Triangle Calculator
Solve all angles, area, perimeter, and altitude for any triangle from its three side lengths (SSS).
Area
6
Perimeter
12
Angle A
36.8699°
Angle B
53.1301°
Angle C
90°
Height to side a
4
Area = sqrt(s(s-a)(s-b)(s-c)), s=(a+b+c)/2How to Use the Triangle Calculator
- Enter side lengths a, b, and c (making sure they satisfy triangle inequality: a+b>c, a+c>b, b+c>a).
- The calculator computes all internal angles A, B, C in degrees.
- View the area calculated via Heron's formula, perimeter, and height to side a.
Formulas & Principles
Semi-perimeter: s = (a + b + c) / 2
Heron's Area: Area = √(s(s - a)(s - b)(s - c))
Law of Cosines: Angle A = arccos((b² + c² - a²) / (2bc)) × (180 / π)
Altitude to side a: h = (2 × Area) / a
Frequently Asked Questions
What is Heron's Formula?
Heron's formula calculates area from three sides: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter s = (a + b + c) / 2.
What is the Triangle Inequality Theorem?
For three sides to form a valid triangle, the sum of lengths of any two sides must always be strictly greater than the length of the third side.
How are triangle angles calculated from sides?
Angles are derived using the Law of Cosines: cos(A) = (b² + c² - a²) / (2bc).
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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