How do I use the Triangle Calculator?

Enter the required values, then calculate. The Triangle Calculator shows results, formulas, and step-by-step work when available. No account is required.

Triangle Calculator – Sides, Angles & Area

How it works

Provide three values including at least one side. Labels: side a opposite A, b opposite B, c opposite C.

a/sin A = b/sin B = c/sin C · c²=a²+b²−2ab cos C · Heron · r=Area/s

When to use

Use this tool when you need to: try 3-4-5 (right, area 6, r=1, R=2.5) or SAS a=9, b=7, C=30° (area 15.75).

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Try 3-4-5 (right, area 6, r=1, R=2.5) or SAS a=9, b=7, C=30° (area 15.75).

Frequently asked questions

What is the Triangle Calculator?: Provide three values including at least one side. Labels: side a opposite A, b opposite B, c opposite C.
How do I use the Triangle Calculator?: Enter the required values, then calculate. The Triangle Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Triangle Calculator use?: a/sin A = b/sin B = c/sin C · c²=a²+b²−2ab cos C · Heron · r=Area/s

Browse categories

Triangle calculator

Enter any three of sides a, b, c and angles A, B, C (at least one side). Solves the remaining measures, area, medians, inradius, and circumradius — same workflow as a full triangle calculator.

How it works

What is a triangle?

A triangle has three sides and three interior angles that always sum to 180°. Side a lies opposite vertex A, b opposite B, and c opposite C. By sides: equilateral (all equal), isosceles (two equal), or scalene (all different). By angles: acute (all < 90°), right (one = 90°), or obtuse (one > 90°). At most one angle can be ≥ 90°. The sum of any two sides is greater than the third (triangle inequality).

Laws and theorems

Pythagorean theorem (right triangles): a² + b² = c² with c the hypotenuse. Law of sines: a/sin A = b/sin B = c/sin C (also equal to 2R). Law of cosines: c² = a² + b² − 2ab cos C, and cyclic permutations — used to find a side (SAS) or an angle (SSS). When two angles are known the third is 180° − A − B. SSA can be ambiguous: zero, one, or two triangles may fit the data.

Area formulas

Base and height: Area = ½bh. Two sides and included angle: Area = ½ab sin C. With three sides (Heron): s = (a+b+c)/2 and Area = √[s(s−a)(s−b)(s−c)]. Example: sides 3, 4, 5 give s = 6 and Area = 6. SAS example: a = 9, b = 7, C = 30° → Area = ½·9·7·sin 30° = 15.75.

Medians, inradius, circumradius

Median from A to the midpoint of a is mₐ = ½√(2b² + 2c² − a²) (and cyclic). Inradius r = Area / s, the radius of the inscribed circle. Circumradius R = abc / (4·Area) = a / (2 sin A), the circle through all three vertices.

Related geometry

Area and solid tools share common formulas with circle, triangle, and coordinate geometry calculators.

How it works

Provide three values including at least one side. Labels: side a opposite A, b opposite B, c opposite C.

a/sin A = b/sin B = c/sin C · c²=a²+b²−2ab cos C · Heron · r=Area/s

When to use

Use this tool when you need to: try 3-4-5 (right, area 6, r=1, R=2.5) or SAS a=9, b=7, C=30° (area 15.75).

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Try 3-4-5 (right, area 6, r=1, R=2.5) or SAS a=9, b=7, C=30° (area 15.75).

Frequently asked questions

What is the Triangle Calculator?: Provide three values including at least one side. Labels: side a opposite A, b opposite B, c opposite C.
How do I use the Triangle Calculator?: Enter the required values, then calculate. The Triangle Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Triangle Calculator use?: a/sin A = b/sin B = c/sin C · c²=a²+b²−2ab cos C · Heron · r=Area/s