Altitude of a Triangle Calculator
How to Use This Calculator
- 1
Enter Triangle Area
Input the total surface area of the triangle in square units.
- 2
Enter Base Length
Provide the length of the base side. The altitude will be measured perpendicular to this baseline.
- 3
Review Results & Insights
View the exact altitude, aspect ratio, apex angle, centroid height, and geometric summary in the results section.
Example Calculation
Finding the altitude and properties of a triangle with an area of 36 square units and a base of 12 units.
Triangle Area
36
Base Length
12
Results
Altitude (h)
6.0000 units
Aspect Ratio (h/b)
0.5000
Apex Angle (Isosceles)
90.00°
Tips
Maintain Unit Consistency
Ensure area and base are expressed in matching unit systems (e.g., square meters and meters). The output altitude will be in the linear equivalent.
Perpendicular Distance Rule
Remember that altitude represents the shortest (90°) perpendicular distance from the baseline to the opposite apex vertex.
Check Centroid Placement
The geometric center of mass (centroid) of any triangle always lies exactly at ⅓ of the altitude height above the baseline.
Altitude of a Triangle Calculator
The Altitude of a Triangle Calculator determines the perpendicular height of any triangle when its surface area and base length are known.
It also calculates derived geometric metrics including the aspect ratio (h/b), apex angle, isosceles side length, and centroid location.
These measurements are essential across architecture, drafting, civil engineering, and structural design in 2026.
Formula for Triangle Altitude
Triangle area is fundamentally defined as half of the product of its base and perpendicular height:
$$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Altitude}$$
Rearranging the formula to solve for the altitude ($h$):
$$\text{Altitude } (h) = \frac{2 \times \text{Area}}{\text{Base}}$$
Worked Example
Consider a triangle with an area of 36 square units and a base of 12 units:
Calculate Altitude ($h$): $$h = \frac{2 \times 36}{12} = \frac{72}{12} = 6.0000 \text{ units}$$
Calculate Aspect Ratio ($h/b$): $$\text{Aspect Ratio} = \frac{6}{12} = 0.5000$$
Apex Angle (Isosceles Model): $$\theta = 2 \times \arctan\left(\frac{12 / 2}{6}\right) = 2 \times \arctan(1) = 2 \times 45^\circ = 90.00^\circ$$
Equal Leg Length & Perimeter: $$\text{Leg Length} = \sqrt{6^2 + 6^2} = \sqrt{72} \approx 8.4853 \text{ units}$$ $$\text{Perimeter} = 12 + 2 \times 8.4853 = 28.9706 \text{ units}$$
Centroid Height: $$\text{Centroid Height} = \frac{6}{3} = 2.0000 \text{ units above base}$$
Geometry Principles & Orthocenter Insights
Every triangle possesses three distinct altitudes corresponding to its three vertices.
The intersection point of these three altitudes is called the orthocenter:
- Acute Triangles: The orthocenter lies entirely inside the triangle.
- Right Triangles: The orthocenter coincides with the right-angled vertex.
- Obtuse Triangles: The orthocenter lies outside the triangle boundary.
Furthermore, the center of mass (centroid) always resides at a height of $\frac{1}{3}h$ measured perpendicularly from the base.
Frequently Asked Questions
What is the altitude of a triangle?
The altitude of a triangle is a perpendicular line segment drawn from a vertex to the opposite side (or an extension of the opposite side). The length of this segment represents the height of the triangle relative to that base.
How do you calculate altitude from area and base?
Because Area = ½ × Base × Altitude, rearranging the equation yields Altitude = (2 × Area) / Base. For example, if Area = 36 sq units and Base = 12 units, Altitude = (2 × 36) / 12 = 6 units.
Can the altitude fall outside the triangle?
Yes. In an obtuse triangle, two of the three altitudes fall outside the triangle body and intersect the extended line containing the base side.
Where is the centroid located relative to the altitude?
The centroid (center of mass) always lies along a line parallel to the base at exactly one-third (⅓) of the altitude height from the base.
What is the orthocenter of a triangle?
The orthocenter is the point where all three altitudes of a triangle intersect. It lies inside acute triangles, at the right-angle vertex in right triangles, and outside obtuse triangles.