Isosceles Triangle Side Calculator
An isosceles triangle has two equal sides (legs) and a base. Enter the leg length and base length to get the height, area, perimeter and all three interior angles instantly.
units
units
Perpendicular height from base to apex
- 1
Half base
b ÷ 2 = 8 ÷ 2 = 4 - 2
Leg squared
a² = 10² = 100 - 3
Radicand
a² − (b÷2)² = 100 − 16 = 84 - 4
Height
h = √84 = 9.1652Perpendicular distance from base midpoint to apex.
How does this calculator work?
Given equal leg length a and base b, the height is h = √(a² − (b/2)²). Area = ½·b·h, Perimeter = 2a + b. Base angles = cos⁻¹(b/2a) and apex angle = 180° − 2 × base angle. All computed instantly from just two inputs.
Formula
How this is calculated
An isosceles triangle has two equal legs of length a and a base of length b. The height h is found by dropping a perpendicular from the apex to the midpoint of the base, splitting it into two congruent right triangles. Pythagoras then gives h = √(a² − (b/2)²). This height is used to compute the area as ½ × b × h, and the perimeter is simply 2a + b.
The base angles (at the two ends of the base) are equal and computed from cos⁻¹(b / 2a). The apex angle is 180° minus twice the base angle. The triangle inequality requires each leg to be longer than half the base (a > b/2); otherwise the apex would not rise above the baseline and no valid triangle exists.
All results are in whatever unit you enter for the sides — if you enter centimetres, the height and perimeter are centimetres and the area is cm².
Frequently asked questions
A triangle is isosceles when exactly two of its three sides are equal in length. Those two equal sides are called legs, and the third side is the base. The angles opposite the equal sides are also equal.
If the leg were equal to or shorter than half the base, the apex would land on or below the baseline, meaning no real triangle can be formed. Mathematically, h = √(a² − (b/2)²) would become zero or imaginary.
First compute the height h = √(a² − (b/2)²), then use Area = ½ × base × height. This calculator does both steps automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Isosceles Triangle Side Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-triangle-side-calculator
TG we-Calculate Editorial Team. "Isosceles Triangle Side Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-triangle-side-calculator.
TG we-Calculate Editorial Team, "Isosceles Triangle Side Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-triangle-side-calculator
@misc{wecalculate_isosceles_triangle_side_calculator, title = {Isosceles Triangle Side Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-triangle-side-calculator}}, year = {2026}, note = {TG we-Calculate} }
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