Triangle Height Calculator: Find Altitude from Base, Area, or Sides (2026)
Calculate the height (altitude) of any triangle from base and area, three sides, or base and angle. Find all three altitudes.
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Put these formulas into practice with our instant, step-by-step Triangle Height Calculator.
The height (altitude) of a triangle is the perpendicular distance from a vertex to the opposite side. Every triangle has three altitudes, one from each vertex. The triangle height calculator computes these altitudes from the base and area, three sides (SSS), or other known dimensions, with step-by-step derivations.
Key Takeaway
The height is found using h = 2A/b, where A is the area and b is the base. For three sides, use Heron\'s formula to find the area first, then compute each altitude as h = 2A/side.
The Height Formula
This formula is derived from the area equation A = (1/2) × b × h. Solving for h gives h = 2A/b. The altitude is always perpendicular to the base it corresponds to, and different bases have different corresponding altitudes.
Finding Height from Three Sides
When you know all three sides, first find the area using Heron\'s formula: s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)). Then compute each altitude: h_a = 2A/a, h_b = 2A/b, h_c = 2A/c.
Can a Height Fall Outside the Triangle?
Yes! In an obtuse triangle, two of the three altitudes fall outside the triangle. The altitude from an acute angle vertex to the opposite side lands on the extension of that side. The length is still the perpendicular distance.
Frequently Asked Questions
- How do I find the height from the area and base?
- h = 2A/b. For area 30 and base 10: h = 60/10 = 6.
- What is the orthocenter?
- The point where all three altitudes intersect. It is inside acute triangles and outside obtuse triangles.
- Can the height be zero?
- Only for degenerate triangles (zero area). All valid triangles have positive heights.
Conclusion
The triangle height is a fundamental property that connects area and base length. Use our free triangle height calculator to find altitudes from any known dimensions.