About the Area calculator
This area calculator covers nine common shapes: rectangle, square, triangle, circle, trapezoid, parallelogram, ellipse, circle sector and regular hexagon. Pick a shape, enter its measurements, and you get the area. For shapes whose perimeter is fixed by those measurements, you get the perimeter too.
The steps show the formula and how your numbers are substituted in. It is useful for geometry homework and for real projects, like working out flooring, turf, paint, fabric or the size of a room. Use any unit you like; the area comes out in that unit squared.
How to use it
- Choose the Shape.
- Fill in the measurements that appear, such as Length and Width, Base and Height, or Radius.
- For a trapezoid, use side a and side b for the two parallel sides; for an ellipse, they are the two semi-axes.
- Read the area, and the perimeter where it applies.
- Check the formula used in the steps.
The formula
- Rectangle:
A = l × w,P = 2(l + w) - Square:
A = s²,P = 4s - Triangle:
A = ½ × base × height - Circle:
A = πr²,C = 2πr - Trapezoid:
A = (a + b) ÷ 2 × h, where a and b are the parallel sides - Parallelogram:
A = base × height - Ellipse:
A = πab, where a and b are the semi-axes; the perimeter uses Ramanujan's close approximation - Circle sector:
A = πr² × θ ÷ 360,P = 2r + arc length, with the arc2πr × θ ÷ 360 - Regular hexagon:
A = (3√3 ÷ 2) × s²,P = 6s
The height in the triangle, trapezoid and parallelogram formulas is always the perpendicular height, measured at a right angle to the base.
Worked example: a trapezoid-shaped garden bed
A garden bed has parallel sides of 5 m and 3 m, and the distance straight across between them is 4 m. The area is the average of the parallel sides times the height: (5 + 3) ÷ 2 × 4 = 4 × 4 = 16 m².
If bags of mulch cover 2 m² each, you need 8 bags. For a whole floor or yard, the square footage calculator handles rooms and costs.
Odd shapes can be split into simple ones. An L-shaped room is two rectangles; add their areas together. A room with a curved bay might be a rectangle plus a semicircle, which is half the area of a circle.
Mistakes that give the wrong area
Using the slanted side instead of the height. For a parallelogram with base 6 and slanted sides of 5, the area is not 6 × 5. You need the perpendicular height, which is less than 5.
Mixing units. A room 4 m by 350 cm must be written as 4 m by 3.5 m, giving 14 m². Convert first, or use the area converter afterwards.
Radius or diameter? The circle and sector formulas use the radius, which is half the diameter.
Forgetting the ½ for triangles. A triangle is half of a rectangle with the same base and height.
Area tells you how much surface a shape covers, while perimeter tells you the distance around it. Fencing depends on perimeter; seeding a lawn depends on area.
Frequently asked questions
How do I calculate the area of a rectangle?
Multiply the length by the width. A 12 ft by 10 ft room has an area of 120 square feet.
How do I find the area of a triangle?
Multiply the base by the perpendicular height and halve it. Base 8 and height 5 give 20 square units. If you only know the three sides, use the triangle calculator's Heron's formula.
Why is there no perimeter for a triangle, trapezoid or parallelogram?
Their perimeter depends on the slanted sides, which base and height do not tell you. Add the side lengths yourself if you know them.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and circles, find each area, and add them. Subtract any pieces that are cut out.
What units does the area come out in?
Square versions of whatever unit you used. Metres give m², feet give ft², and so on.
Last updated October 24, 2026. Results are estimates for education and planning — see our disclaimer.