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Triangle from three sides

Find the area, perimeter, angles, inradius and circumradius from three sides. The calculator checks the triangle inequality.

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01

Your inputs

The starting values are an example.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

Your calculation will appear here.

Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

With s=(a+b+c)/2, A=√[s(s−a)(s−b)(s−c)]. cos(α)=(b²+c²−a²)/(2bc).

Worked example

For sides of 3, 4 and 5 cm, the area is 6 cm², perimeter 12 cm, inradius 1 cm and circumradius 2.5 cm.

Things to check

  • Each side must be shorter than the sum of the other two. Equality would give a flat, degenerate triangle.
  • Enter all three sides in the same unit. Each angle is opposite the side with the matching name.

Frequently asked questions

Can I calculate a triangle from only two sides?

Not a general triangle: this calculator needs three sides. For a right triangle, the Pythagoras calculator can find the missing side.