Geometry Tool
Triangle Calculator
Calculate Area and Perimeter using SSS (Heron's Formula).
Σ The Formula
Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 | Perimeter = a + b + c
Real World Examples
Equilateral
Sides: 5, 5, 5 → Area=10.83, Perimeter=15
Scalene
Sides: 3, 4, 5 → Area=6, Perimeter=12
Isosceles
Sides: 6, 6, 8 → Area=17.89, Perimeter=20
Right Triangle
Sides: 5, 12, 13 → Area=30, Perimeter=30
# About This Calculator
Heron's formula is a powerful method for calculating the area of any triangle when you know all three side lengths, without needing to know angles or height. Named after Hero of Alexandria (1st century AD), this formula works for all triangle types: equilateral, isosceles, scalene, and right triangles.
The formula uses the semi-perimeter (s = (a+b+c)/2) and calculates area as √(s(s-a)(s-b)(s-c)). This elegant approach only requires the three side lengths, making it perfect for situations where measuring height or angles is impractical.
Triangle Types
- Equilateral: All 3 sides are equal.
- Isosceles: 2 sides are equal.
- Scalene: No sides are equal.
- Right: Has one 90° angle (can be scalene or isosceles).
How To Use
- Enter lengths for **Side A**, **Side B**, and **Side C**.
- Click **Calculate Attributes**.
- Review the **Area** and **Perimeter** results.
Frequently Asked Questions
What types of triangles can this calculate?+
All types! Equilateral (all sides equal), isosceles (two sides equal), scalene (all sides different), and right triangles. As long as the three sides satisfy the triangle inequality (sum of any two sides > third side), Heron's formula works.
Why does it say 'Invalid Triangle'?+
The triangle inequality was violated: the sum of any two sides must be greater than the third side. For example, sides 1, 2, 10 don't form a triangle because 1+2 < 10. You can't connect those sticks to make a closed shape!
How is this different from base × height ÷ 2?+
Both give the same area, but Heron's formula doesn't require knowing the height. Base × height ÷ 2 needs a perpendicular height measurement, which can be difficult to find in real life. Heron's only needs sides.
Can I use this for right triangles?+
Yes! For a right triangle (like 3-4-5), Heron's gives 6. Using (3×4)/2 also gives 6. It's a universal formula.
What is the semi-perimeter (s)?+
The semi-perimeter is exactly half of the total perimeter: s = (a+b+c)/2. It's a key intermediate step in Heron's formula to simplify the math.
Is Triangle Calculator free to use?+
Yes, Triangle Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.