An isosceles triangle with legs a and base b has height h = √(a² − (b/2)²) and area b × h ÷ 2. With legs of 5 and a base of 6, half the base is 3, the height is 4 and the area is 12 square units. Each base angle is arccos(b ÷ 2a), here 53.13°, leaving 73.74° at the apex.
Isosceles triangles turn up in roof pitches, gable ends, A-frame braces and geometry homework, and the question is usually the same: given two measurements, what are the rest? Pick the pair you know, leg and base or base and height, type the two lengths, and the widget returns the area, perimeter, missing side or height, both base angles and the apex angle, along with the working line by line. The altitude from the apex always meets the base at its midpoint, which is why every figure here comes from one right triangle with half the base as one side. Lengths are unitless, so the area is in square units of whatever you entered. The calculator assumes the two equal sides are the legs; if you only know angles, you still need one length to fix the size.
Select Leg and base, or Base and height. The fields below change to match.
Use any one unit for both values. In leg-and-base mode the base must be shorter than twice the leg.
Area is the headline; perimeter, the missing length and the three angles appear beneath, with the working shown step by step.
Result Area (square units): 12
Perimeter: 16
Leg length: 5
Height: 4
Each base angle (°): 53.13
Apex angle (°): 73.74
The altitude cuts this triangle into two 3-4-5 right triangles, so the height is exactly 4 and the area is 12.
Result Area (square units): 60
Perimeter: 36
Leg length: 13
Height: 12
Each base angle (°): 67.38
Apex angle (°): 45.24
Half the base (5) and the height (12) form a 5-12-13 right triangle, so each leg is 13 and the perimeter is 36.
h = √(a² − (b/2)²); A = b·h/2; P = 2a + b; base angle = arccos(b / 2a); apex = 180° − 2 × base angle
abhA, PThe altitude from the apex bisects the base at a right angle, so it splits the triangle into two congruent right triangles with hypotenuse a and legs b/2 and h. The Pythagorean theorem gives the missing length in either mode. Cosine of a base angle is the adjacent side over the hypotenuse, (b/2) ÷ a, and the three angles sum to 180°.
The triangle inequality requires any two sides together to be longer than the third. With legs a and a, the base must be under 2a. At exactly 2a the apex flattens onto the base and the height and area become zero.
The two angles at the ends of the base, opposite the equal legs, are equal. The third angle sits at the apex between the two legs. Legs 5 and base 6 give base angles of 53.13° each and an apex of 73.74°.
Under the inclusive definition used in most modern textbooks, yes: it has at least two equal sides. Enter the same value for leg and base and you get 60° at every corner, with a note that the triangle is also equilateral.
Switch to Base and height mode. Each leg is √(h² + (b/2)²). A base of 10 and height of 12 gives √(144 + 25) = 13, so the perimeter is 36.
Yes. When the base is longer than a leg times √2, the apex angle exceeds 90°. For example, legs of 5 with a base of 9 give an apex of about 128.3° and a shallow height of about 2.18.
Square units of whatever length you typed. Enter centimetres and the area is in cm²; enter feet and it is in ft². The angles are always in degrees.
Using this tool in an assignment, article or report? Copy a citation, or a link for your website.
Tools Directory Editorial Team. (2026, October 13). Isosceles Triangle Calculator. Tools Directory. Retrieved October 27, 2026, from https://tools.milunir.com/math/triangles-and-trigonometry/isosceles-triangle-calculator/
Tools Directory Editorial Team. “Isosceles Triangle Calculator.” Tools Directory, 13 Oct. 2026, https://tools.milunir.com/math/triangles-and-trigonometry/isosceles-triangle-calculator/. Accessed 27 Oct. 2026.
Tools Directory Editorial Team. “Isosceles Triangle Calculator.” Tools Directory. Last modified October 13, 2026. Accessed October 27, 2026. https://tools.milunir.com/math/triangles-and-trigonometry/isosceles-triangle-calculator/.
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