Pythagorean Theorem Calculator

Pythagorean Theorem Formula

Worked Example

A right triangle with legs 6 and 8:

1. a² + b² = c²
2. c = √(6² + 8²) = √100
3. = 10

Area ½ab: 24 · Perimeter: 24 · Pythagorean triple: yes (all sides are whole numbers)

Test-day tip

Check for a scaled triple before calculating: legs 9 and 12 are 3 × (3, 4), so the hypotenuse is 3 × 5 = 15.

More Geometry and Trigonometry Calculators

• Distance Formula Calculator

  d = √[(x₂ − x₁)² + (y₂ − y₁)²]

  the Pythagorean theorem on the coordinate plane

  Example: The points (1, 2) and (7, 10): Distance d = 10.

  Open the distance formula calculator →

• Special Right Triangles Calculator

  30-60-90: 1 : √3 : 2; 45-45-90: 1 : 1 : √2

  short leg : long leg : hypotenuse; leg : leg : hypotenuse

  Example: A 30-60-90 triangle with short leg 5: Sides: short leg = 5, long leg = 5√3, hypotenuse = 10.

  Open the special right triangles calculator →

• Right Triangle Calculator

  sin A = a/c, cos A = b/c, tan A = a/b

  SOH-CAH-TOA; A + B = 90°

  Example: A right triangle with legs 3 and 4: Hypotenuse c = 5.

  Open the right triangle calculator →

• Midpoint Calculator

  M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

  endpoint: x₂ = 2Mx − x₁, y₂ = 2My − y₁

  Example: The segment from (−2, 3) to (6, −5): Midpoint = (2, -1).

  Open the midpoint calculator →

Frequently asked questions

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.