Free · Triangle calculators 🔺

Hypotenuse from an Equal Right-Triangle Leg

Calculate hypotenuse from an equal right-triangle leg with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked inputs B = 3 give Hypotenuse (A) = 4.2426407. Values use the initial displayed units.

c = a√2

Worked example

Enter these known values and leave the other values blank.

B
3 cm
Hypotenuse (A)
4.243 cm

Assumptions and limitations

  • The entered leg belongs to a 45–45–90 triangle. For unequal legs, both leg measurements are needed and this relationship does not apply.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

The entered leg belongs to a 45–45–90 triangle. For unequal legs, both leg measurements are needed and this relationship does not apply.

Can this formula be used when the legs differ?

No. For unequal perpendicular legs, use c = √(a²+b²). The single-leg formula c = a√2 requires equal legs.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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