Triangle Height Calculator

Find triangle altitude from sides, area, or coordinates. Built for lessons, checks, and geometry work. Fast outputs keep every triangle calculation clear and dependable.

Calculated Height Result

Primary height
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Area
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Base used
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Perimeter
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Method
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Checks
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Triangle Height Calculator

Choose a method, enter values, and calculate altitude instantly. The form uses a three-column layout on large screens, two columns on tablets, and one column on mobile devices.

Area unit is square of selected length unit.

Example Data Table

Case Inputs Chosen base Area Height
Area and base Area = 36, base = 12 12 36 6
Three sides a = 13, b = 14, c = 15 15 84 11.2
Coordinates (0,0), (6,0), (2,5) 1-2 15 5

Formula Used

From area and base: height = (2 x area) / base
From three sides: s = (a + b + c) / 2, area = sqrt[s(s-a)(s-b)(s-c)], then height = (2 x area) / chosen base
From two sides and included angle: area = 0.5 x side1 x side2 x sin(angle), then height = (2 x area) / chosen base
From coordinates: area = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2, then height = (2 x area) / selected side length

These equations return the altitude perpendicular to the base you choose. If the triangle is invalid or degenerate, the calculator flags the issue instead of showing misleading values.

How to Use This Calculator

  1. Select the method that matches your available information.
  2. Choose the length unit and output precision.
  3. Enter all required values for the chosen method.
  4. Pick the side that should act as the base when needed.
  5. Press Calculate Height to show the result above the form.
  6. Use the CSV button to save a data row or the PDF button to print a neat result sheet.

Frequently Asked Questions

1. What is triangle height?

Triangle height, or altitude, is the perpendicular distance from a vertex to the chosen base line. Each triangle can have three different heights.

2. Why can one triangle have several heights?

Each side may be treated as a base. Changing the base changes the matching perpendicular distance, so the same triangle can produce three valid altitudes.

3. Can I use coordinates instead of side lengths?

Yes. The coordinate method calculates area from point locations, then divides twice that area by the chosen side length to get the altitude.

4. What happens if the side lengths cannot form a triangle?

The calculator checks triangle validity. If the sum of two sides is not greater than the third, it stops and shows an error.

5. Why does the area matter?

Area links directly to altitude through the formula area = 0.5 x base x height. Knowing any two of these values lets you solve the third.

6. Does the calculator support right, acute, and obtuse triangles?

Yes. The formulas work for any valid triangle. For obtuse triangles, the perpendicular line may meet the extension of the selected base.

7. Are units converted automatically?

The calculator keeps all length outputs in the selected unit. Area input should already match the square of that same selected length unit.

8. When should I export the result?

Export when you need a saved calculation trail for homework, engineering checks, design notes, or quick sharing with students and teammates.