Calculate the missing side or hypotenuse of a right triangle from any two values, with results in inches, feet, yards, centimeters, or meters.
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Reverse Hypotenuse Formula
Use this calculator when you know the hypotenuse and one side of a right triangle and need the other side. Select the correct unit for each input and choose the result unit; the calculator converts mixed units automatically.
H² = S₁² + S₂²
S₂ = √(H² - S₁²)
Variable Guide
| Term | Meaning |
|---|---|
| Hypotenuse | The longest side of the right triangle. |
| Known side | The leg length you already have. |
| Unknown side | The missing leg calculated from the other two values. |
| Units | Select inches, feet, yards, centimeters, or meters for each input and the output. |
How to Calculate the Missing Side
- Square the hypotenuse.
- Square the known side.
- Subtract the known-side square from the hypotenuse square.
- Take the square root of the result.
Examples
S₂ = √(50² - 20²) = 45.826
S₂ = √(30² - 10²) = 28.284
| Hypotenuse | Known Side | Unknown Side |
|---|---|---|
| 50 | 20 | 45.826 |
| 30 | 10 | 28.284 |
| 13 | 5 | 12 |
Input Rules
- The hypotenuse must be longer than the known side.
- This calculation applies only to right triangles.
- If both values are equal, the result is zero, which is a degenerate case rather than a true triangle.
- If the value inside the square root would be negative, the inputs are not valid for a right triangle.
Quick Reference
| Situation | What to Check |
|---|---|
| Mixed units | Select each input’s actual unit; the calculator converts all measurements to a common unit before calculating. |
| Unexpected answer | Make sure the larger value was entered as the hypotenuse. |
| Need more precision | Round only the final result, not the intermediate squares. |
| Sanity check | The missing side will always be shorter than the hypotenuse. |
Common Uses
| Application | Known Measurements | Find |
|---|---|---|
| Roof framing | Rafter length and one leg | Remaining rise or run |
| Ladders | Ladder length and wall height | Distance from the wall |
| Ramps | Ramp length and rise | Horizontal run |
| Layout and surveying | Diagonal distance and one side | Perpendicular offset |
