Trapezoid Calculator - Area, Perimeter, Midsegment, Angles

A trapezoid calculator takes the two parallel bases, the perpendicular height, and the two non-parallel legs and returns the area, perimeter, midsegment, interior base angles, and height. It is the fastest way to move from a sketch to a clean numerical answer for a roof face, ramp, table top, or piece of fabric.

• • Roofing and sheathing estimates: Confirm the area of a trapezoidal roof slope before you order felt or shingles.
• • Garden, ramp, and landscape footprints: Work out the area of a tapered garden bed, accessibility ramp, or retaining wall footing.
• • Fabric, paper, and craft layouts: Size a trapezoidal piece of fabric, sheet metal, or card stock before you cut.
• • Classroom and homework checks: Verify the result of A = (a + b) * h / 2 in geometry, algebra, or trigonometry homework.

The calculator uses the same trapezoid area formula taught in geometry, so the numbers match what a textbook would give. Switch to 'Height from a known area' when the plan gives the finished area and the two bases but not the height of a tapered slab.

If your homework only needs the area, the Area Of A Trapezoid Calculator returns the same result with a tighter form that hides the perimeter and angle fields.

The calculator applies the standard area of a trapezoid formula, the polygon perimeter sum, and right-triangle trigonometry. Numbers update as soon as you change a base, the height, or a leg.

• a, b: Lengths of the two parallel sides (bases) of the trapezoid.
• h: Perpendicular distance between the two bases, also called the height of the trapezoid.
• c, d: Lengths of the two non-parallel sides (legs). Optional; only needed for the perimeter and the interior angles.
• m: Midsegment (median), the line that connects the midpoints of the two legs and has length (a + b) / 2.
• A: Area of the trapezoid, the two-dimensional space enclosed by the four sides.

The area formula uses only the two bases and the perpendicular height, so the result is the same for an isosceles, right, or irregular trapezoid with the same three numbers. The legs only feed the perimeter and angles.

When the mode is 'Height from a known area', the calculator inverts the area formula and returns h = 2 * A / (a + b). The rest of the table clears to zero so the focus stays on the solved height value.

According to Wolfram MathWorld, the area of a trapezoid with parallel sides of length a and b and perpendicular height h is A = (a + b) * h / 2, and the midsegment has length (a + b) / 2.

When the two non-parallel sides are equal, the Isosceles Trapezoid Calculator handles the extra leg-length output and the matching base angles that an isosceles trapezoid has on top of the general area and perimeter.

A few geometric terms carry the rest of the calculator, so it helps to know exactly what each label means.

If your area number looks wrong, re-measure the perpendicular height rather than the leg; the height is the only input the area formula actually uses.

When one leg is perpendicular to the bases, the height equals that leg and the Right Trapezoid Area Calculator returns the area, perimeter, and the right-angle base pair directly from the two bases and the perpendicular side.

Work through these steps in order and the calculator gives a clean area, perimeter, midsegment, and angle table.

1. 1 Measure the two parallel bases: Pick the longer parallel side as base a and the shorter as base b, then enter both in the same unit.
2. 2 Measure the perpendicular height: Use a plumb line or square to measure the shortest distance between the two bases, then type that value into the height field.
3. 3 Add the leg lengths when needed: If you need the perimeter or the interior angles, also enter the two non-parallel sides. Leave them at 0 for area and midsegment only.
4. 4 Pick the right mode: Keep 'Area (and other results)' for normal use, or switch to 'Height from a known area' when the plan gives the finished area and you need the height.
5. 5 Read the results in the right panel: The primary result is the area, with the perimeter, midsegment, and base angles listed underneath. Each value updates as you edit a number.
6. 6 Reset before starting a new shape: Click the Reset button to clear every field back to the default.

A woodworker is cutting a tapered shelf 18 in at the back, 12 in at the front, and 9 in deep. The calculator returns an area of 135 sq in, a midsegment of 15 in, and a perimeter of 50.66 in once the slanted edges are added.

If the two legs of your trapezoid are different lengths and the plan only gives you an irregular footprint, the Irregular Trapezoid Area Calculator keeps the same area formula but adds the explicit leg inputs that the irregular case is most likely to need.

Using a focused trapezoid calculator gives you results you can trust for a design, a quote, or homework, and saves the arithmetic slip that often hides in long handwritten work.

• • Fast, accurate area in any unit: The calculator handles the average and the multiplication, so the area is consistent in inches, feet, centimetres, or metres.
• • Perimeter and midsegment in one table: The same form returns the perimeter, the midsegment, and the base angles alongside the area, which is what planning sheets need.
• • Height-from-area solve mode: Switching the mode turns the calculator into a quick reverse solver, so you can recover the perpendicular height of a tapered slab from a finished area.
• • Angles for cut lists and joinery: Once the leg lengths are in, the calculator returns the interior base angles for miter saws and slanted joinery.
• • Validation that catches obvious mistakes: Negative or zero bases stop the calculation with a clear message, so a single mistyped number does not silently corrupt the rest of the table.

The same tool answers the questions you usually have in sequence: size material from the area, confirm the average width with the midsegment, and read the base angles to plan cuts.

If the shape on your plan is not strictly a trapezoid, the Area Quadrilateral Calculator lets you switch between rectangle, parallelogram, rhombus, kite, trapezoid, and general quadrilateral mode without restarting.

A few details of the geometry change what the calculator returns, so it helps to know which inputs control the area, the perimeter, and the angles.

• • The calculator assumes a planar trapezoid. Curved or three-dimensional surfaces, such as a tapered cone, need a different tool.
• • The angle calculation uses the perpendicular height and the leg length. If you only enter one leg, the other leg is not inferred, so the angles return 0 to flag missing data.
• • Measurement rounding matters: a 0.01 in error in the height multiplies by the average of the bases, so the area is sensitive to small errors when the trapezoid is large.

If a result surprises you, the most common cause is a height measured along a leg instead of perpendicular to the bases. The area formula assumes the shortest distance between the two bases, not a slanted side.

A quick sanity check is to compute the area in two units and confirm they agree: 1 sq ft is also 144 sq in, and 1 sq m is 10,000 sq cm.

According to Wikipedia, a trapezoid is a quadrilateral with at least one pair of parallel sides, and the angles along each leg are supplementary, meaning alpha + beta = 180 degrees and gamma + delta = 180 degrees.

According to Wolfram MathWorld, the trapezoid perimeter formula is P = a + b + c + d, and for a right trapezoid the perpendicular leg equals the height, which is the cleanest way to sanity-check the area result before quoting the number.

Once you have the area of the trapezoidal face from this calculator, the Trapezoidal Prism Volume Calculator extends that result into the volume of a three-dimensional prism of any depth in the same units.