Altitude of Isosceles Triangle Calculator

Calculator Input

Choose one method. Enter the known values. The result appears above this form after submission.

Calculation Method

Length Unit

Decimal Places

Equal Side Length

Base Length

Area

Apex Angle (degrees)

Perimeter

Reset

Altitude Plot

The graph keeps the equal side fixed and shows how altitude changes as the base changes.

Example Data Table

Method	Known Values	Altitude Formula	Altitude Result
Equal Side + Base	Equal Side = 10, Base = 12	√(10² - 6²)	8.0000 units
Area + Base	Area = 24, Base = 8	2 × 24 / 8	6.0000 units
Equal Side + Apex Angle	Equal Side = 9, Apex Angle = 50°	9 × cos(25°)	8.1568 units
Perimeter + Base	Perimeter = 26, Base = 10	√(8² - 5²)	6.2450 units

Formula Used

1) From Equal Side and Base

h = √(a² - (b/2)²)
a is the equal side, b is the base, and h is the altitude.

2) From Area and Base

h = 2A / b
A is the triangle area and b is the base.

3) From Equal Side and Apex Angle

h = a × cos(θ/2)
θ is the apex angle between the equal sides.

4) From Perimeter and Base

a = (P - b) / 2, then h = √(a² - (b/2)²)
P is the perimeter and b is the base.

How to Use This Calculator

Select the method that matches your known values.
Choose a length unit and preferred decimal precision.
Enter the required triangle values in the form.
Press Calculate Altitude to get the result.
Review the steps, chart, and supporting triangle measurements.
Use the export buttons to save the result as CSV or PDF.

FAQs

1) What is the altitude of an isosceles triangle?

It is the perpendicular line from the apex to the base. In an isosceles triangle, this line also bisects the base and the vertex angle.

2) Why does the altitude split the base into two equal parts?

Because the two sloping sides are equal. That symmetry makes the altitude from the apex act as a median and angle bisector at the same time.

3) Can I calculate altitude using area and base only?

Yes. Use h = 2A / b. This comes directly from the triangle area formula A = ½bh.

4) What happens if the base is too large?

The triangle becomes invalid. For a real isosceles triangle, the base must be smaller than twice the equal side length.

5) Can this calculator find more than altitude?

Yes. It also reports the equal side, base, area, perimeter, and apex angle when enough values can be derived.

6) Is the apex angle required in every method?

No. It is only needed when you choose the equal side plus apex angle method. Other methods derive it automatically when possible.

7) Does the unit choice change the mathematics?

No. The formulas stay the same. The selected unit only labels the output and keeps the displayed values organized.

8) Why is the graph useful?

It shows how altitude falls as the base widens while the equal side stays fixed. That helps you visualize triangle geometry quickly.