Isosceles Triangle Calculator
Enter the two equal sides and the base of an isosceles triangle to instantly compute the area, height, perimeter, interior angles, and medians.
Area = ½ × base × height
- 1
Height (Pythagorean theorem)
√(5² − (6 ÷ 2)²) = √(16) = 4The altitude bisects the base into two halves of b/2. - 2
Area
½ × 6 × 4 = 12
How does this calculator work?
For an isosceles triangle with equal sides a and base b, compute h = √(a² − (b/2)²), area = ½bh, perimeter = 2a + b, base angle = arccos(b/(2a)), and apex angle = 180° − 2 × base angle. Requires 2a > b for a valid triangle.
Formula
How this is calculated
An isosceles triangle has two sides of equal length a and one unequal base b. The apex lies directly above the midpoint of the base (by symmetry), so dropping a perpendicular from the apex to the base bisects the base into two halves of length b/2 and creates a right triangle with hypotenuse a and one leg b/2. The height is therefore h = √(a² − (b/2)²).
With the height known, the area is ½ × b × h, and the perimeter is 2a + b. The base angle (the two equal angles at the ends of the base) equals arccos(b / (2a)), derived from the same right triangle: cos(base angle) = (b/2) / a. The apex angle is 180° − 2 × base angle, because all three angles of a triangle must sum to 180°.
For completeness the calculator also reports the two types of medians. The median from the apex to the midpoint of the base coincides with the height h (they are the same line in an isosceles triangle). The median from each base vertex to the midpoint of the opposite equal side has length √(a² + 2b²) / 2, derived from the general median-length formula. The triangle is valid only when 2a > b — otherwise the two equal sides are too short to meet above the base.
Frequently asked questions
An isosceles triangle has exactly two sides of equal length (called the legs) and a third unequal side (the base). The two base angles — the angles adjacent to the base — are also equal.
The height from the apex bisects the base into two equal halves b/2. Applying the Pythagorean theorem to the resulting right triangle gives h = √(a² − (b/2)²), where a is the equal side.
When the two equal sides together do not exceed the base, i.e., 2a ≤ b. This violates the triangle inequality: the sum of any two sides of a triangle must be strictly greater than the third side.
TG we-Calculate Editorial Team. (2026). Isosceles Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-triangle-calculator
TG we-Calculate Editorial Team. "Isosceles Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-triangle-calculator.
TG we-Calculate Editorial Team, "Isosceles Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-triangle-calculator
@misc{wecalculate_isosceles_triangle_calculator, title = {Isosceles Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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