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Pythagorean Right-Triangle Sides, Area and Boundary

Calculate pythagorean right-triangle sides, area and boundary with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
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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 Side length a = 3, Side length b = 4 give Side length c = 5, Area = 6, Perimeter = 12. Values use the initial displayed units.

a²+b² = c²; A = ab/2; P = a+b+c

Worked example

Enter these known values and leave the other values blank.

Side length a
3 cm
Side length b
4 cm
Side length c
5 cm
Area
6 cm²
Perimeter
12 cm

Assumptions and limitations

  • The side c is the hypotenuse opposite the right angle. Recovering a leg uses a positive square root and requires a hypotenuse longer than the known leg. For the retained perimeter inverse, provide the hypotenuse and other leg too.
  • 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 side c is the hypotenuse opposite the right angle. Recovering a leg uses a positive square root and requires a hypotenuse longer than the known leg. For the retained perimeter inverse, provide the hypotenuse and other leg too.

How is a missing leg recovered from the hypotenuse?

For a known leg a and hypotenuse c, the other leg is √(c²−a²). The hypotenuse must exceed the known positive leg.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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