the area divided by its side.
What is the height of an equilateral triangle?
The side length times √3 / 2, about 0.866 of the side.