Triangle Calculator

Choose the measurements you know. Lowercase letters name sides; the matching uppercase letter names the opposite angle. All side lengths use the selected unit, and all angles use degrees.

Use three sides, two sides with their included angle, two angles with side c, or sides a and b with angle A opposite a. The last case can produce zero, one or two triangles; both valid solutions are displayed.

A + B + C = 180°; area = ab sin(C) / 2
c² = a² + b² − 2ab cos(C); a/sin(A) = b/sin(B) = c/sin(C)

For three sides, area follows Heron’s formula: √[s(s−a)(s−b)(s−c)], where s is half the perimeter. A triangle with sides 5, 5 and 6 has area 12 and equal angles opposite the two sides of length 5.

The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.

Length unit

cm

Known measurements

Three sides (SSS)

Side a

3 cm

Side b

4 cm

Side c

5 cm

Primary result: Area: 6 cm².

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

Requires a non-degenerate flat triangle. The longest side must be shorter than the sum of the other two. Nearly degenerate triangles are sensitive to measurement error. The drawing is a schematic, not a full-size template or an answer to a missing worksheet image.