Calculating your hypotenuse is straightforward once you know the 45-45-90 Triangle 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 45-45-90 Triangle Calculator.
What is 45-45-90 Triangle?
The 45-45-90 Triangle calculation tells you your hypotenuse from a few simple inputs. The figure you are solving for here is the hypotenuse.
The 45-45-90 Triangle formula
The core formula is:
Hypotenuse = Leg length × √(2)Here is what each input means:
- Leg length — a number. Example: 5.
How to calculate it step by step
- Write down the leg length (for example, 5).
- Apply the formula above to get your hypotenuse.
- Double-check the result with the 45-45-90 Triangle Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Leg length | 5 |
| Hypotenuse | 7.0711 |
| Area | 12.5000 |
With leg length of 5, the hypotenuse works out to 7.0711.
Example 2
With leg length of 10, the hypotenuse works out to 14.1421.
| Result | Value |
|---|---|
| Hypotenuse | 14.1421 |
| Area | 50.0000 |
Example 3
With leg length of 2.5, the hypotenuse works out to 3.5355.
| Result | Value |
|---|---|
| Hypotenuse | 3.5355 |
| Area | 3.1250 |
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 45-45-90 Triangle Calculator does it instantly, for free, with the formula and a worked example built in.
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