This free online triangle calculator finds the perimeter, area, and all three interior angles of a triangle from its three side lengths. Enter sides a, b, and c to get an instant solution using Heron's formula and the law of cosines.
How to Use the Triangle Calculator
Enter the length of "Side a".
Enter the length of "Side b".
Enter the length of "Side c".
Click "Calculate" to see the perimeter, area, and all three angles.
What the Calculator Does With Your Three Sides
Three side lengths fix a triangle completely, so nothing else is needed. The tool first checks the triangle inequality: each pair of sides must add up to more than the third. It then works out:
Perimeter = a + b + c.
Area by Heron's formula, using the semi-perimeter s = (a + b + c) ÷ 2 and Area = √(s(s − a)(s − b)(s − c)).
Each angle by the law of cosines. Angle A is the angle opposite side a, Angle B is opposite side b, and Angle C is opposite side c. The three angles always add up to 180°, allowing for rounding.
Every result is rounded to 2 decimal places. Angles are in degrees, and the area is in the square of the unit you entered.
Worked Example: Sides 7, 8 and 9
Check: 7 + 8 = 15 is more than 9, 8 + 9 = 17 is more than 7, and 7 + 9 = 16 is more than 8, so the sides form a triangle.
Perimeter = 24, so s = 12. Then s − a = 5, s − b = 4 and s − c = 3.
Angle A = arccos((8² + 9² − 7²) ÷ (2 × 8 × 9)) = arccos(96 ÷ 144) ≈ 48.19°. In the same way, Angle B ≈ 58.41° and Angle C ≈ 73.40°.
Identifying the Type of Triangle From the Result
Sides
Area
Angles A, B, C
Type
5, 5, 5
10.83
60°, 60°, 60°
Equilateral (all sides and angles equal)
3, 4, 5
6
36.87°, 53.13°, 90°
Right-angled (one angle is exactly 90°)
7, 8, 9
26.83
48.19°, 58.41°, 73.4°
Acute scalene (all angles under 90°)
25, 30, 40
374.53
38.62°, 48.51°, 92.87°
Obtuse scalene (one angle over 90°)
A quick check without angles: if the square of the longest side equals the sum of the squares of the other two, the triangle is right-angled. If it is larger, the triangle is obtuse; if smaller, acute.
Practical Uses
Land and plot measurement: an irregular plot can be split into triangles with a measuring tape, and Heron's formula gives each area without measuring any angle. A plot with sides 25 m, 30 m and 40 m covers about 374.53 m², roughly 4,031 sq ft. For legal or registration purposes, rely on a licensed surveyor and your land records.
Checking a right angle on site: masons mark 3, 4 and 5 units (or 6, 8 and 10) along two walls and the diagonal. If the tape reads exactly, the corner is 90°, as the table above confirms.
School geometry: Heron's formula is part of the Class 9 mathematics syllabus, and this tool is handy for checking homework answers.
Very flat triangles, where two sides only just exceed the third, are sensitive to small measuring errors. Sides 5, 5 and 9.99 give an area of only 1.12 and an angle of 174.87°, so a tiny change in one side changes the answer a lot.
Frequently Asked Questions
It uses Heron's formula: first the semi-perimeter s = (a + b + c) / 2 is found, then the area is the square root of s(s - a)(s - b)(s - c).
Each angle is found with the law of cosines, for example Angle A = arccos((b² + c² - a²) / (2bc)), then converted from radians to degrees.
The calculator checks the triangle inequality theorem (the sum of any two sides must exceed the third). If your sides fail this check, or any value is zero, negative, or missing, it shows an error instead of a result.
Not directly, because the tool needs all three sides. If you know sides b and c and the angle A between them, find the third side first with a = √(b² + c² − 2bc × cos A), then enter all three sides here.
Each angle is rounded to 2 decimal places on its own, so the small rounding differences can add up to a hundredth of a degree. The unrounded angles always total exactly 180°.