NumberTally Triangle Calculator
Find the area and perimeter of any triangle in seconds. Enter a base and height for the classic area formula, enter all three sides to get the perimeter plus the area from Heron's formula — or switch to the solver to find every missing side and angle from any three values (SSS, SAS, ASA, AAS, or the ambiguous SSA).
Advanced options
Fill in any 3 values, including at least one side — the solver detects the case and finds everything else. Angles are in degrees. Side a sits opposite angle A, side b opposite B, side c opposite C.
Two roads to the area
Base × height ÷ 2 is the fastest when you know the altitude. Heron's formula — area = √(s(s−a)(s−b)(s−c)) with s = perimeter/2 — needs only the three sides and works for any triangle, no height required. When you enter three sides, the comparison box checks both routes against each other.
The triangle inequality rule
Three lengths only form a triangle if each pair sums to more than the third side: a+b>c, a+c>b, b+c>a. The calculator validates this automatically — 2, 3, 10 can never close into a triangle, no matter how you arrange them.
Frequently Asked Questions
How do you find the area of a triangle with base and height?
Multiply base × height and halve it: A = ½bh. The height must be perpendicular to the base.
What is Heron's formula?
Area = √(s(s−a)(s−b)(s−c)), where s is the semiperimeter (a+b+c)/2. It finds the area from three sides alone.
What is the triangle inequality rule?
The sum of any two sides must exceed the third. If it doesn't, the shape cannot close.
Can you find a triangle's area using only its three sides?
Yes — that is exactly what Heron's formula is for. No angles or heights needed.
How do I check if three side lengths make a valid triangle?
Test all three pair-sums against the remaining side. This calculator does it for you and explains any failure.
What do SSS, SAS, ASA, and AAS mean?
They name which three values you know: three sides (SSS), two sides and the included angle (SAS), or one side and two angles (ASA/AAS). Each case has its own solving path — the solver above detects yours automatically.
What is the ambiguous SSA case?
With two sides and a non-included angle, the law of sines can give two valid angles (an acute one and its supplement), so two different triangles fit the same inputs. The solver shows both solutions when they exist.