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45–45–90 Triangle Equal Legs and Size

Calculate 45–45–90 triangle equal legs and size with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

Calculator inputs

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

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Worked inputs a = 3 give b = 3, c = 4.2426407, Area = 4.5, Perimeter = 10.242641. Values use the initial displayed units.

a = b; c = a√2; A = a²/2; P = a(2+√2)

Enter these known values and leave the other values blank.

The two perpendicular legs are equal and the other angles are both 45°. A leg and the hypotenuse are different measurements.
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.

The two perpendicular legs are equal and the other angles are both 45°. A leg and the hypotenuse are different measurements.

Multiply the leg length by √2. Each leg is the hypotenuse divided by √2.

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