The triangle calculator computes every measurement of a triangle from just its three side lengths: area, perimeter, all three angles, and the type of triangle. It uses Heron's formula for area and the law of cosines for angles — the same methods used in engineering, architecture, surveying, and mathematics.
Enter the three side lengths. The calculator instantly computes the area using Heron's formula, the perimeter, and all three interior angles using the law of cosines. It also identifies whether the triangle is acute, right, or obtuse.
Use this calculator whenever mental arithmetic introduces uncertainty — particularly when the result will inform a decision rather than just satisfy curiosity. Even confident mathematicians use calculation tools when precision matters.
Many errors with this type of calculation stem from unit inconsistency: mixing metric and imperial, or mixing annual and monthly rates. Ensure all inputs use the same unit system before running the calculation.
A shopper sees two versions of the same product at different prices: one at £14.50 for 400g and another at £11.99 for 300g. Running both price-per-gram calculations reveals the larger pack is 7% cheaper per unit — the kind of comparison that is impossible to do reliably in your head at the shelf.
Triangle Area & Angle Formulas
Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2
cos(A) = (b²+c²-a²)/(2bc)
Heron's formula needs only the three sides. The law of cosines finds any angle when all three sides are known.
Triangle with sides a=5, b=12, c=13. Find area and angles.
Result: Area = 30 sq units, C = 90° (right triangle — a 5-12-13 Pythagorean triple)
Use Heron's formula: Area = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 is the semi-perimeter.
Use the law of cosines: cos(A) = (b² + c² − a²) / (2bc). Solve for each angle in turn.
The triangle inequality states each side must be less than the sum of the other two. If a=3, b=4, c=10: 3+4=7 < 10, so this is NOT a valid triangle.
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