Free · Mathematical relations and geometry

Trapezoid Height from Leg–Angle or Area

Calculate perpendicular trapezoid height from a sloping leg and its angle, or from area and the parallel bases.

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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A leg of 5 at 30° gives height 2.5. Parallel bases 8 and 4 with area 15 give the same height 2.5.

h=c sin α=d sin δ; h=2A/(a+b)

Enter these known values and leave the other values blank.

The angle is between a sloping leg and a parallel base, strictly between zero and 180 degrees.
The parallel bases and legs are positive, and area uses the square of the length unit.
The three panels are independent alternatives. Supplying inconsistent data in different panels does not force their heights to agree.
Angle inverses select the acute principal angle. The supplementary angle yields the same sine and height.

Supplementary angles have equal sine. The inverse selects the acute branch, so an obtuse angle is not uniquely recovered.

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