Calculation result
Choose a calculation mode, enter known values, then select Calculate.
Formula used
An isosceles triangle has two equal sides. Its altitude splits the base into equal halves. This creates two congruent right triangles.
Height: h = √(a² − b² ÷ 4)
Area: A = b × h ÷ 2
Perimeter: P = 2a + b
Semiperimeter: s = P ÷ 2
Vertex angle: θ = 2 × sin⁻¹(b ÷ 2a)
Base angle: α = (180° − θ) ÷ 2
Inradius: r = A ÷ s
Circumradius: R = a²b ÷ 4A
Here, a is an equal side. The base is b, and height is h. Angles use degrees unless radians are selected.
How to use
- Select the pair of measurements you already know.
- Choose the required length and angle units.
- Enter positive values in the visible input fields.
- Select Calculate to view every derived property.
- Copy, print, or export the finished calculation.
Example data
| Equal side | Base | Height | Area | Perimeter |
|---|---|---|---|---|
| 5 | 6 | 4 | 12 | 16 |
| 10 | 12 | 8 | 48 | 32 |
| 13 | 10 | 12 | 60 | 36 |
| 17 | 16 | 15 | 120 | 50 |
| 25 | 14 | 24 | 168 | 64 |
Common applications
Isosceles triangles appear in roof frames, bridge supports, signs, and decorative layouts. They also support surveying, machining, and classroom geometry. Accurate measurements reduce layout and cutting errors.
Frequently asked questions
What makes a triangle isosceles?
Two sides must have equal length. The angles opposite those sides are also equal. The third side is called the base.
Can an isosceles triangle be right angled?
Yes, its vertex angle can equal ninety degrees. Both base angles then equal forty-five degrees. The equal sides form the right angle.
Can an equilateral triangle be isosceles?
Yes, under the inclusive mathematical definition. It has at least two equal sides. Some school materials treat it separately.
Why must the base be shorter than twice the equal side?
The triangle inequality requires this relationship. Otherwise, the sides cannot close together. The calculator rejects that impossible geometry.
How is the height calculated?
The altitude splits the base in half. Pythagoras then gives the missing height. The calculation uses one resulting right triangle.
Are the two base angles always equal?
Yes, they face the two equal sides. Equal sides produce equal opposite angles. This is a defining isosceles property.
What unit is used for area?
Area uses the selected length unit squared. Metres produce square metres, for example. Unit changes convert existing entries automatically.
Why can rounded answers differ slightly?
Displayed values use the chosen decimal precision. Internal calculations retain more numerical detail. Small rounding differences are therefore normal.
What does the triangle classification mean?
It describes the triangle using its angles. Results may be acute, right, or obtuse. Equilateral cases are identified separately.