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Triangle Calculator: Area, Angles and Type from 3 Sides

This free triangle calculator takes three side lengths and returns the area, perimeter, all three angles and the type of triangle. It checks that the sides can really form a triangle.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

Three side lengths fix a triangle completely. From them you can get the area, the angles, the type of triangle and even the radius of the circle drawn inside it. This is useful for plots of land, roof trusses, sails, crafts and geometry class.

Type the three sides and the tool does the rest, after checking that they form a valid triangle.

How to Use This Tool

  1. Type the lengths of sides a, b and c.
  2. Press Calculate.
  3. Read the area, perimeter and the three angles.
  4. Check the type of triangle in the table.

How the Calculation Works

Perimeter = a + b + c. Semi-perimeter s = perimeter ÷ 2. Area (Heron) = √(s(s − a)(s − b)(s − c)). Angles come from the law of cosines. The inradius is area ÷ s, and the circumradius is abc ÷ (4 × area).

Worked Example

For sides 7, 8 and 9, s = 12 and the area is √(12 × 5 × 4 × 3) = 26.83. The angles are 48.19°, 58.41° and 73.40°, so the triangle is scalene and acute.

Common Uses

  • Land and plot measurements.
  • Roof, truss and frame design.
  • Sewing and craft patterns.
  • Maths and exam work.

Tips and Common Mistakes

  • Use the same unit for all sides.
  • Angles add up to 180 degrees, a quick check.
  • If the sides satisfy a² + b² = c², the triangle is right-angled.

Next, you may need the Pythagorean theorem calculator, area calculator, distance, midpoint and slope calculator, volume calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Use Heron’s formula. Let s be half the perimeter. The area is √(s(s − a)(s − b)(s − c)).
With the law of cosines. The angle opposite side a is arccos((b² + c² − a²) ÷ 2bc), and the same pattern gives the others.
When each side is shorter than the sum of the other two. This is the triangle inequality, and the tool checks it.
By sides: equilateral (all equal), isosceles (two equal) or scalene (none equal). By angles: acute, right or obtuse.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.