Triangle Calculator
Solve a triangle using side lengths, angles, or two perpendicular legs. View the triangle diagram and calculate its area, perimeter, height, and missing measurements.
Choose what you know
Select a method and enter your measurements below.
Enter measurements
Enter the lengths of all three sides.
Triangle diagram
Changes as you enter measurements
Illustrative diagram, scaled to the calculated proportions.
Your results
How to use the Triangle Calculator
This free Triangle Calculator helps you work with the three sides and three interior angles of a triangle. Choose the calculation method that matches your known measurements, enter the numbers, and select your unit. The diagram updates to show the calculated shape, while the results display its missing sides, angles, area, perimeter, and height.
You can solve a triangle in four ways. With three sides (SSS), enter the lengths of a, b, and c. With two sides and their included angle (SAS), enter sides a and b and the angle C between them. With two angles and a side, enter angles A and B and the length of side c, opposite the remaining angle. For a right triangle, enter its two perpendicular legs. You do not need to convert the values into a particular unit before calculating; just keep all side measurements in the same unit.
What do the letters mean?
Triangles have three vertices labeled A, B, and C. The side opposite vertex A is called a, the side opposite B is b, and the side opposite C is c. This naming rule connects each side to its opposite angle. The calculator follows that convention so its diagram and formulas stay consistent in every mode.
Triangle area formulas
Area is the amount of space inside the triangle. When you know the base and the perpendicular height, multiply them and divide by two. When you know the three side lengths but not the height, Heron’s formula finds the area using the semiperimeter.
Heron’s formula: Area = √[s(s − a)(s − b)(s − c)], where s = (a + b + c) / 2
The calculator also shows the height measured perpendicular to side c. Because c is treated as the base for this calculation, that height equals twice the area divided by c. The unit for area is squared: if sides are measured in centimeters, the area is in square centimeters.
How perimeter and angles are calculated
Perimeter is the total distance around the triangle. Add the lengths of the three sides: a + b + c. A triangle’s interior angles always sum to 180 degrees. The calculator uses the law of cosines when sides are known and the law of sines when two angles and a side are known. For a right triangle, the Pythagorean theorem finds the hypotenuse.
For example, a right triangle with perpendicular sides of 3 cm and 4 cm has a hypotenuse of 5 cm. Its perimeter is 12 cm and its area is 6 cm². Try these measurements using the Right Triangle tab to see the matching diagram and results.
Types of triangles
Triangles are classified by both their side lengths and their angles. Equilateral triangles have three equal sides and three 60° angles. Isosceles triangles have at least two equal sides. Scalene triangles have three different side lengths.
An acute triangle has three angles smaller than 90°. A right triangle has one 90° angle. An obtuse triangle has one angle greater than 90°. Results show both classifications, making it easier to check your work.
Frequently asked questions
Can three side lengths always make a triangle?
No. The sum of the two shorter sides must be greater than the longest side. For example, 2, 3, and 6 cannot form a triangle because 2 + 3 is less than 6. The calculator checks this rule and displays an error for impossible measurements.
Does this calculator work with inches and feet?
Yes. Select inches, feet, centimeters, meters, or unitless values. Angles are entered in degrees. The selected unit changes the displayed labels; it does not convert values you have already entered. Keep the side measurements in the same unit.
Why do I need two angles and a side?
Angles alone determine the shape of a triangle but not its size. One side length is needed to establish the scale, after which the remaining sides can be calculated with the law of sines.
How accurate are the results?
The calculator uses JavaScript arithmetic and displays rounded results, usually to four decimal places. Small rounding differences are normal. For measurements used in construction, design, or manufacturing, verify the inputs and required tolerances independently.
What is the height shown in results?
It is the perpendicular distance from vertex C to the straight line containing side c, also known as the altitude to c. For an obtuse triangle, that line may extend beyond the triangle itself.
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Tip: The diagram is a guide, not a substitute for accurate drawing or a scaled engineering plan. Use the numerical results for calculations and check that your chosen method matches the measurements you actually know.