Calculate the missing side or hypotenuse of a right triangle from any two values, with results in inches, feet, yards, centimeters, or meters.

For a right triangle with positive sides. Each input can use its own unit.

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

  1. Square the hypotenuse.
  2. Square the known side.
  3. Subtract the known-side square from the hypotenuse square.
  4. 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