Triangle Calculator: Solve Any Triangle Online
This triangle calculator solves any triangle the moment you give it enough measurements. Enter three sides, two sides and an angle, or two angles and a side, and it finds every remaining property — the missing sides, angles, area, and perimeter — automatically as you type.
Three modes cover the work: a General solver for any triangle, a Right Triangle solver that turns two legs into the full solution, and a focused Pythagorean mode for finding the hypotenuse. A live diagram and step-by-step formulas accompany every result.
How to Use the Triangle Calculator
Choose a mode
Click a tab at the top: General for any triangle, Right Triangle when you know both legs of a 90° triangle, or Pythagorean to find the hypotenuse from two legs.
Pick a method (General mode)
Select the method that matches what you know: SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), AAS (two angles and a non-included side), or SSA (two sides and a non-included angle).
Enter your values
Fill in the input fields. Set the length unit (mm, cm, m, in, ft) and angle mode (degrees or radians) from the dropdowns. Results update automatically as you type.
Read the results
The results show every computed property — sides, angles, area, perimeter, inradius, and circumradius — while the live diagram redraws to match. Open Solution Steps to see each formula and how the values were derived.
Features
General Solver with 5 Methods
Solve any triangle using the Law of Cosines and Law of Sines, covering all five cases: SSS, SAS, ASA, AAS, and SSA.
Right Triangle Solver
Enter two legs to get the hypotenuse, all three angles, area, perimeter, and the sin, cos, and tan ratios for the acute angles.
Pythagorean Theorem
A focused mode for a² + b² = c². Enter two legs and get the hypotenuse with a clear breakdown of each step.
Step-by-Step Solutions
Every result comes with the formula that was applied and how each value was derived, so you can verify and learn the math.
Live Triangle Preview
An SVG diagram redraws in real time as you type, showing accurate proportions with labeled sides and angles.
Flexible Units & Angles
Choose from five length units (mm, cm, m, in, ft) and switch between degrees and radians without re-entering values.
Complete Results
Beyond sides and angles, get area via Heron's formula, perimeter, inradius, and circumradius for every valid triangle.
Input Validation
Inputs are checked against the triangle inequality and angle limits, with clear messages when no valid triangle can be formed.
Frequently Asked Questions
How do I find a missing side of a triangle?
Pick the General method that matches what you already know. If you have two sides and the angle between them, use SAS and the Law of Cosines fills in the third side. If you have two angles and a side, use ASA or AAS and the Law of Sines finds the rest. The missing sides appear instantly in the results.
How do I find the angles of a triangle from three sides?
Choose the SSS method and enter all three side lengths. The calculator applies the Law of Cosines to each angle and returns all three. Open Solution Steps to see the exact cos(A) = (b² + c² − a²) / (2bc) calculation.
How is the area of a triangle calculated?
For a general triangle, the area is computed with Heron's formula: √(s(s − a)(s − b)(s − c)), where s is half the perimeter. Once all three sides are known from any method, the area, perimeter, inradius, and circumradius are reported automatically.
What do SSS, SAS, ASA, AAS, and SSA mean?
Each letter describes one known measurement, where "S" is a Side and "A" is an Angle, listed in order around the triangle. SSS means all three sides are known; SAS means two sides and the angle between them; ASA and AAS mean two angles with an included or non-included side; SSA means two sides and a non-included angle.
How do I find the hypotenuse of a right triangle?
Use the Pythagorean tab, enter the two legs, and it returns the hypotenuse from c = √(a² + b²). The Right Triangle tab does the same and adds all angles, area, perimeter, and the sin, cos, and tan ratios.
What is the difference between the Right Triangle and Pythagorean tabs?
Both start from two legs of a right triangle. The Pythagorean tab focuses on one answer — the hypotenuse via a² + b² = c². The Right Triangle tab gives a complete solution: all sides, all angles, area, perimeter, inradius, circumradius, and the trigonometric ratios.
Why does it say the triangle is invalid?
A valid triangle must satisfy the triangle inequality — the sum of any two sides must exceed the third — and its angles must stay within range (each between 0° and 180°, summing to less than 180°). If your values break these rules, no real triangle exists and the calculator shows an error.
What are inradius and circumradius?
The inradius (r) is the radius of the largest circle that fits inside the triangle (the inscribed circle). The circumradius (R) is the radius of the circle that passes through all three vertices (the circumscribed circle). Both are reported for every valid triangle.
Can I use radians instead of degrees?
Yes. Use the angle mode dropdown to switch between degrees and radians, and every angle input and result adjusts accordingly. You can also change the length unit at any time without re-entering values.
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