Triangle Height
Quickly find the height of any triangle from its area and base using h = 2A ÷ b. Free online triangle height calculator with formula, examples, and instant results for students and professionals.
About This Calculator
This free online triangle height calculator finds the perpendicular height of any triangle from its area and base length. Simply enter the area in square units and the base length in units, and the calculator applies the standard formula h = 2A ÷ b to compute the height instantly. Whether you are working with scalene, isosceles, equilateral, or right triangles, as long as you know the area and the corresponding base, this tool will give you the accurate height.
The formula is derived from the fundamental triangle area equation: Area = (1/2) x base x height. By rearranging the equation to solve for height, we get height = (2 x Area) / base. The height is always measured perpendicular (at a right angle) to the chosen base side. Every triangle has three heights, one for each side as the base -- this calculator computes the height corresponding to the base you provide. The result is displayed with two decimal precision for clarity.
Understanding triangle height is essential in many real-world contexts. Architecture and construction professionals use height calculations for roof trusses, gable ends, and triangular structural supports. In engineering, triangle height helps determine forces acting on triangular components. Geometry students frequently encounter triangle height problems in coursework and standardized tests. Landscape designers calculate triangular garden bed dimensions, and artists use proportional triangle measurements in perspective drawing.
This calculator is particularly useful when you already know the area of a triangular surface (perhaps from surveying or design plans) and need to find the height dimension. For example, if a triangular plot has an area of 200 square meters and a base of 40 meters, the height would be h = 2 x 200 ÷ 40 = 10 meters. The tool supports any positive numeric values and works with any unit system (meters, feet, inches, etc.) as long as you use consistent units for area and base.
For those who need to explore other triangle properties, Calculy also offers complementary calculators for triangle area via base and height, base length from area and height, triangle side lengths, Heron's formula area from three sides, and many more geometry tools covering circles, squares, polygons, and 3D shapes.
Frequently Asked Questions
How do you calculate the height of a triangle?
If you know the area (A) and the base (b), the height is h = 2A/b. This formula comes from rearranging the triangle area formula A = (1/2) x b x h.
What formula does this calculator use?
The calculator uses h = 2A/b, derived from the standard triangle area formula A = (1/2) x base x height. Solving for height gives height = (2 x Area) / base.
What inputs do I need to provide?
Enter the area of the triangle in square units and the base length in units. The calculator will compute the height perpendicular to that base.
Can I calculate height without knowing the area?
For special triangles like right triangles, the height may be one of the sides. For a general triangle, you need the area and base, or you can use Heron's formula to find the area first from three sides, then calculate the height.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration required. You can bookmark any calculation with shareable URLs that preserve your inputs for future reference.
What units should I use for area and base?
You can use any consistent unit system. If the base is in meters, the area must be in square meters, and the height will be in meters. Similarly for feet, inches, centimeters, or any other unit. The calculator works with any positive numeric values without unit conversion.
Can I use this calculator for right triangles?
Yes, this calculator works for any triangle type -- right, acute, obtuse, equilateral, isosceles, or scalene. As long as you know the area and the length of the base corresponding to that area, you can find the perpendicular height. For right triangles, the height can also be one of the legs if the base is the other leg.
What if I need to find the base instead of the height?
If you know the area and the height, you can find the base using the rearranged formula b = 2A/h. Calculy offers a dedicated Base of a Triangle calculator for this purpose, which works the same way in reverse.