Calculating your hypotenuse (c) is straightforward once you know the Pythagorean Theorem formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Pythagorean Theorem Calculator.
What is Pythagorean Theorem?
The Pythagorean Theorem calculation tells you your hypotenuse (c) from a few simple inputs. The figure you are solving for here is the hypotenuse (c).
The Pythagorean Theorem formula
The core formula is:
Hypotenuse (c) = √(Leg a ^ 2 + Leg b ^ 2)Here is what each input means:
- Leg a — a number. Example: 3.
- Leg b — a number. Example: 4.
How to calculate it step by step
- Write down the leg a (for example, 3).
- Write down the leg b (for example, 4).
- Apply the formula above to get your hypotenuse (c).
- Double-check the result with the Pythagorean Theorem Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Leg a | 3 |
| Leg b | 4 |
| Hypotenuse (c) | 5.000000 |
| Area of triangle | 6.00 |
| Perimeter | 12.0000 |
With leg a of 3 and leg b of 4, the hypotenuse (c) works out to 5.000000.
Example 2
With leg a of 6 and leg b of 4, the hypotenuse (c) works out to 7.211103.
| Result | Value |
|---|---|
| Hypotenuse (c) | 7.211103 |
| Area of triangle | 12.00 |
| Perimeter | 17.2111 |
Example 3
With leg a of 1.5 and leg b of 4, the hypotenuse (c) works out to 4.272002.
| Result | Value |
|---|---|
| Hypotenuse (c) | 4.272002 |
| Area of triangle | 3.00 |
| Perimeter | 9.7720 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Pythagorean Theorem Calculator does it instantly, for free, with the formula and a worked example built in.
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