Triangle Calculator

What does it work out from three sides?

Area, perimeter, all three angles, whether the triangle is right-angled, and whether it is equilateral, isosceles or scalene.

How is the area calculated without a height?

Heron's formula. With s as half the perimeter, the area is √(s(s−a)(s−b)(s−c)). It needs only the three side lengths, which is why you are not asked for a height.

How are the angles found?

The law of cosines, rearranged for the angle: each angle is the arc-cosine of (b² + c² − a²) / 2bc, converted from radians to degrees. The third angle is then taken as 180 minus the other two, which also guards against small rounding drift.

Why did it refuse my three numbers?

Because they cannot form a triangle. Any two sides must together exceed the third — the triangle inequality — so 1, 2 and 5 has no solution. Rather than return a nonsense area, the tool declines. A negative or zero length is rejected for the same reason.

How does it decide a triangle is right-angled?

By looking at the angles it has already solved, not by testing Pythagoras on the sides. All three angles come from the law of cosines first, and the triangle is reported as right-angled when any one of them is within 0.01 degrees of 90.

Working from the angles is what makes the check usable on measured input. An exact side-based comparison would almost never report true, because sides taken from real measurements rarely satisfy the equation exactly. A hundredth of a degree is tight enough that nothing visibly off-square passes, and loose enough that 3-4-5 and its scaled cousins are recognised despite the rounding in between.

What is the difference between isosceles and equilateral here?

Equilateral means all three sides equal; isosceles means at least two. A triangle with all three equal satisfies both, and the tool reports the more specific one — equilateral.

Can I solve from two sides and an angle instead?

Not in this tool. It works from three sides only, the case where the triangle is fully determined without ambiguity. Other combinations sometimes admit two valid triangles, which needs a different interface to resolve.

Do the angles always add to 180?

In the output, yes, because the third is computed as the remainder rather than independently. That is deliberate — it keeps the result internally consistent instead of showing 179.9999 from accumulated rounding.

Is anything sent to a server?

No. The geometry runs in your browser.