Pythagorean Theorem Calculator
Find the missing side of a right triangle from the other two sides.
How to use the Pythagorean Theorem Calculator
- Choose the solve for.
- Enter the leg a – Any unit; the answer uses the same unit.
- Enter the leg b.
- Enter the hypotenuse c.
- Press Calculate. The result updates automatically as you type.
About the Pythagorean Theorem Calculator
The Pythagorean theorem is the oldest and most used result in geometry: in any right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. It lets you find a distance you cannot measure directly from two you can.
Carpenters use the 3-4-5 rule to square a deck or foundation corner: measure 3 ft along one edge and 4 ft along the other, and the diagonal should be exactly 5 ft. Scaled-up versions such as 6-8-10 or 9-12-15 work the same way. Other uses include ladder placement, the diagonal size of a TV screen, roof rafter length and the straight-line distance between two points on a grid. Keep all sides in the same unit; the answer comes out in that unit.
Formula
a² + b² = c²
c = √(a² + b²) a = √(c² − b²) b = √(c² − a²)
Here a and b are the legs that form the right angle and c is the hypotenuse, the side opposite the right angle. Angle α (opposite a) = arctan(a ÷ b), and β = 90° − α.
Example calculation
Using the default values:
- Solve for = Hypotenuse c
- Leg a = 3
- Leg b = 4
the calculator returns:
- Missing side: 5
- All sides (a, b, c): 3, 4, 5
- Area: 6
- Perimeter: 12
- Angles: α = 36.8699°, β = 53.1301°, γ = 90°
Frequently asked questions
How do I find the hypotenuse?
Square both legs, add them, and take the square root. With legs 3 and 4: √(9 + 16) = √25 = 5.
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root. With c = 13 and a = 5: √(169 − 25) = 12.
Does the Pythagorean theorem work for every triangle?
No, only for right triangles. For other triangles use the law of cosines, c² = a² + b² − 2ab·cos C.
What are Pythagorean triples?
Sets of whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
Last updated: · Category: Math calculators