CalcArcade.

Triangle Calculator

Enter the lengths of the three sides. The calculator checks that they can make a triangle, then gives the area, the perimeter, all three angles and the type of triangle.

Your numbers

Result

How we calculate it

Three lengths make a triangle only when the longest is shorter than the other two added together. The area comes from Heron’s formula, area = √(s × (s − a) × (s − b) × (s − c)), where s is half the perimeter.

Each angle comes from the law of cosines: cos A = (b² + c² − a²) ÷ (2 × b × c). The type by sides is equilateral (all equal), isosceles (two equal) or scalene (none). By angles it is acute, right or obtuse, found by comparing the square of the longest side with the squares of the other two. For 3, 4 and 5 the area is 6 and the triangle is right.

Assumptions and limits

  • Use the same unit for all three sides. The area is in that unit squared.
  • Sides that only just fail the test, such as 1, 2 and 3, make a flat shape with no area, so they are rejected.
  • Angles are shown in degrees and add up to 180.

Frequently asked questions

How do I know if three lengths can make a triangle?

Add the two shorter sides. If the total is greater than the longest side, they can form a triangle. For 2, 3 and 6, 2 + 3 is 5, which is less than 6, so they cannot.

What is Heron’s formula?

It gives the area of a triangle from its three sides alone. Work out s, half the perimeter, then take the square root of s times (s − a) times (s − b) times (s − c).

How do I tell if a triangle is right, acute or obtuse?

Compare the square of the longest side with the sum of the squares of the other two. Equal means right, larger means obtuse and smaller means acute.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Side a = 3; Side b = 4; Side c = 5.

  • Area 6
  • Perimeter 12
  • Angle A 36.87 degrees
  • Angle B 53.13 degrees
  • Angle C 90.00 degrees
  • Type by sides Scalene
  • Type by angles Right

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.