SSS triangle angle calculator
Works out the angles of any triangle from its sides alone using the law of cosines. Useful for drawing, woodwork and land plots.
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How to use it
- Enter side a, side b and side c.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
cos A = (b² + c² - a²) / (2bc), and the same pattern for B and C. Area by Heron: √(s(s-a)(s-b)(s-c)), where s is half the perimeter.
Example
Inputs: Side a = 7, Side b = 8, Side c = 9. Result: Angle A (opposite a): 48.1897 °; Angle B (opposite b): 58.4119 °; Angle C (opposite c): 73.3985 °.
Limits and caveats
- Any two sides must add up to more than the third, or there is no triangle.
- Use one length unit; the area is in that unit squared.
Questions about this tool
Do three sides fix a triangle completely?
Yes. Three valid lengths give exactly one triangle with fixed angles, which is the SSS congruence case.
Do the angles always add up to 180?
Yes, for every flat triangle. A tiny difference far after the decimal point can appear from floating point arithmetic.
Which angle is the largest?
The largest angle is always opposite the longest side, and the smallest is opposite the shortest.