Triangle Solver
Solve any triangle from three known values — get every side, angle, perimeter and area with a scale diagram.
- Side a
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- Side b
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- Side c
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- Angle A
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- Angle B
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- Angle C
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- Perimeter
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- Area
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- Type
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How it works
Angle A is opposite side a, angle B is opposite side b and angle C is opposite side c;
angles are always in degrees. Pick what you already know — three sides (SSS), two sides and the angle between them (SAS),
two angles and a side (ASA or AAS), or two sides and a non-included angle (SSA) — and the
remaining sides and angles are solved instantly. SSS and SAS use the law of cosines
(a² = b² + c² − 2bc·cos A); ASA, AAS and SSA use the law of sines
(a / sin A = b / sin B = c / sin C). Area comes from
½·a·b·sin C, so it is exact for every case, not just right triangles.
SSA is the ambiguous case: when the given side is shorter than the other one, two different triangles can fit the same numbers. The solver detects this, tells you, and lets you switch between the acute and obtuse solution with one button. Impossible inputs are caught too — sides that break the triangle inequality (like 1, 2 and 5) or two angles that already add up to 180° get a plain-English explanation instead of a wrong answer. The scale drawing updates with every keystroke so you can see the shape you just described. Everything is computed in your browser with plain JavaScript: nothing is uploaded, and there are no ads or sign-ups.
Frequently asked questions
What three values do I need to solve a triangle?
Any three, as long as at least one is a side: three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), two angles and a side beside them (AAS), or two sides and a non-included angle (SSA). Three angles alone only fix the shape, not the size, so they cannot give you side lengths.
What is the SSA ambiguous case?
When you know two sides and an angle that is not between them, and the given side is shorter than the other one, two different triangles can satisfy the same numbers — one with an acute second angle and one with its obtuse supplement. This solver detects that situation, says so on screen, and lets you switch between both valid triangles with one button.
Is my data sent anywhere?
No. Every calculation runs in your browser with plain JavaScript using the law of sines and the law of cosines. Nothing is uploaded, nothing is stored, and there are no ads or sign-ups — you can even use the page offline once it has loaded.