A trapezoid is the shape you reach for whenever one side of a project is wider than the opposite side: a flower bed that narrows toward a fence, a roof gable, a wall section under a sloped ceiling, a highway ramp shoulder, a parcel of land that tapers along a river, a tailoring pattern, or the cross-section of a drainage ditch. People usually try to estimate these shapes as a rectangle or a triangle and end up 10–30% off the true area — which is how you end up buying too much sod, too little concrete, or the wrong amount of paint. This trapezoid area calculator takes the two parallel bases and the perpendicular height and returns the exact area in the same squared unit you measured in, plus the average base length that makes the arithmetic intuitive.
Type your three numbers into the boxes and the result updates as you type. Enter feet and you get square feet; enter meters and you get square meters; enter centimeters and you get square centimeters. Keep all three measurements in the same unit — mixing inches and feet is the single most common mistake.
How to Use
- Identify the two parallel sides of the trapezoid. These are called the bases. The longer one goes in Base 1; the shorter one goes in Base 2. It does not matter which is which for the formula, but labeling them keeps your notes honest.
- Measure the Height — the perpendicular distance between the two parallel bases, at a right angle to both. Do not measure along a slanted side; that is a leg, not a height. If the shape is sitting on paper, drop a ruler straight down from the shorter base to the longer one.
- Read the highlighted Area result. That is the number to use when pricing sod, carpet, tile, paint, concrete, soil, or fertilizer.
- Use the Average Base line to sanity-check your work: the trapezoid's area equals a rectangle whose width is the average base and whose height is the measured height. If your average base times height looks too small or too large, re-measure one of the inputs.
- If your dimensions are mixed (say, Base 1 is 12 ft 6 in and Base 2 is 8 ft 3 in), convert first: 12 ft 6 in is 12.5 ft and 8 ft 3 in is 8.25 ft, then enter those decimals.
- For a trapezoid on a plot plan, measure the two parallel property lines directly on the ground — do not read them off a scaled drawing unless you know the scale factor.
The engine applies the standard formula A = (base1 + base2) / 2 × height. It rejects negative inputs outright, because a side length below zero has no physical meaning and would silently produce a plausible-looking but wrong number.
The Trapezoid Formula, Explained
A trapezoid has two parallel sides (the bases) and two non-parallel sides (the legs). The area formula that every geometry textbook, engineering handbook, and contractor uses is:
A = (b₁ + b₂) / 2 × h
Where:
- b₁ and b₂ are the lengths of the two parallel bases.
- h is the perpendicular height between them.
- (b₁ + b₂) / 2 is the average length of the two bases — the width the trapezoid would have if it were a rectangle of the same area.
Why does this work? If you slice the trapezoid horizontally halfway up its height and rotate the top half 180 degrees, the two pieces snap together into a perfect rectangle whose width is the average of the two bases and whose height is h. That rectangle's area is exactly the trapezoid's area — which is why the formula feels like "rectangle area with an average width."
Worked example on the default shape: Base 1 = 10 ft, Base 2 = 6 ft, Height = 4 ft. The average base is (10 + 6) / 2 = 8 ft, and the area is 8 × 4 = 32 square feet. You can verify this by splitting the shape into a 6-by-4 rectangle (24 sq ft) plus two side-by-side right triangles whose combined base is 4 ft and height 4 ft (½ × 4 × 4 = 8 sq ft), for a total of 32 sq ft.
If the height is 0, the area collapses to 0 no matter how long the bases are — the shape has become a line segment.
When to Use a Trapezoid vs a Rectangle or Triangle
Most real-world shapes fall into one of three families:
- Both pairs of opposite sides parallel → rectangle. Use length × width. A standard bedroom, a concrete slab, a soccer field, a sheet of drywall.
- One side shrinks to a point → triangle. Use ½ × base × height. A gable end, a sail, a yield sign, a pizza slice.
- One pair of opposite sides parallel but unequal → trapezoid. Use (b₁ + b₂)/2 × h. A tapered garden bed, a hip-roof wall section, a river-front parcel, a trapezoidal window, the cross-section of an I-beam flange.
If you are unsure, sketch the shape on graph paper and count the squares: count full squares inside the outline, then add half squares for the clipped corners. The total should land within a few percent of what this calculator returns. When it does not, you probably measured a leg instead of the height, or swapped a non-parallel side for a base.
Examples
Example 1 — The default tapered garden bed (10 ft × 6 ft × 4 ft). A homeowner builds a raised bed that is 10 ft along the fence (Base 1), 6 ft along the house side (Base 2), and 4 ft deep between them. The average base is 8 ft and the area is 32 square feet. At $2.50 per square foot for organic topsoil 6 inches deep, the soil bill is 32 × $2.50 = $80, and a bag of fertilizer covering 1,000 sq ft means one bag will cover this bed roughly 30 times — buy one small bag, not the bulk pallet.
Example 2 — A fractional patio under a sloped eave (12.5 ft × 8.25 ft × 9 ft). A concrete patio butts up against a house whose eave slopes, so the near edge is 12 ft 6 in and the far edge is 8 ft 3 in, with a 9 ft depth. Converting to decimals gives 12.5, 8.25, and 9. The average base is (12.5 + 8.25)/2 = 10.375 ft, and the area is 10.375 × 9 ≈ 93.4 square feet. Pouring 4 inches of concrete requires about 93.4 × 0.33 = 3.1 cubic yards — order 3.5 yards to leave room for the 10% waste factor concrete suppliers always recommend.
Example 3 — A large river-front parcel (200 ft × 120 ft × 400 ft). A lot along a river has a 200 ft road frontage (Base 1), a 120 ft river frontage (Base 2), and is 400 ft deep between them. The average base is 160 ft and the area is 160 × 400 = 64,000 square feet, which is about 1.47 acres (an acre is 43,560 sq ft). At a property tax rate of 1.1% per year on an assessed value of $8.50 per square foot, the assessed value is 64,000 × $8.50 = $544,000, and the annual tax bill is roughly $5,984 — which is why surveyors measure the two parallel frontages precisely rather than guessing.
Example 4 — Paint for a trapezoidal gable wall (18 ft × 10 ft × 8 ft). A gable end of a garage has a horizontal ceiling line 18 ft long (Base 1), a ridge that is effectively a point at the top — which we treat as Base 2 = 0 — and an 8 ft height from ceiling to ridge. The average base is 9 ft and the area is 9 × 8 = 72 square feet. At 350 sq ft per gallon per coat, two coats need about 144 / 350 ≈ 0.42 gallons, so a single quart can covers both sides with room to spare.
FAQ
How do I calculate the area of a trapezoid?
Add the two parallel bases, divide by two to get the average width, then multiply by the perpendicular height between them: Area = (Base 1 + Base 2) / 2 × Height. Make sure both bases and the height are in the same unit. A 10-foot base, a 6-foot base, and a 4-foot height give an area of (10 + 6) / 2 × 4 = 32 square feet.
What is the difference between a trapezoid and a trapezium?
In American English, a trapezoid has exactly one pair of parallel sides; a trapezium has none. In British English, the two words are swapped — a trapezium has one pair of parallel sides, and a trapezium sometimes means any irregular quadrilateral. The area formula (bases-average × height) is the same regardless of which word your country uses, as long as you measure two parallel sides and the perpendicular distance between them.
Which side is the height, and why is it not a slanted side?
The height is the perpendicular distance between the two parallel bases — measured at a right angle to both. A slanted side (called a leg) is not the height unless the trapezoid is a rectangle. If you measure along a leg and plug that number into the formula, you will overstate the area, because the leg is always longer than the perpendicular height. To find the true height, drop a line straight down from the shorter base until it touches the longer base at a right angle.
What if one of the bases is zero?
Then the trapezoid collapses into a triangle, and the formula still works: (b + 0) / 2 × h = ½ × b × h, which is exactly the triangle area formula. This is why gable ends, sail shapes, and yield signs can be measured with this calculator by setting the shorter base to 0.
What if the two bases are equal?
Then the trapezoid is actually a rectangle, and the formula reduces to b × h, which is the standard rectangle area. The calculator handles this correctly — you do not need a separate rectangle tool, though the rectangle area calculator will also give you the perimeter and diagonal if you need those.
How do I convert the result to acres or square yards?
The area this calculator returns is in the square of whatever unit you entered. To convert: 1 square yard = 9 square feet; 1 acre = 43,560 square feet; 1 square meter ≈ 10.764 square feet; 1 hectare = 10,000 square meters. If you measured in feet and want square yards, divide the square footage by 9. If you measured in feet and want acres, divide by 43,560.
Why does the calculator reject a negative base or height?
A length below zero has no physical meaning, so the engine returns an error instead of a nonsense result. If you typed a minus sign by accident, re-enter the measurement as a positive number. Negative numbers inside the formula can produce a positive-looking area (because a negative base times a negative height is positive), which would look correct on paper while being completely wrong — so the calculator refuses them at the door.
Can I use this for an isosceles trapezoid or a right trapezoid?
Yes. The formula does not care whether the legs are equal (isosceles), whether one leg is perpendicular to the bases (right trapezoid), or whether the shape is skewed (scalene trapezoid). As long as you know the two parallel bases and the perpendicular height, the area is the same. Isosceles and right trapezoids are just special cases with extra symmetry — they do not need a different formula.
Disclaimer
This trapezoid area calculator is provided for informational purposes only and does not constitute engineering, surveying, construction, or design advice. Results are based on the dimensions you enter and the standard Euclidean formula A = (b₁ + b₂)/2 × h; actual material quantities, waste factors, survey boundaries, and project costs vary by location, product, and contractor. Always double-check measurements on site, confirm property boundaries with a licensed surveyor when buying or selling land, and verify material quantities with your supplier before ordering.