Trapezoid Calculator

Solve a trapezoid from the two parallel bases plus height, area, or an isosceles leg. Get area, height, midline, perimeter, and equal diagonals without re-deriving the geometry.

How It Works

Formula

m = \frac{a + b}{2}

A = \left(\frac{a + b}{2}\right) h

h = \frac{2A}{a + b}

d = \frac{b-a}{2}

h = \sqrt{\ell^2 - d^2}

P = a + b + 2\ell

Variables, symbols and units

$a$: Short parallel base
$b$: Long parallel base
$m$: Midline / median length
$h$: Perpendicular height
$A$: Area
$d$: Half of the base difference in the isosceles branch
$\ell$: Equal leg length in the isosceles branch
$P$: Perimeter

Calculation method explained

A trapezoid is defined here by its two parallel bases. The calculator first finds the midline $m = (a+b)/2$ , then uses the active solve mode to unlock the rest of the geometry. The result panel stays conservative: it only shows perimeter, equal legs, or diagonals when those values are actually determined by the chosen inputs.

In bases + height, the calculator goes straight to area with $A = mh$ and only totals perimeter when both non-parallel sides are supplied.

In bases + area, it rearranges the area formula to solve the missing height and then confirms the original area.

In isosceles bases + leg, it treats the base difference symmetrically: $d = (b-a)/2$ , then $h = \sqrt{\ell^2-d^2}$ . That same centered geometry gives one shared diagonal length for both diagonals.

Frequently Asked Questions

What counts as the short base and the long base?

They are the two parallel sides of the trapezoid. Enter them explicitly as the shorter and longer base instead of assuming the calculator will reorder them from your numbers.

Why does bases + area solve height but not perimeter?

Area and the two bases determine the height through h = 2A / (a + b), but they do not determine the non-parallel sides. Without those side lengths, perimeter is still unknown.

Why are the extra leg fields optional in bases + height mode?

Area and midline need only the two parallel bases and the height. The leg inputs stay out of the main path unless you also want perimeter from a sketch that already labels those sides.

What makes an isosceles trapezoid impossible from bases + leg?

In the isosceles branch, each leg must be longer than half the base difference. If the leg is shorter than or equal to (b - a) / 2, the height collapses to zero and the shape cannot exist.

Is this enough for engineering or fabrication sign-off?

No. This page is a geometry helper for sketches, worksheets, and cut-list checks. Use your project tolerances, material allowances, and any required professional review separately.

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