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Trapezoid Calculator

Calculate the area of a trapezoid using the two parallel sides (bases) and the height.

Reviewed by Chase FloiedUpdated

This free online trapezoid calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Length of the first parallel side

Length of the second parallel side

Perpendicular distance between the two bases

Results

Area

32 sq units

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Trapezoid Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Trapezoid Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Trapezoid Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Trapezoid Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Trapezoid Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate the area of a trapezoid using the two parallel sides (bases) and the height. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Trapezoid Calculator

A trapezoid (known as a trapezium in British English) is a quadrilateral with exactly one pair of parallel sides, called the bases. The area of a trapezoid is calculated using the formula A = ½(a + b)h, where a and b are the lengths of the two parallel sides and h is the perpendicular distance between them. This formula represents the average of the two bases multiplied by the height. Trapezoids appear frequently in architecture, engineering, and everyday objects — from bridge cross-sections to lamp shades to the side view of a bucket. The trapezoidal rule in numerical analysis uses this shape to approximate areas under curves, making it fundamental to applied mathematics. This calculator provides accurate area computations for any trapezoid when you know both bases and the height.

The Math Behind It

The trapezoid area formula A = ½(a + b)h can be understood as the area of a rectangle with width h and length equal to the average of the two bases, (a + b)/2. This is called the midsegment or median of the trapezoid. The formula can also be derived by dividing the trapezoid into two triangles sharing the same height: one with base a and one with base b, giving total area ½ah + ½bh = ½(a + b)h. An isosceles trapezoid has equal non-parallel sides (legs) and equal base angles. For an isosceles trapezoid, the diagonals are equal in length. The trapezoidal rule in calculus approximates ∫f(x)dx by dividing the interval into n strips, each approximated as a trapezoid: ∫ₐᵇ f(x)dx ≈ (h/2)[f(x₀) + 2f(x₁) + ... + 2f(xₙ₋₁) + f(xₙ)]. This method has error of order O(h²), making it more accurate than the left or right Riemann sum.

Formula Reference

Trapezoid Area

A = ½ × (a + b) × h

Variables: a, b = parallel sides (bases), h = height

Worked Examples

Example 1: Cross-section of a ditch

A ditch has a top width of 3 m, bottom width of 1.5 m, and depth of 1.2 m.

Step 1:A = ½ × (3 + 1.5) × 1.2
Step 2:A = ½ × 4.5 × 1.2
Step 3:A = ½ × 5.4

A = 2.7 square meters

Common Mistakes & Tips

  • !Using a slant side length instead of the perpendicular height.
  • !Forgetting to average the two bases (dividing by 2).
  • !Assuming the formula works for shapes with no parallel sides — it requires exactly one pair of parallel sides.

Related Concepts

Area of a Rectangle

A rectangle is a special trapezoid where both bases are equal.

Area of a Triangle

A triangle is a degenerate trapezoid where one base has length zero.

Frequently Asked Questions

What is the difference between a trapezoid and a parallelogram?

A trapezoid has exactly one pair of parallel sides, while a parallelogram has two pairs. A parallelogram can be seen as a special trapezoid.

What is the trapezoidal rule?

The trapezoidal rule is a method of numerical integration that approximates the area under a curve by dividing it into trapezoids. It uses the same area formula as this calculator.