Triangle Calculator
Enter your values below and click Calculate for instant results.
Solve any triangle from three known values. Supports SSS, SAS, ASA, and right triangle inputs. Shows all sides, angles, area, and perimeter.
Enter your values below and click Calculate for instant results.
A triangle has six measurements: three sides and three angles. If you know at least three of these values (with at least one being a side), you can calculate all the others. This calculator handles four common scenarios: three sides known (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), and right triangle problems.
The three angles of any triangle always sum to exactly 180 degrees. This is one of the most fundamental theorems in Euclidean geometry and can be used as a quick check on any triangle calculation.
The law of cosines generalizes the Pythagorean theorem to work for all triangles, not just right triangles. It states that c squared equals a squared plus b squared minus 2ab times the cosine of angle C. This calculator uses the law of cosines when solving SSS and SAS triangles.
The law of sines states that the ratio of each side to the sine of its opposite angle is constant throughout any triangle. This is used to solve ASA triangles and other cases where the law of cosines does not apply directly.
Once all three sides are known, the area can be calculated using Heron's formula: the area equals the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (half the total perimeter). This calculator applies Heron's formula to all triangle types once the sides have been determined.