Classifying Triangles Calculator
Classify any triangle by its side lengths as equilateral, isosceles, or scalene and by its angles as acute, right, or obtuse. Enter three sides for instant results with our free geometry calculator.
About This Calculator
This classifying triangles calculator takes the three side lengths of a triangle and automatically classifies it using two independent systems. First, it classifies by side lengths into equilateral, isosceles, or scalene. Second, it computes the three interior angles using the law of cosines and classifies by angles into acute, right, or obtuse.
The law of cosines states that for any triangle with sides a, b, c and opposite angles A, B, C: cos(A) = (b^2 + c^2 - a^2) / (2bc). Once all three angles are known, the triangle type is determined. If any angle equals 90 deg (within floating-point tolerance), the triangle is classified as right. Otherwise, if any angle exceeds 90 deg it is obtuse, and if all are less than 90 deg it is acute.
Before classifying, the calculator validates the input using the triangle inequality theorem to ensure the three sides can actually form a valid triangle. This calculator is useful for students learning geometry, teachers preparing lesson materials, and anyone working with triangle measurements in construction, design, or engineering.
Frequently Asked Questions
How does triangle classification work?
Triangles are classified by their sides as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different). By angles, they are acute (all angles < 90 deg), right (one angle = 90 deg), or obtuse (one angle > 90 deg). The calculator uses the law of cosines to compute angles from the three side lengths.
What is the difference between equilateral, isosceles, and scalene triangles?
An equilateral triangle has all three sides equal in length and all three angles equal to 60 deg. An isosceles triangle has at least two sides equal and two base angles equal. A scalene triangle has all sides of different lengths and all angles of different measures.
What is the difference between acute, right, and obtuse triangles?
An acute triangle has all three interior angles less than 90 deg. A right triangle has exactly one angle equal to 90 deg (a right angle). An obtuse triangle has one angle greater than 90 deg. A triangle can be both isosceles and right, or scalene and obtuse, combining both classification systems.
Can any three side lengths form a triangle?
No. The triangle inequality theorem states that the sum of any two sides must be greater than the third side. If a + b <= c, a + c <= b, or b + c <= a, the side lengths cannot form a valid triangle. This calculator validates inputs against this rule before classifying.
What units should I use for side lengths?
You can use any consistent units such as inches, feet, centimeters, or meters. All three sides must use the same unit. The classification is dimensionless and does not depend on the unit system.
How does the calculator compute angles from side lengths?
The calculator uses the law of cosines: cos(A) = (b^2 + c^2 - a^2) / (2bc), where A is the angle opposite side a. It computes all three angles, then checks if any angle equals 90 deg (right), exceeds 90 deg (obtuse), or all are under 90 deg (acute).
Is this triangle classification calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration, limits, or hidden fees.