This triangle calculator works two ways: enter the three side lengths to get area (Heron’s formula), perimeter and triangle type — or use base and height for a direct area. It also flags right triangles automatically.
Two Ways to Find a Triangle's Area
- Base × height ÷ 2 — when you know a base and its perpendicular height.
- Heron's formula — when you know only the three sides: s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)).
This calculator handles both, in our Math Calculators collection.
Worked Example (Verified)
The famous 3-4-5 triangle:
- Perimeter = 3 + 4 + 5 = 12
- s = 6 → area = √(6 × 3 × 2 × 1) = √36 = 6
- And 3² + 4² = 5², so it is a right triangle — the calculator detects this and labels it. (Base × height agrees: ½ × 3 × 4 = 6 ✔)
The Triangle Inequality (Why Some Sides Fail)
Any two sides must sum to more than the third — otherwise the ends cannot meet. Sides 2, 3 and 6 make no triangle (2 + 3 < 6); sides 2, 3, 4.9 make a very flat one. The calculator validates this and tells you plainly instead of returning a square root of a negative number. Right triangles get their own dedicated treatment in the Pythagorean Theorem Calculator, and triangles on coordinate grids pair with the Slope Calculator.
Triangle Types at a Glance
- Equilateral: all sides equal, all angles 60°.
- Isosceles: two equal sides.
- Scalene: all sides different.
- Right: one 90° angle — orthogonal to the side-length classification, so a triangle can be "Isosceles · Right".
Related Tools
- Pythagorean Theorem Calculator
- Circle Calculator
- Math Calculators — the full collection
Frequently Asked Questions
How do I find the area of a triangle with only the sides?
Use Heron's formula: halve the perimeter to get s, then area = √(s(s−a)(s−b)(s−c)). The 3-4-5 triangle gives √(6·3·2·1) = 6.
What is the formula for the area of a triangle?
Area = ½ × base × height when you know a height; Heron's formula (above) when you know only sides.
How can I tell if a triangle is right-angled from its sides?
Check Pythagoras: if a² + b² = c² for the longest side c, the angle opposite c is exactly 90°.
What is the perimeter of a triangle?
The sum of the three sides: a + b + c.
Can the sides 5, 5 and 11 form a triangle?
No — 5 + 5 = 10 < 11 violates the triangle inequality; the two short sides cannot reach each other.
Is this triangle calculator free?
Yes — free, instant, no sign-up.