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Triangle Calculator

Calculate area, perimeter, angles and heights of a triangle from its three sides.

Details

Your Results

What Triangle Calculator does

Given three side lengths, everything else about a triangle is determined. Area comes from Heron's formula, angles from the law of cosines, and each height from the area and the corresponding base.

The tool also checks the triangle inequality, since not every set of three lengths can form a triangle at all.

  • Area via Heron's formula
  • Perimeter
  • All three interior angles
  • Height to each side
  • Validity check on the three lengths

How to use Triangle Calculator

  1. 1

    Enter the three sides

    Use the same unit for all three; the result follows that unit.

  2. 2

    Read the results

    Area, perimeter, angles and heights are calculated together.

Example

The 3-4-5 right triangle

Input

a = 3, b = 4, c = 5

Output

Area      = 6
Perimeter = 12
Angles    = 36.87°, 53.13°, 90°

The right angle appears opposite the longest side, which is what makes 3-4-5 a right triangle.

When to use it

Checking a plot or a roof pitch

Three measured sides are enough to establish the area and every angle without a protractor.

Confirming a right angle

If one calculated angle comes out at 90 degrees, the corner is square. This is the builder's 3-4-5 check with arbitrary lengths.

Geometry homework

Verify an answer where Heron's formula and the law of cosines are the intended methods.

Limits and known behaviour

  • Only the side-side-side case is supported. Combinations involving known angles, such as side-angle-side, are not.
  • Any two sides must sum to more than the third, or no triangle exists; the tool reports that rather than returning a number.
  • Results are unitless — enter centimetres and the area is in square centimetres.
  • Angles are reported in degrees.
  • Floating-point rounding can leave the angle sum a fraction away from exactly 180 degrees.

Privacy and data handling

Runs entirely in your browser

  • The calculation runs in this page. Nothing you enter is transmitted or stored.
  • The tool works offline once the page has loaded.

Site-wide data handling, including analytics and advertising, is described in the privacy policy.

Frequently asked questions

Why does it say my triangle is invalid?

Because of the triangle inequality: each side must be shorter than the sum of the other two. Sides of 1, 2 and 5 cannot close into a triangle.

Can I calculate from two sides and an angle?

Not with this tool, which takes three sides.