Enter three side lengths and get the area, all three angles, the perimeter and both radii.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
Enter three positive side lengths in the same unit. Length results use that input unit (u), and area uses its square (u²); this calculator does not choose or convert a measurement unit.
Recomputed from this page's implementation at build time · checked 2026-10-22
The triangle inequality is strict: two sides must sum to more than the third, not to the same amount. That single word decides which inputs are refused, and it leaves a narrow band of legal but almost flat triangles where some results stop being usable.
| 1.9 | 1.99 | 1.999 | 1.9999 | 1.999999 | |
|---|---|---|---|---|---|
| Area | 0.297 | 0.099 | 0.032 | 1.0e-2 | 1.0e-3 |
Every column is a legal triangle. The area falls by roughly a factor of three for each extra digit, and no column is ever rejected, because the triangle inequality is strict but the margin is not bounded below.
Every field lands on a round number, which makes this the reference case for the rest of the page. The right angle sits opposite the longest side, so here it lands on angle C purely because side C is the one measuring 5.
Equal sides produce equal angles, and the inradius lands at half the circumradius: 1.7321 against 3.4641 once both are rounded, which is the ratio you should expect for any equilateral triangle at any size.
Legal, because the two short sides still add up to slightly more than the long one. The area is now below the two-decimal display precision, so it switches to exponential form and prints as 1e-3, which is 0.001. The circumradius climbs to 500 while the height to side A collapses to 0.002. Correct results, and a display that has quietly changed notation on you.
The area is unchanged, but the right angle has moved to angle A. Sides are read by position, not sorted by length, so the angle named for a side is always the one opposite it — no reordering happens behind your back.
triangle
Two sides that add up to exactly the third
This is a segment with a point on it, not a triangle. Equality fails the strict inequality, so the input is refused rather than returned with zero area and angles of zero and 180 degrees.
triangle
A degenerate isosceles case
The same failure with equal short sides. It is worth testing separately because it is the shape most people type when they want to see what happens at the boundary.
inputError
A side of zero
A zero-length side is rejected before the geometry check runs, so it produces a different error from the degenerate cases above. Two kinds of failure, two messages — that distinction is what makes the refusal diagnosable.
inputError
A negative side
Lengths are not signed. Taking the absolute value would quietly turn a typo into a valid triangle, so the input is rejected instead.
calculator.netchecked 2026-10-22
Why they built it that waySix fields, three sides and three angles, so any three values can drive the solution. That flexibility is the product - a solver that only accepted sides would be a different tool, and the side-side-angle ambiguity has to be handled rather than avoided.
If you know two angles and one side, this page cannot solve it and will not attempt to. The scope limit is deliberate: a three-field page cannot silently mis-handle a combination it never offered to accept.
Enter 1, 1 and 1.999999: the result is accepted, with an angle close to 180 degrees and a circumradius in the hundreds. Then change the long side to 2 and confirm the triangle is refused outright.
Verified Heron's area against the base-height formula on the 3-4-5 case · impl f5e3515f
Start with the semiperimeter s = (a + b + c) / 2. Heron’s formula gives the area A = √[s(s − a)(s − b)(s − c)]. Each angle comes from the cosine rule; Angle opposite a is opposite Side a, and likewise for b and c. The inradius A/s is the radius of the circle inside and tangent to all three sides. The circumradius abc/(4A) is the radius of the circle through all three vertices. Height to side a is 2A/a. Enter the sides in the same unit: centimetres give length results in centimetres and area in square centimetres. Decimal results are rounded; very small positive areas use scientific notation.
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
A = √(s(s−a)(s−b)(s−c)); α = acos((b²+c²−a²) ÷ 2bc); r = A ÷ s; R = a × b × c ÷ 4A
Enter all sides in the same unit u. Length outputs use u and area uses u²; no unit is selected or converted. Invalid triangles suppress results.
Enter the lengths of all three sides in the same unit. This calculator uses those sides to find the area, angles, perimeter, inradius and circumradius.
The two shorter sides must add up to more than the longest side. Since 1 + 2 is less than 5, those lengths cannot form a triangle. The calculator shows an error and withholds results until the sides are valid.
Enter all three side lengths from 0.01 to 100,000 in the same unit. The sum of any two sides must be greater than the third; equality is a flat, degenerate shape and is rejected. The symbol u stands for your chosen length unit and u² for its square. For example, if the sides are in metres, area is in square metres. This tool does not convert units.
For Side a = 5, Side b = 4 and Side c = 3, the semiperimeter is 6 and Heron’s formula gives area √(6 × 1 × 2 × 3) = 6 square units. The perimeter is 12 units. The angles opposite a, b and c are 90°, about 53.13° and about 36.87°. The inradius is 1 unit, the circumradius 2.5 units, and the height to side a is 2.4 units.