Isosceles Triangle Calculator
Enter any two measurements, then click Calculate. The tool will compute the missing value, area, perimeter, and angles.
Assumption: the triangle has two equal sides a and one base b.
An isosceles triangle is one of the most common geometric shapes in school math, engineering sketches, architecture, and design work. This calculator helps you quickly solve the most useful measurements without doing every step by hand. If you know any two values among equal side, base, and height, you can calculate the full triangle accurately in seconds.
What is an isosceles triangle?
An isosceles triangle has two equal sides. Those equal sides create symmetry, which leads to several useful properties:
- The two base angles are equal.
- The altitude from the top vertex to the base bisects the base into two equal halves.
- The altitude is also a median and an angle bisector in this specific case.
Because of these properties, isosceles triangles are simpler to analyze than general triangles, and they show up often in practical calculations.
How to use this calculator
Step-by-step
- Enter any two positive values: a, b, or h.
- Optionally enter a unit label like cm or in.
- Click Calculate.
- Read the computed side lengths, area, perimeter, and angles.
If you enter all three values, the tool checks whether they are internally consistent with isosceles triangle geometry.
Formulas used in the calculator
1) Given equal side and base
When you know a and b:
- Height: h = √(a² − (b²/4))
- Perimeter: P = 2a + b
- Area: A = (b × h) / 2
2) Given base and height
When you know b and h:
- Equal side: a = √((b²/4) + h²)
- Area: A = (b × h) / 2
3) Given equal side and height
When you know a and h:
- Base: b = 2√(a² − h²)
Angles are derived from trigonometric relationships, including the apex angle and the two equal base angles.
Worked example
Suppose you have an isosceles triangle with equal side a = 10 and base b = 12.
- Height: h = √(10² − 6²) = √64 = 8
- Area: A = (12 × 8) / 2 = 48
- Perimeter: P = 10 + 10 + 12 = 32
This is exactly the kind of quick workflow the calculator automates.
Common input mistakes to avoid
- Using zero or negative values (triangle lengths must be positive).
- Entering a base that is too large for the side length (must satisfy b < 2a).
- Mixing units (for example, base in inches and height in centimeters).
- Providing inconsistent values when all three fields are filled.
Where this is useful
You can use an isosceles triangle calculator in many settings:
- School assignments and exam prep for geometry and trigonometry.
- Construction layouts and roof truss planning.
- Graphic design and CAD sketches.
- Fabrication, woodworking, and metalwork templates.
Quick FAQ
Can an isosceles triangle be right-angled?
Yes. A right isosceles triangle has angles 45°, 45°, and 90°.
Can I calculate with decimals?
Absolutely. Decimal inputs are supported.
What if I only know one value?
One value is not enough to uniquely determine a general isosceles triangle. You need at least two independent measurements.