Find the height of a triangle from its area and base, or from side lengths using Heron's formula.
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Triangle Geometry
The triangle height calculator finds the altitude of a triangle when you know either the area and a base, or all three side lengths. Height is the perpendicular distance from a side to the opposite vertex.
The simplest approach rearranges the standard area formula. If the area and one base are known, the height relative to that base is twice the area divided by the base length.
height = 2 * Area / base
Derived from Area = (1/2) * base * height.
When only the three side lengths are known, find the area first using Heron's formula, then apply the height formula above for whichever side you choose as the base. This two-step method gives the altitude to any selected side.
Area = sqrt(s(s-a)(s-b)(s-c))
Heron's formula gives the area from sides a, b, c and semi-perimeter s.
h_a = 2 * Area / a
The height to side a.
Frequently asked questions
Yes. Every triangle has three altitudes, one from each vertex perpendicular to the opposite side. They generally have different lengths unless the triangle is equilateral.
Not always. In an obtuse triangle, the altitude from the vertex of the obtuse angle falls outside the triangle.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Calculate the area of any triangle from its three side lengths using Heron's formula with semi-perimeter breakdown.
Calculate the area, perimeter, height, inradius, and circumradius of an equilateral triangle from its side length.
Calculate the area, perimeter, height, base angles, and leg length of an isosceles triangle from any two known measurements.
Solve a triangle using the law of cosines — find a missing side from two sides and the included angle, or find an angle from three sides.
