Area Calculator
Calculate the area of 12 shapes, from squares and circles to sectors, rings and regular polygons, in any unit.
How it works
Tap a shape, choose your length unit, and enter the measurements shown on the labeled drawing.
For triangles you can use base and height, or all three sides with Heron's formula. Circles accept a radius or diameter.
The area is shown in your squared unit and converted to square inches, feet, yards, centimeters, meters, acres and hectares.
Formula
Circle: A
Where:
- s (Heron)
- = Half the triangle's perimeter
- n, s (polygon)
- = Number of sides and side length
Worked example
A circle with radius 5, a 3-4-5 triangle and a regular hexagon with side 2.
Circle: π × 25 = 78.5398. Triangle: s = 6, √(6·3·2·1) = 6. Hexagon: 6 × 4 ÷ (4 × tan 30°) = 10.3923.
Precision in Complex Spatial Planning
When measuring irregular spaces, a helpful tip is to break the area down into basic shapes like rectangles and triangles. For instance, an L-shaped room is simply two rectangles joined together. By calculating the area of each component separately and summing them, you can find the total square footage of complex floor plans. Always measure each side twice; a small error in a single dimension can compound significantly when calculating total area, especially in large-scale residential projects.
Unit Consistency and Overlap Issues
One of the biggest mistakes in area calculation is mixing units during the measurement phase. Measuring one wall in feet and another in inches will lead to incorrect results if they are multiplied directly. Furthermore, remember that square units are not linear; there are 9 square feet in a square yard, not 3. This 'squaring of the factor' is a frequent source of under-ordering materials like carpet or sod for landscaping and construction tasks.
Modern Engineering and Agriculture
In agriculture, area calculations are used for precision farming to determine the exact amount of fertilizer or seed needed for a specific field. Drones map out the acreage, and calculators help farmers optimize resources to reduce waste. Similarly, in renewable energy, calculating the surface area of a roof determines the potential power output of a solar array, helping homeowners decide if the investment is viable based on their specific local energy needs and roof dimensions.
Frequently asked questions
Split it into rectangles (and triangles if needed), calculate each, then add them together.