Isosceles Triangle Calculator
Two equal sides and a base — enter both for the apex and base angles, the area, the height and the perimeter.
An isosceles triangle is symmetric about the line from the apex to the middle of the base, which makes the two base angles equal.
How the isosceles triangle calculator works
An isosceles triangle is symmetric about the line from the apex to the middle of the base, which makes the two base angles equal. The height splits it into two identical right triangles, so the height is √(a² − (b ÷ 2)²) where a is an equal side and b the base. The base must be shorter than the two equal sides together, or they cannot meet.
Formula: a² = b² + c² − 2bc·cos A; a / sin A = b / sin B = c / sin C; area = ½ab·sin C
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Equal sides 5, base 6 | 12 | height 4, area 12 |
| Equal sides 10, base 12 | 48 | height 8, area 48 |
| A tall narrow triangle | 39.7995 | nearly a spike |
FAQFrequently asked questions
What makes a triangle isosceles?
At least two sides of equal length, which forces the two angles opposite them to be equal too.
How do I find the height?
Drop a line from the apex to the middle of the base: height = √(a² − (b ÷ 2)²), where a is an equal side and b the base.
What is the area?
Half the base times the height — so ½ × b × √(a² − (b÷2)²).
Can the base be longer than the equal sides?
Yes, but not longer than both added together, or the sides cannot reach across.
Is an isosceles triangle ever right-angled?
Yes — the 45-45-90 triangle is both, with the two legs equal.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.