# Pythagorean Theorem Calculator

URL: https://speedycalculator.com/calculators/math/pythagorean-theorem/
Last updated: 2026-10-25

> The Pythagorean theorem calculator finds the hypotenuse of a right triangle from its two legs using c = √(a² + b²). It also gives the triangle’s area and the angle opposite side a, and can solve for a missing leg when you type the hypotenuse.

## Inputs

- Side a (m, cm, mm, km, in, ft, yd, mi)
- Side b (m, cm, mm, km, in, ft, yd, mi)

## Results

- Hypotenuse c
- Triangle area
- Angle opposite a

## Formula

```
c = √(a² + b²)
a = √(c² − b²)
```

## Explanation

In any right triangle, the square on the hypotenuse equals the sum of the squares on the other two sides. The rule underpins distance calculations, construction layout and navigation.

### How to use it

Enter both legs to get the hypotenuse. To find a missing leg, type the known hypotenuse into the result box and side a is solved.

### Practical use: squaring a corner

Builders use the 3-4-5 rule: mark 3 units along one wall and 4 along the other; if the diagonal is exactly 5, the corner is square.

### Inputs explained

FieldWhat to enterSide aUnits: m, cm, mm, km, in, ft …Side bUnits: m, cm, mm, km, in, ft …

### What each result means

- **Hypotenuse c** = sqrt([Side a]^2 + [Side b]^2)
- **Triangle area** = [Side a]×[Side b]÷2
- **Angle opposite a** = deg(atan2([Side a], [Side b]))

### Example values

How the main result changes when **Side a** changes and everything else stays at the example values above:

Side a (m)Hypotenuse c (m)1.54.272.254.59353.755.484.56.0267.21

## Worked example

Legs a = 3 m and b = 4 m.

c = √(3² + 4²) = √25 = **5 m**. Area = 3 × 4 ÷ 2 = 6 m². Angle opposite a ≈ 36.87°.

## Key terms

- **Hypotenuse**: The longest side of a right triangle, opposite the right angle.
- **Leg**: Either of the two sides that form the right angle.
- **Pythagorean triple**: Whole numbers that satisfy a² + b² = c², such as 3, 4, 5.

## FAQ

**Does it work for any triangle?**
Only right triangles. Use the law of cosines for others.

**Can I mix units?**
Yes, each side has its own unit menu and is converted automatically.

**How do I find distance between two points?**
Treat the x and y differences as the legs.

**What formula does the Pythagorean Theorem Calculator use?**
c = √(a² + b²).

**Can I work backwards from the result?**
Yes. Type the result you want into Hypotenuse c and the calculator finds the matching side a.


## Sources

- [Wolfram MathWorld – Pythagorean Theorem](https://mathworld.wolfram.com/PythagoreanTheorem.html)