Triangle Calculator
Pick what you know — three sides, two sides and an angle, or two angles and a side — and the full triangle is solved instantly.
Three sides. Side a is opposite angle A, b opposite B, c opposite C.
How it works
- Choose the input mode that matches what you know: SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side) or AAS (two angles and a non-included side).
- Type the known side lengths and angles in degrees — results update live as you type, and invalid combinations show a clear error.
- Read off every side, angle, the area, perimeter, heights, inradius and circumradius, and check the to-scale drawing with labeled vertices.
Frequently asked questions
- How does the triangle calculator solve for the unknown sides and angles?
- It applies standard trigonometry: the Law of Cosines for SSS and SAS cases and the Law of Sines for ASA and AAS cases. Once all three sides are known, angles are recovered with inverse cosine, so the angle sum is always exactly 180 degrees.
- How is the area of the triangle calculated?
- For SSS input the area comes from Heron’s formula using the semi-perimeter. For SAS input it uses the direct formula ½·a·b·sin(C), which is exact for two sides and the included angle. The result panel notes which formula was applied.
- Why do I get an error saying my sides can’t form a triangle?
- Three lengths only form a triangle when each side is shorter than the sum of the other two — the triangle inequality. If one side is too long, the other two can’t reach each other. Likewise, two angles must sum to less than 180 degrees or no third angle remains.
- Are my measurements sent to a server?
- No. Every calculation and the triangle drawing run entirely in your browser with JavaScript — nothing is uploaded or stored. You can even keep using the page offline once it has loaded.
- What are the inradius and circumradius shown in the results?
- The inradius is the radius of the largest circle that fits inside the triangle, computed as area divided by semi-perimeter. The circumradius is the radius of the circle passing through all three vertices, from the formula abc / 4·area. Both are useful in geometry problems and construction layout.
About this tool
This triangle calculator solves a complete triangle from the minimum information that defines one. Choose SSS to enter three sides, SAS for two sides and the included angle, ASA for two angles and the side between them, or AAS for two angles and a side opposite one of them. From that input it computes every remaining side and angle, then derives the area, perimeter, all three heights, the inradius and circumradius, and classifies the triangle as equilateral, isosceles or scalene, and as acute, right or obtuse.
Everything runs client-side in your browser — no values are transmitted anywhere, and results appear live as you type. The math follows the classical solution paths: the Law of Cosines converts three sides into angles (SSS) or closes the third side from two sides and an included angle (SAS), while the Law of Sines scales a triangle whose angles are fully known (ASA and AAS). Area uses Heron’s formula when three sides are given and the ½·a·b·sin(C) formula for angle-based input; the panel tells you which was used. Input is validated continuously, so a violated triangle inequality or an angle sum reaching 180 degrees produces an immediate, specific error instead of nonsense numbers.
Typical uses include checking geometry homework step by step, laying out rafters, braces and gussets in carpentry or metalwork, verifying survey sketches, and computing material area for triangular panels or sails. Because heights and both radii are included, it also covers problems that most basic solvers skip, such as finding the altitude to a specific side or sizing an inscribed circle.
A practical tip: measure in one consistent unit — the calculator is unit-agnostic, so sides in centimeters give area in square centimeters. Angles are always entered and reported in degrees. The drawing below the results is rendered to scale from the solved vertices, so a quick glance confirms whether the shape matches what you expect before you rely on the numbers.