Triangle Calculator
Solve Any General (Non-Right) Triangle
Choose a tab based on what you know, then solve for the remaining sides, angles, area, and perimeter. Uses the standard convention: side a is opposite angle A, side b opposite angle B, side c opposite angle C.
Enter all three side lengths.
Enter two sides and the angle between them (the included angle).
Enter two angles and the side between them (the included side).
Enter two angles and a side that is not between them — e.g. side a, opposite angle A.
Understanding General Triangle Solving
Unlike the Pythagorean theorem, which only works for right triangles, the Law of Cosines and Law of Sines can solve any triangle — acute, obtuse, or right — from just three known measurements.
A generalization of the Pythagorean theorem to any triangle. It's the go-to tool when you know three sides (SSS) or two sides and the angle between them (SAS), since it lets you solve directly for a missing side or angle without ambiguity.
Relates every side to the sine of its opposite angle in one consistent ratio. It's the natural fit when you know two angles and a side (ASA or AAS), since the third angle follows immediately from the fact that all angles sum to 180°.
The Formulas
Law of Cosines
Law of Sines
Once all three sides are known, the area comes from Heron's formula: with semi-perimeter s = (a + b + c) / 2,
Which Mode Should I Use?
Use SSS when you have all three side lengths and need the angles. Use SAS when you have two sides and know the angle trapped between them. Use ASA when you have two angles and the side that connects them. Use AAS when you have two angles and a side that sits opposite one of them rather than between them. If your triangle happens to contain a 90° angle, the dedicated Right Triangle Calculator offers a more focused workflow built specifically around that case, and the narrower Pythagorean Theorem Calculator handles just a missing side of one.
SSS, SAS, ASA, and AAS each uniquely determine a triangle.
The three interior angles of any triangle always add up to 180°.
Acute, obtuse, or right — the Law of Cosines and Law of Sines apply to them all.
Key Takeaways
- The Law of Cosines and Law of Sines solve any triangle, not just right triangles.
- SSS and SAS lean on the Law of Cosines, while ASA and AAS lean on the Law of Sines.
- For SSS inputs, the triangle inequality must hold — the sum of any two sides must exceed the third.
- Already know it's a right triangle? The Right Triangle Calculator is a faster, purpose-built alternative.
Frequently Asked Questions
- Pick the tab that matches what you know about the triangle: SSS (three sides), SAS (two sides and the angle between them), ASA (two angles and the side between them), or AAS (two angles and a side that isn't between them).
- Fill in the fields for that tab.
- Click "Calculate" to solve every remaining side, every remaining angle, the area, and the perimeter.
They describe which three pieces of a triangle you already know, using S for a known side and A for a known angle, in the order you'd encounter them around the triangle. SSS is three sides. SAS is two sides with the angle between them (the included angle). ASA is two angles with the side between them (the included side). AAS is two angles and a side that is not between them.
Yes — a right triangle is just a special case of a general triangle, so any of the four modes will solve one correctly. That said, if you already know it's a right triangle, the dedicated Right Triangle Calculator is a faster, simpler tool built specifically for that case.
This calculator uses the universal convention: side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C. Keeping this pairing straight is essential — mixing up which side is "included" between two angles is the most common input mistake.
For SSS inputs, the three side lengths must satisfy the triangle inequality — the sum of any two sides must be greater than the third. If it isn't, no triangle can physically close, so the calculator rejects it. For the angle-based modes, the two given angles must add up to less than 180°, since all three angles of any triangle must sum to exactly 180°.
Once all three sides are known (either given directly or solved for), the calculator uses Heron's formula — computing the semi-perimeter s first, then the area as the square root of s(s−a)(s−b)(s−c). This works for any triangle regardless of which mode was used to solve it.