Enter the three side lengths of a triangle to calculate its area, perimeter, and angles.
A triangle calculator finds the area, perimeter, and interior angles of a triangle when you know the lengths of its three sides, using Heron's formula and the law of cosines.
"Solving" a triangle means finding all its unknown sides and angles, and the method depends entirely on what information you already have. If you know two sides and the included angle, the Law of Cosines finds the third side. If you know two angles and one side, the Law of Sines finds the rest. For right triangles specifically, basic trigonometric ratios (sine, cosine, tangent) or the Pythagorean theorem are usually simpler and faster than the general laws.
This comes up constantly outside math class - carpenters and construction workers use triangle calculations to verify that a corner is truly square (using the 3-4-5 rule, a practical application of the Pythagorean theorem), surveyors use triangulation to measure distances that can't be measured directly, and navigation historically relied on triangle-solving to calculate position from known reference points.
Not every combination of three side lengths forms a real triangle - the triangle inequality theorem states that the sum of any two sides must be greater than the third side. A calculator that checks this before attempting to solve saves you from getting a nonsensical result when the input values don't actually describe a possible triangle.
Depending on which triangle measurements are already known — sides, angles, or a combination — different formulas apply to calculate the remaining unknown properties. The Pythagorean theorem works specifically for right triangles, while the Law of Sines and Law of Cosines extend triangle calculations to any triangle shape, not just right triangles, making them essential tools whenever a triangle doesn't contain a 90-degree angle.
Triangle calculations show up constantly in practical surveying, construction, and navigation contexts — calculating an unreachable distance using known angles and a measured baseline (a technique called triangulation), determining structural angles for roof framing, and calculating indirect distances in GPS and mapping systems all rely on the same fundamental triangle relationship formulas.
Not every combination of three side lengths can actually form a valid triangle — the triangle inequality theorem states that the sum of any two sides must be greater than the third side, or the shape simply can't close into a triangle at all. This is worth checking before attempting further triangle calculations with a given set of three side lengths, since inputting an invalid combination will produce a meaningless or undefined result rather than a genuine triangle solution.
Triangles are classified by their angles (acute, right, or obtuse, based on whether all angles are under 90 degrees, one equals 90 degrees, or one exceeds 90 degrees) and separately by their sides (equilateral, isosceles, or scalene, based on how many sides are equal length). A given triangle has both an angle classification and a side classification simultaneously, and knowing both helps quickly identify which specific formulas and shortcuts apply.
The tool checks the triangle inequality rule and will show an error if the sides you entered cannot form a valid triangle.
The calculator checks the triangle inequality theorem first - if the sum of any two sides isn't greater than the third, the inputs can't form a real triangle and will be flagged.
Yes, right triangles can be solved with simpler methods like the Pythagorean theorem or basic trigonometric ratios, both of which the calculator handles.
The Law of Sines works best when you know angles and their opposite sides, while the Law of Cosines works best when you know two sides and the angle between them.
