📐 Triangle Height Calculator
Calculate the height (altitude) of a triangle
How to Use This Calculator
Select Method
Choose whether you know three sides or base and area.
Enter Values
Input the known measurements. For three sides method, specify which side is the base.
Calculate
Click "Calculate Height" to find the altitude.
Review Results
See the calculated height, along with area if calculated from sides.
Formula
From Base and Area:
Height = (2 × Area) / Base
This comes from the formula: Area = (Base × Height) / 2
From Three Sides:
Step 1: Calculate area using Heron's formula:
s = (a + b + c) / 2
Area = √[s(s-a)(s-b)(s-c)]
Step 2: Calculate height:
Height = (2 × Area) / Base
About Triangle Height Calculator
The Triangle Height Calculator finds the altitude (height) of a triangle. The height is the perpendicular distance from a vertex to the opposite side (base). A triangle has three heights, one for each side as base.
When to Use This Calculator
- Geometry: Find triangle heights in problems
- Construction: Calculate perpendicular distances
- Education: Learn about triangle altitudes
- Engineering: Design calculations requiring heights
Why Use Our Calculator?
- ✅ Multiple Methods: Works with sides or base/area
- ✅ Accurate: Uses precise mathematical formulas
- ✅ Complete: Also calculates area when using sides
- ✅ Educational: Helps understand height calculation
- ✅ Free: No registration required
Key Concepts
- Altitude: Perpendicular line from vertex to opposite side
- Base: The side to which the height is perpendicular
- Three Heights: Each triangle has three altitudes (one per side as base)
- Area Relationship: Area = ½ × base × height
Frequently Asked Questions
What is the height of a triangle?
The height (altitude) is the perpendicular distance from a vertex to the opposite side (base). It's the shortest distance from the vertex to the line containing the base.
How many heights does a triangle have?
Three! Each triangle has three altitudes, one corresponding to each side as the base.
Can the height be outside the triangle?
Yes! In an obtuse triangle, the altitude from the obtuse angle vertex falls outside the triangle.
What's the difference between height and altitude?
They're the same thing! "Height" and "altitude" both refer to the perpendicular distance from a vertex to the opposite side.