Free · Triangle calculators 🔺

30–60–90 Triangle from a Known Measurement

Calculate 30–60–90 triangle from a known measurement 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.

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

Worked inputs a = 2 give b = 3.4641016, c = 4, Area = 3.4641016, Perimeter = 9.4641016. Values use the initial displayed units.

b = a√3; c = 2a; A = a²√3/2; P = a(3+√3)

Enter these known values and leave the other values blank.

The short leg a faces 30°, the long leg b faces 60°, and the hypotenuse c faces 90°. One positive measurement fixes the size.
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 short leg a faces 30°, the long leg b faces 60°, and the hypotenuse c faces 90°. One positive measurement fixes the size.

Short leg, long leg and hypotenuse have ratio 1 : √3 : 2. Scale all three by the same positive short-leg length.

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