# Triangle Calculator

> Triangle calculator: solve sides, angles, and area from any three known values, including right triangles and Heron's formula. Free, runs in your browser.

- **Canonical URL:** https://boringtoolskit.com/triangle-calculator/
- **Category:** Everyday Calculators
- **Evidence level:** authored-methodology
- **Reviewed:** August 2026
- **Last verified:** 2026-10-12
- **Privacy:** Inputs and results stay in this browser unless the page clearly labels an external request.

## How it works

Area uses Heron's formula: A = √(s(s−a)(s−b)(s−c)), where s is the semiperimeter (a+b+c)/2. Angles come from the law of cosines, e.g. cos A = (b²+c²−a²)/(2bc). Height to side a is h = 2A/a; inradius r = A/s; circumradius R = abc/(4A).

## Worked example

For a triangle with sides 5, 6, and 7, the semiperimeter is 9, the area is √(9···) = √(9×4×3×2) ≈ 14.70, and the angle opposite side 5 is about 44.4°.

## Assumptions

- You enter three side lengths that satisfy the triangle inequality (each side is shorter than the sum of the other two).
- Angles are reported in degrees.
- The triangle is assumed to be planar (Euclidean).

## Common questions

### How do you find the area of a triangle from its sides?

Use Heron's formula: A = √(s(s−a)(s−b)(s−c)), where s is half the perimeter. For sides 5, 6, and 7 the area is about 14.70 square units.

### How do you find the angles of a triangle?

Use the law of cosines on each angle, then the fact that all three angles sum to 180°. This calculator computes all three from the three side lengths.

### What is the triangle inequality?

A set of three side lengths forms a triangle only if each side is shorter than the sum of the other two. If not, no such triangle exists.

### What is the inradius of a triangle?

The inradius is the radius of the largest circle that fits inside the triangle, tangent to all three sides. It equals the area divided by the semiperimeter (r = A/s).

### What is the circumradius?

The circumradius is the radius of the circle that passes through all three vertices. It equals abc/(4A), where a, b, c are the sides and A is the area.

## Related tools

- /square-footage-calculator/
- /triangle-calculator/
- /square-feet-to-linear-feet/

## Sources

- [Law of cosines](https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-law-of-cosines/a/law-of-cosines)
- [Heron's formula](https://mathworld.wolfram.com/HeronsFormula.html)

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