Triangle Calculator
Find a triangle’s area, perimeter, angles and type. Choose base × height for the quick formula, or enter all three sides and the calculator applies Heron’s formula, verifies the triangle inequality and solves every interior angle with the law of cosines.
TheCalculators — Triangle Calculator
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Triangle Area (Heron)
6 units²
Perimeter 12 units · Scalene, right-angled triangle
- Side a
- 3 units
- Side b
- 4 units
- Side c
- 5 units
- Semi-perimeter s
- 6
- Perimeter
- 12 units
- Area
- 6 units²
- Angle A
- 36.87°
- Angle B
- 53.13°
- Angle C
- 90°
- Type
- Scalene
Sides and opposite angles
Angles sum to 180° (small rounding differences possible).
Heron’s formula, step by step
- 1Check the triangle inequalitya+b = 7 > c = 5 ✓ · a+c = 8 > b ✓ · b+c = 9 > a ✓
- 2Semi-perimeters = (a + b + c) / 2 = (3 + 4 + 5) / 2 = 6
- 3Heron’s formulaA = √(s(s−a)(s−b)(s−c)) = √(6 × 3 × 2 × 1)
- 4EvaluateA = √36 = 6 units²
- 5Angles (law of cosines)A = acos((b²+c²−a²)/(2bc)) = 36.87° · B = 53.13° · C = 180° − A − B = 90°
Most useful next
Formula
A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2; A = ½·b·h
Pro tips
- • The triangle inequality (any two sides sum to more than the third) must hold or no triangle exists.
- • Angles are recovered from the law of cosines — they always sum to exactly 180°.
- • For right triangles, the Pythagorean theorem tool gives extra outputs like altitude to the hypotenuse.
FAQ
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