Triangle Height Calculator
Know the area and base of a triangle but need the height? Enter those two values and get the height immediately using the rearranged area formula.
Understanding Triangle Height (Altitude)
The height of a triangle is the perpendicular distance from a vertex to the line containing the opposite side. Every triangle has three different heights, one for each base-vertex pair. The height is also called the altitude.
For a right triangle, one leg can serve as the height when the other leg is the base. For non-right triangles, the height may fall inside or outside the triangle depending on the angle at the vertex. Obtuse triangles have two heights that extend outside the triangle boundaries.
The area formula A = ½ × base × height captures this relationship. If you know the area and the base, solving for height gives h = (2A) / b. This calculator performs that rearrangement automatically.
Practical Uses for Triangle Height Calculations
Carpenters and builders often know the footprint area of a triangular surface and need to determine the rise or peak height. Roof trusses, gable ends, and ramps all involve height calculations from known area and base measurements.
In land surveying, the area of a triangular plot might be measured directly or computed from GPS coordinates. Finding the height helps verify measurements, plan grading, or estimate material coverage like sod or gravel.
Graphic designers working with triangular elements in logos or layouts may specify area for visual balance, then calculate height to fit design constraints. Engineers use height to determine clearance, load distribution, and structural stability in triangular components.
Height vs. Median vs. Angle Bisector
The height is perpendicular to the base, but it is not the same as the median or the angle bisector. The median connects a vertex to the midpoint of the opposite side. The angle bisector splits the vertex angle into two equal parts. All three are different lines unless the triangle is equilateral.
In an equilateral triangle, the height, median, and angle bisector from any vertex all coincide. For isosceles triangles, they coincide only for the vertex angle between the equal sides. For scalene triangles, they are always distinct.
This calculator finds the height specifically. If you need the median or angle bisector, you will need additional information like side lengths or angles and different formulas.
Frequently Asked Questions
What is the formula for triangle height from area and base?
Rearrange the area formula A = ½ × base × height to get height = (2 × area) / base. Multiply the area by 2 and divide by the base.
Does this work for all triangle types?
Yes. The formula A = ½bh applies to any triangle, so solving for h works universally as long as you know the correct base and corresponding area.
What if my triangle has multiple heights?
Every triangle has three heights, one from each vertex perpendicular to the opposite side. Choose the base corresponding to the height you want to find, then use the total area.
Can the height be longer than the base?
Yes. In tall, narrow triangles (like those with a very acute angle at the top), the height can exceed the base length. The formula still applies.
How is height different from side length?
Height (or altitude) is the perpendicular distance from a vertex to the opposite side. It may or may not coincide with a side. In a right triangle, one leg serves as the height relative to the other leg as the base.