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Right-Triangle Perimeter from Legs or Three Sides

Calculate right-triangle perimeter from legs or three sides 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 Base = 3, Perpendicular = 4 give Perimeter = 12. Values use the initial displayed units.

P = a+b+√(a²+b²); three-side mode: P = a+b+c

Worked example

Enter these known values and leave the other values blank.

Given
Two perpendicular legs
Base
3 cm
Perpendicular
4 cm
Perimeter
12 cm

Assumptions and limitations

  • The two-leg mode computes the hypotenuse. The three-side mode requires c² = a²+b² within the stated numeric tolerance, rather than accepting any triangle.
  • 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.
  • Three-side consistency permits a relative squared-length residual no larger than 1e−12. This is a numeric tolerance, not a measurement error model.

Common questions

Which measurements and inverse branch does this model use?

The two-leg mode computes the hypotenuse. The three-side mode requires c² = a²+b² within the stated numeric tolerance, rather than accepting any triangle.

Will any three valid triangle sides form a right triangle?

No. A three-side right-triangle input must satisfy c² = a²+b², with c the hypotenuse. Triangle inequality alone is insufficient.

References

Require acute right-triangle angles, a real positive hypotenuse and consistent three-side geometry.

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