Area Calculator — Free Online Area Calculator

How to Use the Area Calculator

1. Select a shape: Choose from the dropdown menu: Rectangle, Triangle, Circle, Trapezoid, Ellipse, or Parallelogram. The input fields automatically adjust to show the required dimensions for the selected shape.
2. Enter dimensions: Type the required measurements into the input fields. Rectangles and parallelograms need length/base and width/height. Triangles need base and height. Circles need only the radius. Trapezoids need two parallel sides and the height. Ellipses need both semi-axes.
3. Read the result: The right panel instantly shows the calculated area in square units. The formula used for the computation is displayed below the result for educational reference. Results update in real time as you change any input value.
4. Compare shapes: Quickly switch between shapes to compare their areas with different dimensions. Default values load automatically when you change the shape selection, so you can see how each shape's area calculation works.

The calculator works with any unit system. If you enter measurements in feet, the area will be in square feet. If you enter in meters, the result is in square meters. Just ensure all inputs use the same unit for accurate results.

Area Formulas for All Shapes

Variables Explained

• Length / Width: For rectangles, the two perpendicular dimensions. Length is typically the longer dimension and width the shorter, though the formula works regardless of which is which.
• Base / Height: For triangles and parallelograms, the base is any side chosen as the reference, and the height is the perpendicular distance from the base to the opposite vertex (triangle) or side (parallelogram).
• r (Radius): For circles, the distance from the center to the edge. Related to diameter by r = d/2.
• a, b (Parallel Sides): For trapezoids, the two parallel sides. The height is the perpendicular distance between them.
• a, b (Semi-axes): For ellipses, the semi-major axis (a) is the longer half-axis and the semi-minor axis (b) is the shorter half-axis.

Step-by-Step Example (Trapezoid)

Calculate the area of a trapezoid with parallel sides of 10 and 6, and height of 4:

1. Identify the parallel sides: a = 10, b = 6
2. Identify the height: h = 4
3. Add the parallel sides: 10 + 6 = 16
4. Multiply by the height: 16 x 4 = 64
5. Divide by 2: 64 / 2 = 32 square units

Practical Examples

Example 1: Brian's Room Flooring

Brian is installing new hardwood floors in his living room, which measures 18 feet by 14 feet. He needs to calculate the area to determine how many boxes of flooring to buy.

• Shape: Rectangle, Length = 18 ft, Width = 14 ft
• Area = 18 x 14 = 252 sq ft
• With 10% waste factor: 252 x 1.10 = 277.2 sq ft of flooring needed

Brian needs about 277 square feet of flooring material. If each box covers 20 square feet, he needs 14 boxes (277.2 / 20 = 13.86, rounded up). The 10% waste factor accounts for cuts, mistakes, and matching patterns. For rooms with complex shapes, break them into rectangles and calculate each section separately.

Example 2: Emily's Garden Bed Design

Emily is designing a triangular garden bed in the corner of her backyard. The two sides along the fence are 8 feet and 6 feet, forming a right angle. She needs to know the area to buy the right amount of soil and mulch.

• Shape: Triangle (right triangle), Base = 8 ft, Height = 6 ft
• Area = (8 x 6) / 2 = 24 sq ft
• For 4 inches of soil: 24 x (4/12) = 8 cubic feet of soil

Emily needs 24 square feet of mulch and 8 cubic feet of soil. This triangular bed makes efficient use of the corner space while requiring less material than a full rectangular bed would. For calculating the soil volume, she would multiply the area by the depth, making the area calculation the essential first step.

Example 3: Carlos's Elliptical Patio

Carlos is building an elliptical patio. The longer dimension is 20 feet and the shorter dimension is 14 feet. He needs the area to order pavers and the approximate perimeter for edging stones.

• Semi-major axis: a = 20 / 2 = 10 ft
• Semi-minor axis: b = 14 / 2 = 7 ft
• Area = π x 10 x 7 = 219.91 sq ft

Carlos needs approximately 220 square feet of pavers. With an average paver size of 0.5 square feet, he needs about 440 pavers plus 10% extra for cuts and waste, totaling approximately 484 pavers. The elliptical shape provides an elegant look compared to a rectangular patio while fitting naturally into curved landscaping.

Example 4: Laura's Window Parallelogram

Laura is a stained glass artist creating a parallelogram-shaped window panel. The base measures 30 inches and the perpendicular height is 18 inches. She needs the area to estimate glass and lead requirements.

• Shape: Parallelogram, Base = 30 in, Height = 18 in
• Area = 30 x 18 = 540 sq in = 3.75 sq ft

Laura needs 540 square inches (3.75 square feet) of glass material. She should add 15-20% for cutting waste, especially for stained glass where irregular shapes reduce efficiency. The parallelogram shape creates a dynamic visual effect that traditional rectangular panels cannot achieve. For calculating the volume of 3D glass objects, try our volume calculator.

Area Formula Quick Reference Table

Tips and Complete Guide

Breaking Down Complex Shapes

Most real-world areas are not simple geometric shapes. The key technique is to break complex shapes into simpler ones and add or subtract areas. An L-shaped room becomes two rectangles. A house floor plan might be a large rectangle minus a smaller rectangle (for a cutout). A circular driveway with a rectangular house in the center is a circle area minus a rectangle area. Practice identifying which basic shapes compose your complex shape, and you can calculate any area.

Measuring Height Correctly

A common source of error is measuring the wrong "height." For triangles and parallelograms, the height must be perpendicular to the base, not the length of a slanted side. Imagine dropping a plumb line from the top vertex (triangle) or opposite side (parallelogram) straight down to the base. That vertical distance is the height. If you use the slanted side length instead, your area will be too large. The only exception is rectangles, where the sides are already perpendicular.

Waste Factors for Material Estimation

When calculating area for material purchases, always add a waste factor. Typical factors: flooring 10%, paint 5-10%, sod/turf 5%, tile 10-15% (more for diagonal patterns), mulch 5%, fabric 15-20% (for pattern matching). Irregular shapes require higher waste factors because more cutting and fitting is needed. It is always better to have slightly more material than to run short and face color/lot matching issues with a second purchase.

Area vs. Volume: When You Need Both

Area tells you how much surface a shape covers, but for many projects you also need volume (area times depth). For example, calculating how much soil to fill a garden bed requires area times depth. How much paint to cover a wall requires area divided by the paint's coverage rate. Understanding the relationship between area and volume is essential for practical applications. For volume calculations, try our volume calculator.

Common Mistakes to Avoid

• Using the slant height instead of perpendicular height: For triangles, parallelograms, and trapezoids, the height must be perpendicular to the base. The slant side is not the height unless the shape happens to be a right triangle or rectangle.
• Forgetting to halve the triangle formula: The area of a triangle is (base x height) / 2, not base x height. Forgetting the division by 2 doubles your answer.
• Confusing radius with diameter for circles: Using the diameter in the formula A = pi x r squared gives an area four times too large. If you know the diameter, divide by 2 first, or use A = (pi/4) x d squared.
• Mixing units: If you measure length in feet and width in inches, convert one measurement before multiplying. All dimensions must be in the same unit for the area to be correct.
• Forgetting to add a waste factor: Calculated area is the minimum you need. Real-world projects always require extra material for cuts, mistakes, and fitting. Add 5-20% depending on the material and complexity.

Frequently Asked Questions