Triangle Calculator

Solve any triangle given sides and angles. Supports SSS, SAS, AAS, and ASA configurations.

100% Free No Sign-Up Calculated in Your Browser

Side a

Side b

Side c

Side a

Included Angle C (°)

Side b

Angle A (°)

Angle B (°)

Side a (opposite A)

Area

Perimeter

Angle A

Angle B

Angle C

Property	Value

Solve any triangle — find every missing side, angle, and the area — starting from three sides (SSS), two sides and the angle between them (SAS), or two angles and a side (AAS).

How It Works

How Triangle Calculator Works

Given three sides (SSS), the calculator applies the Law of Cosines twice — cos(A) = (b² + c² − a²) / (2bc) and the equivalent formula for angle B — to find two angles directly, then subtracts both from 180° to get the third.

Given two sides and the included angle (SAS), it first uses the Law of Cosines to find the unknown third side, then applies the Law of Cosines again to recover one of the missing angles.

Given two angles and a side (AAS), the third angle follows immediately since a triangle's angles always sum to 180°, and the Law of Sines (a/sin A = b/sin B = c/sin C) finds the remaining sides. Regardless of which mode was used, the area is always computed from the three final side lengths using Heron's formula: Area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter.

Worked Example

See It In Action

For the classic 3-4-5 right triangle (SSS, a=3, b=4, c=5): cos(A) = (16+25−9)/40 = 0.8, so A ≈ 36.87°; cos(B) = (9+25−16)/30 = 0.6, so B ≈ 53.13°; and C = 180 − 36.87 − 53.13 = 90°. With semi-perimeter s = 6, Heron's formula gives Area = √(6×3×2×1) = √36 = 6 sq units, and the perimeter is 12 units — a right scalene triangle.

Real-World Use Cases

Who Uses Triangle Calculator and Why

Solving a triangle from three field-measured side lengths (SSS), such as verifying a surveyed plot's angles.
Finding a triangle's remaining side and angles from two known sides and the angle between them (SAS), common in roof pitch or bracket design.
Computing a triangle's dimensions from two known angles and one side (AAS), as in navigation or bearing problems.
Getting the area of an irregular triangular plot or panel once its three side lengths are known.

Common Mistakes

Mistakes to Avoid

Entering side lengths that violate the triangle inequality (one side longer than the sum of the other two) — the calculator returns no result because no such triangle can physically exist.
Picking the wrong input mode for the values actually known — SSS, SAS, and AAS each expect a specific combination, and mismatching them will produce an invalid or nonsensical solve.
In SAS mode, entering an angle that puts the Law of Cosines calculation outside the valid −1 to 1 cosine range, which also produces no result.

Pro Tips

Tips for Best Results

Before entering SSS values, do a quick check that no one side is longer than the sum of the other two — it takes a few seconds and avoids a wasted calculation.
Once you have a result, the three angles should sum to 180° — use that as a fast sanity check on the output.

Troubleshooting

Fixing Common Problems

I get no result at all after entering my values. — Check that your sides satisfy the triangle inequality (no side longer than the sum of the other two), or in SAS mode that the entered angle doesn't push the cosine calculation out of its valid range.

Glossary

Terms Explained

Law of Cosines: A formula relating a triangle's three sides and one angle — cos(A) = (b² + c² − a²) / (2bc) — used to solve triangles from SSS or SAS input.

Heron's formula: A method for finding a triangle's area directly from its three side lengths, using the semi-perimeter s: Area = √(s(s−a)(s−b)(s−c)).

FAQ

Frequently Asked Questions

What do SSS, SAS, and AAS mean?

These abbreviations describe which parts of the triangle you already know: SSS is three sides, SAS is two sides plus the angle between them, and AAS is two angles plus a side not between them. Each combination uniquely determines the triangle.

How is the area calculated regardless of which values I entered?

Once the calculator has solved for all three side lengths, it applies Heron's formula, which only needs the three sides — so the area calculation is the same final step no matter which input mode you started from.

How does the calculator know if a triangle is a right triangle?

It checks whether any of the three computed angles is within a tiny rounding tolerance of 90°, and labels the shape "Right" in the triangle classification if so.

Why did I get no result at all?

This happens when the entered sides or angles can't form a valid triangle — for example, if one side is longer than the sum of the other two (violating the triangle inequality), or if an SAS angle produces a cosine value outside the valid −1 to 1 range.