Pythagorean theorem calculator
Find the hypotenuse or a missing leg of a right triangle, plus its angles, area and perimeter.
- ๐บ๐ธ US federal & state rules
Hypotenuse c
5 ft
- Angles opposite a and b
- 36.87ยฐ and 53.13ยฐ
- Area
- 6 ftยฒ
- Perimeter
- 12 ft
- Pythagorean triple
- Yes, 3-4-5 (primitive)
This is an example. Enter your numbers above and press the button to see your own result.
All three sides
| a | 3 ft |
|---|---|
| b | 4 ft |
| c (hypotenuse) | 5 ft |
- Assumes a right triangle. The hypotenuse is the side across from the 90ยฐ angle.
Show the math
| Formula | c = โ(aยฒ + bยฒ) |
|---|---|
| Plug in | c = โ(3ยฒ + 4ยฒ) = โ25 |
| Result | โ25 = 5 โ 5 |
| Angle opposite a | arctan(a รท b) = 36.8699ยฐ |
| Area | a ร b รท 2 = 6 |
What to do next
How it works
The hypotenuse is c = โ(aยฒ + bยฒ). A missing leg is b = โ(cยฒ - aยฒ). When the sides are whole numbers, the exact answer is shown as a simplified square root, so โ32 becomes 4โ2.
The angle across from leg a is arctan(a รท b), and the other acute angle is 90ยฐ minus that. The area is a ร b รท 2.
Things to keep in mind
It only works for right triangles. For a ladder, a ramp or a TV screen diagonal, the hypotenuse is the slanted side or the diagonal.
Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, aยฒ + bยฒ = cยฒ, where c is the side across from the right angle. Legs of 3 and 4 give c = โ25 = 5.
How do I find a missing leg?
Subtract the known leg squared from the hypotenuse squared and take the square root. With c = 13 and a = 5, b = โ(169 - 25) = 12.
How do I check if a corner is square?
Measure 3 ft along one side and 4 ft along the other. If the diagonal between the marks is exactly 5 ft, the corner is 90ยฐ. Builders call this the 3-4-5 rule.
What are common Pythagorean triples?
3-4-5, 5-12-13, 8-15-17 and 7-24-25, plus any multiple of them like 6-8-10.