Isosceles Triangle Calculator
Calculate area, perimeter, height and angles of an isosceles triangle from its equal sides and base.
About Isosceles Triangle Calculator
An isosceles triangle has two equal sides (legs). The height is found using the Pythagorean theorem on the half-base and leg. Base angles are equal and found via inverse cosine.
Formulas
Height
h = √(leg² − (base/2)²)
- l
- Length of the equal side
- b
- Base length
Area
A = ½ × base × height
- b
- Base length
- h
- Height
Worked example
With the default values below, Isosceles Triangle Calculator returns Area of 36.6606. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Equal Side (leg)minimum 0 units
- 10 units
- Baseminimum 0 units
- 8 units
Results
- Area
- 36.6606 sq units
- Perimeter
- 28.0000 units
- Height
- 9.1652 units
- Base Angle
- 66.4218 °
- Apex Angle
- 47.1564 °
Step by step
- 1Height from Pythagorean theorem= 9.1652
- 2Area= 36.6606
- 3Perimeter= 28
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What if I only know the base angle and one side?
If you know the base angle θ and the leg, the base = 2 × leg × cos(θ). Enter those values to get all properties.
Can the apex angle be obtuse?
Yes. If base > leg × √2, the apex angle exceeds 90°.