# Triangle Calculator

Calculate triangle area, perimeter, and type using base-height, three sides (Heron's formula), or two sides and an angle. Free online triangle calculator.

## What this calculates

Calculate any triangle's area, perimeter, and classification with this versatile calculator. Supports three methods: base and height, three sides with Heron's formula, or two sides with an included angle.

## Inputs

- **Calculation Method** — options: Base and Height, Three Sides (Heron's Formula), Two Sides and Included Angle — Choose how you want to define the triangle.
- **Base (or Side a)** — The base of the triangle or the first side.
- **Height (or Side b)** — The height of the triangle or the second side.
- **Side c** — The third side of the triangle.
- **Included Angle (degrees)** — The angle between the two given sides, in degrees.

## Outputs

- **Area** — The area of the triangle.
- **Perimeter** — The total length of all three sides.
- **Triangle Type** — formatted as text — Classification of the triangle (equilateral, isosceles, scalene).
- **Details** — formatted as text — Additional computed information.

## Details

Triangles are the simplest polygon and the foundation of many geometric calculations. Every polygon can be divided into triangles, making triangle formulas essential throughout mathematics and engineering.

Area Formulas

- Base and Height: A = 1/2 x base x height

- Heron's Formula: A = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2

- Two Sides and Angle: A = 1/2 x a x b x sin(C)

Triangle Classification

- By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal).

- By angles: Acute (all < 90 degrees), Right (one = 90 degrees), Obtuse (one > 90 degrees).

The triangle inequality theorem states that the sum of any two sides must be greater than the third side. This calculator validates this before computing results.

## Frequently Asked Questions

**Q: How do I calculate the area of a triangle?**

A: The simplest formula is A = 1/2 x base x height. If you know all three sides, use Heron's formula: find the semi-perimeter s = (a+b+c)/2, then A = sqrt(s(s-a)(s-b)(s-c)). If you know two sides and the included angle, use A = 1/2 x a x b x sin(C).

**Q: What is Heron's formula?**

A: Heron's formula calculates the area of a triangle from the lengths of its three sides. First compute the semi-perimeter s = (a+b+c)/2, then A = sqrt(s(s-a)(s-b)(s-c)). It is named after Hero of Alexandria and works for any triangle without needing to know the height.

**Q: What is the triangle inequality theorem?**

A: The triangle inequality theorem states that the sum of any two sides of a triangle must be strictly greater than the third side. If a + b <= c for any arrangement of sides, no valid triangle exists. This is a fundamental constraint that this calculator checks before computing.

**Q: How do I determine what type of triangle I have?**

A: Compare the side lengths: if all three are equal, it is equilateral. If exactly two are equal, it is isosceles. If all three differ, it is scalene. For angle classification, use the Pythagorean relationship: if a^2 + b^2 = c^2 (with c being the longest side), it is right. If a^2 + b^2 > c^2, it is acute. If a^2 + b^2 < c^2, it is obtuse.

**Q: How do I find the height of a triangle from three sides?**

A: First calculate the area using Heron's formula. Then use h = 2A / b, where b is the base you want the height relative to. For example, if sides are 5, 6, 7: s = 9, A = sqrt(9x4x3x2) = sqrt(216) = 14.697, and height from side 7 is h = 2(14.697)/7 = 4.199.

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Source: https://vastcalc.com/calculators/math/triangle
Category: Math
Last updated: 2026-04-21