Isosceles Triangle — Equal Side Calculator
Given the base of an isosceles triangle plus one more measurement — the height, the area, or the base angle — find the length of the two equal legs and all remaining properties.
Known value
Length of each of the two equal legs
- 1
Half base
6 ÷ 2 = 3 - 2
Equal side (Pythagorean theorem)
√(4² + 3²) = 5
How does this calculator work?
Find the equal leg a of an isosceles triangle from base b plus one known: height h gives a = √(h² + (b/2)²); area A gives h = 2A/b first; base angle θ gives a = b / (2 cos θ). The calculator then reports the full triangle: area, perimeter, and all angles.
Formula
How this is calculated
An isosceles triangle has two equal sides (legs) of length a and a base b. The apex lies directly above the midpoint of the base, creating a right triangle with legs h (the height) and b/2, and hypotenuse a. Rearranging the Pythagorean theorem gives a = √(h² + (b/2)²). This is the most direct route: supply the height and the base.
If you know the area instead of the height, the area formula Area = ½ × b × h lets you first recover h = 2 × Area / b, then apply the same Pythagorean formula to find a. If you know the base angle θ (the interior angle at each end of the base), the cosine ratio in the same right triangle gives cos θ = (b/2) / a, so a = b / (2 cos θ). This mode requires θ strictly between 0° and 90°, since the apex angle must also be positive.
Once a is found, the calculator reports all remaining triangle properties: height, area, perimeter (2a + b), base angle (arccos(b/(2a))), and apex angle (180° − 2 × base angle). The inputs must satisfy the triangle inequality 2a > b — if the computed a is too small, no valid triangle exists.
Frequently asked questions
Choose "Height" if you know how tall the triangle is, "Area" if you know its enclosed area, or "Base angle" if you know the interior angle at either end of the base. All three are mathematically equivalent ways to fix the triangle.
The base angle of an isosceles triangle is always acute (less than 90°) as long as the apex angle is positive. A base angle of exactly 90° would make the apex angle 0°, which is degenerate. A base angle greater than 90° is geometrically impossible for the two base angles together, since they would already exceed 180°.
Convert it first: base angle = (180° − apex angle) / 2. Then enter that value in the "Base angle" mode.
TG we-Calculate Editorial Team. (2026). Isosceles Triangle — Equal Side Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/isosceles-triangle-a-calculator
TG we-Calculate Editorial Team. "Isosceles Triangle — Equal Side Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/isosceles-triangle-a-calculator.
TG we-Calculate Editorial Team, "Isosceles Triangle — Equal Side Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/isosceles-triangle-a-calculator
@misc{wecalculate_isosceles_triangle_a_calculator, title = {Isosceles Triangle — Equal Side Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/isosceles-triangle-a-calculator}}, year = {2026}, note = {TG we-Calculate} }
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