Pythagorean Theorem Calculator
Enter any two sides to compute the rest of the right triangle
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Pythagorean Theorem Calculator
Provide any two values of a right triangle to solve the Pythagorean equation: a² + b² = c². Computes missing side, angles α and β, area, perimeter, and altitude h.
🧮 Input Values
📊 Results
⚠️
Invalid Input
a
—
b
—
c
—
h (altitude)
—
∠α (opposite a)
—
∠β (opposite b)
—
Area
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Perimeter
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Input Guide
Input Formats:
5
→
Enter "5" in coefficient field, leave √ empty
√5
→
Leave coefficient empty, enter "5" in √ field
2√5
→
Enter "2" in coefficient, "5" in √ field
2.5
→
Enter "2.5" in coefficient field, leave √ empty
Requirements: Enter any two sides. All values must be positive. For right triangles: c ≥ max(a, b).
📚 Pythagorean Theorem
The Pythagorean Theorem is a relation between the three sides of a right triangle. For a right triangle with legs a and b, and hypotenuse c:
a² + b² = c²
This relation allows computing any side when the other two are known. The theorem is a special case of the Law of Cosines when the included angle is 90°.
Solving for sides
- c = √(a² + b²)
- a = √(c² − b²)
- b = √(c² − a²)
Angles and other properties
- α = arcsin(a / c), β = arcsin(b / c)
- Area = a × b / 2
- Altitude to hypotenuse: h = a × b / c
- Perimeter = a + b + c