Free Isosceles Trapezoid Calculator

What Is an Isosceles Trapezoid?

An isosceles trapezoid is a four‑sided shape with one pair of parallel sides (the bases) and a pair of non‑parallel legs that are exactly the same length. This geometric figure is a special case of a trapezoid, and it shares several interesting isosceles trapezoid properties that set it apart from other quadrilaterals.

Key Properties

• Equal diagonals: In an isosceles trapezoid, both diagonals have the same length. However, they do not necessarily bisect each other.
• Congruent base angles: The angles adjacent to each base are equal. For example, the two angles at the longer base $a$ are the same, and the two angles at the shorter base $b$ are also the same.
• Supplementary opposite angles: Any pair of opposite angles adds up to $180^{\circ}$.
• Axis of symmetry: Exactly one line of symmetry runs through the midpoints of the two bases. Unless the shape is a rectangle, it does not have rotational symmetry.
• Rectangular case: If a right angle exists in an isosceles trapezoid, the shape becomes a rectangle (a special isosceles trapezoid).

These isosceles trapezoid properties are the foundation for calculating the isosceles trapezoid area, isosceles trapezoid height, isosceles trapezoid diagonal, and isosceles trapezoid angles.

Essential Formulas

The tool uses a set of standard formulas to perform the calculations:

Quantity	Formula	Variables
Area ($A$)	$A = \dfrac{a + b}{2} \times h$	$a,b$ = parallel bases, $h$ = height
Height ($h$)	$h = \sqrt{c^{2} - \left(\dfrac{a - b}{2}\right)^{2}}$	$c$ = leg length
Leg length ($c$)	$c = \sqrt{h^{2} + \left(\dfrac{a - b}{2}\right)^{2}}$	–
Diagonal ($d$)	$d = \sqrt{h^{2} + \left(\dfrac{a + b}{2}\right)^{2}}$	–
Base angle ($\alpha$)	$\alpha = \arccos\left(\dfrac{a - b}{2c}\right)$	angle at the longer base

(Note: The same formulas work for the angles at the shorter base, which are $\beta = 180^{\circ} - \alpha$.)

How to Use the Isosceles Trapezoid Calculator

The calculator is designed to be straightforward: you enter the known values (any combination of bases, legs, height, diagonal, or angles), and it automatically computes all the other dimensions. The tool assumes that the longer base is labeled $a$ and the shorter base is labeled $b$ (they can be equal if the trapezoid is actually a parallelogram). You can input values in any unit, and the results will reflect the same unit system.

With this free isosceles trapezoid calculator, you can quickly obtain the isosceles trapezoid area, height, diagonal, and angles without manual computation. Whether you are a student studying geometry or a professional working on a design project, this tool simplifies the process and helps you verify your results.