What information do I need to solve a triangle?

You need at least 3 pieces of information, and at least one must be a side length. Valid combinations include SSS, SAS, ASA, and AAS. AAA (all angles) defines shape but not size.

What is the law of cosines used for?

The law of cosines is used when you know three sides (SSS) or two sides and the included angle (SAS). It's a generalization of the Pythagorean theorem for non-right triangles.

What is Heron's formula?

Heron's formula calculates triangle area from the three side lengths without needing height. It uses the semi-perimeter s = (a+b+c)/2: Area = √(s(s-a)(s-b)(s-c)).

What is the inradius of a triangle?

The inradius is the radius of the largest circle that fits inside the triangle. It equals Area / s, where s is the semi-perimeter.

What is the circumradius of a triangle?

The circumradius is the radius of the circle that passes through all three vertices of the triangle. It equals a / (2·sin(A)), where a is any side and A is the opposite angle.

Math

↵ to calculate

Triangle Calculator - Area Sides Angles Solver Online

Solve any triangle given sides and angles. Calculate area, perimeter, angles, and height using the law of cosines and sines.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

📏 Some countries say ‘30 degrees’ and others say ‘86 degrees’ for the same weather! Some say ‘5 km’, others say ‘3 miles’. This tool swaps between them instantly so you always know what it means.

📌 Direct Answer & Summary

A triangle calculator solves any triangle given at least three values (with at least one being a side). It computes all missing sides and angles, as well as the area, perimeter, height, inradius, and circumradius using the law of cosines, law of sines, and Heron's formula.

Enter any 3 values (at least one side). Leave the rest blank.

Side a

Side b

Side c

Angle A (°)

Angle B (°)

Angle C (°)

What is Triangle Calculator - Area Sides Angles Solver Online?

How to use it

1️⃣ Enter any three known values — sides a, b, c and/or angles A, B, C — leaving unknowns blank.
2️⃣ At least one side must be provided; angles alone don't define a unique triangle size.
3️⃣ Results including area, perimeter, and all six triangle values appear automatically.
4️⃣ If the combination is impossible or ambiguous, an error message will appear.

Formula

Law of cosines: c² = a² + b² - 2ab·cos(C). Law of sines: a/sin(A) = b/sin(B) = c/sin(C). Heron's formula: Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2.

💡 See it in action — a real example

For a triangle with sides a=3, b=4, c=5: the law of cosines gives angle C = arccos((9+16-25)/24) = 90°. This is a right triangle with area = (3×4)/2 = 6 and perimeter = 12.

❓ Common questions

What information do I need to solve a triangle?: You need at least 3 pieces of information, and at least one must be a side length. Valid combinations include SSS, SAS, ASA, and AAS. AAA (all angles) defines shape but not size.
What is the law of cosines used for?: The law of cosines is used when you know three sides (SSS) or two sides and the included angle (SAS). It's a generalization of the Pythagorean theorem for non-right triangles.
What is Heron's formula?: Heron's formula calculates triangle area from the three side lengths without needing height. It uses the semi-perimeter s = (a+b+c)/2: Area = √(s(s-a)(s-b)(s-c)).
What is the inradius of a triangle?: The inradius is the radius of the largest circle that fits inside the triangle. It equals Area / s, where s is the semi-perimeter.
What is the circumradius of a triangle?: The circumradius is the radius of the circle that passes through all three vertices of the triangle. It equals a / (2·sin(A)), where a is any side and A is the opposite angle.

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