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Free Triangle Calculator

Triangle Calculator

Solve common triangles from sides and angles, then calculate area, perimeter, all three angles, inradius, circumradius and triangle type. Explore more Math Calculators.

△ SSS, SAS & ASA/AAS90° Right triangles✓ Area & perimeter✓ Validation

Calculator

Enter known triangle values

Choose the set of values you know. Side labels follow the standard convention: side a is opposite angle A, side b is opposite B, and side c is opposite C.

The calculator only asks for the values required by the selected solving method.

SSS: enter sides a, b and c
a
b
c
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What is a triangle calculator?

A triangle calculator solves missing sides and angles from a valid set of known measurements. This tool supports several common cases so you can calculate the triangle's area, perimeter and geometric properties without manually switching formulas. For related arithmetic, browse the Scientific Calculator.

Which triangle solving methods are supported?

SSS uses all three sides. SAS uses two sides and their included angle. ASA/AAS uses two angles and one known side. Two right-triangle modes cover either both legs or a hypotenuse plus one leg.

What formulas does the triangle calculator use?

Law of cosines: c² = a² + b² − 2ab cos(C)
Law of sines: a / sin(A) = b / sin(B) = c / sin(C)
Heron's formula: Area = √[s(s − a)(s − b)(s − c)], where s = (a + b + c) / 2

If a calculation involves roots, the Square Root Calculator provides a focused root tool.

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How are triangles classified?

By sides, a triangle can be equilateral, isosceles or scalene. By angles, it can be acute, right or obtuse. The calculator evaluates the solved side and angle values with a small numeric tolerance so rounding does not misclassify a nearly exact relationship.

How do you use this triangle calculator?

  1. Select the known-value mode that matches your problem.
  2. Choose an optional unit label for the side lengths.
  3. Enter the requested sides and/or angles.
  4. Select Solve Triangle.
  5. Review the area, classification, sides, angles, perimeter and radii.

Triangle calculator examples

A 3-4-5 SSS triangle has area 6 and perimeter 12, and it is a scalene right triangle. With SAS values a = 5, b = 7 and C = 60°, the third side is approximately 6.245. You can compare proportional values with the Ratio Calculator.

What are the calculator's limits?

Side lengths must be positive finite numbers. SSS inputs must satisfy the triangle inequality. Angles must form a valid triangle. The page does not accept the ambiguous SSA case because that combination can describe zero, one or two different triangles depending on the measurements.

Frequently asked questions about triangles

It supports SSS, SAS, ASA/AAS, a right triangle from two legs, and a right triangle from a hypotenuse plus one leg.
It validates the triangle inequality, then uses the law of cosines for the angles and Heron's formula for area.
SAS means two sides and the included angle between them. The calculator uses the law of cosines to find the third side, then solves the remaining angles.
ASA and AAS use two angles and one known side. The third angle comes from the 180-degree angle sum, and the remaining sides come from the law of sines.
It identifies the side type as equilateral, isosceles or scalene and the angle type as acute, right or obtuse, using tolerance for floating-point rounding.
The solved side lengths are used with Heron's formula. Right-triangle and SAS inputs are also checked against their standard area relationships.
Yes. Positive finite decimal values are accepted. Angles must be greater than 0 degrees and less than 180 degrees, with valid combinations for the chosen mode.
The calculator uses browser double-precision arithmetic. Irrational side lengths, angles and areas are formatted to a practical number of decimal places for display.

Methodology and calculation scope

The calculator solves real Euclidean plane triangles using the law of cosines, law of sines, Pythagorean theorem and Heron's formula. Trigonometric functions use radians internally and results are displayed in degrees.

Privacy note: The triangle calculations run locally in your browser. Values entered here are not sent to a calculation server.
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