📐 Area Calculator for Rectangle, Triangle, Circle and More Shapes
By ToolNimba Math Team · Updated 2026-06-23
This area calculator finds the area of six common flat shapes: the rectangle, square, triangle, circle, trapezoid and parallelogram. Pick a shape, type in the dimensions it asks for, and the calculator applies the right formula and shows you the working. Area is always measured in square units, so if you enter your lengths in centimeters the answer comes out in square centimeters.
What is the Area Calculator?
Area is the amount of flat surface a shape covers, measured in square units such as square centimeters (cm²), square meters (m²) or square inches (in²). Every shape has its own formula, but they all trace back to one idea: how many unit squares fit inside the outline. A rectangle that is 8 units long and 5 units wide holds 8 x 5 = 40 unit squares, so its area is 40 square units. A square is just a rectangle with equal sides, so its area is the side multiplied by itself.
Triangles, parallelograms and trapezoids all rely on a base and a perpendicular height, not a slanted side. A parallelogram has the same area as a rectangle with the same base and height (b x h), because you can cut a triangle off one end and slide it to the other to form a rectangle. A triangle is exactly half of that parallelogram, which is why its area is 0.5 x b x h. A trapezoid (a four-sided shape with one pair of parallel sides, called a trapezium in British English) averages its two parallel sides and multiplies by the height: 0.5 x (a + b) x h.
The circle is the odd one out because it has no straight sides. Its area is pi x r², where r is the radius (the distance from the center to the edge) and pi is roughly 3.14159. The radius is squared, so doubling the radius does not double the area, it quadruples it. The single most common error across all of these shapes is using a slanted edge in place of the true perpendicular height, which always overstates the area.
Real projects rarely come as a single neat shape, and that is fine. The standard trick for an irregular room, garden or plot is to split it into pieces you do recognize: rectangles, triangles and circle parts. Work out the area of each piece with this tool, then add them up. For an L-shaped room you might add two rectangles; for a plot with a curved end you might add a rectangle and a half circle. If part of the shape is cut out, such as a pillar or a flower bed, calculate that piece separately and subtract it from the total.
Because area is the basis of almost every material estimate, the unit you finish in matters as much as the number. Flooring, tile, carpet, turf, paint and fabric are all sold by area, so once you know the square meters or square feet you divide by the coverage on the product label to get the quantity to buy. Most trades then add a waste allowance of about 5 to 10 percent for cuts, offcuts and pattern matching. For land, an acre is 43,560 square feet and a hectare is 10,000 square meters, which is why large plots are usually quoted in acres or hectares rather than raw square feet.
A quick way to sanity check any answer is to remember that area grows with the square of size. If you double every length of a shape, its area becomes four times larger, not twice as large; triple the lengths and the area is nine times larger. So a room that is twice as long and twice as wide needs four times the flooring. Keeping that rule in mind catches the most expensive mistakes before you order materials.
When to use it
- Working out how much flooring, carpet, turf or tile you need to cover a room or yard, then dividing by the coverage per box or roll.
- Estimating how much paint a wall or ceiling needs by finding the surface area and dividing by the paint coverage per liter or gallon.
- Checking geometry homework for the area of rectangles, triangles, circles, trapezoids and parallelograms with full working shown.
- Converting a land or lot measurement into square feet, square meters, acres or hectares for real estate and gardening.
- Comparing the size of two plots, screens, panels or table tops that have different shapes.
- Breaking an irregular room or garden into simple shapes, calculating each part, and adding them for the total area.
How to use the Area Calculator
- Choose the shape you want from the dropdown (rectangle, square, triangle, circle, trapezoid or parallelogram).
- Enter the dimensions the shape asks for, using the same unit for every length.
- For triangles, parallelograms and trapezoids, use the perpendicular height, not the length of a slanted side.
- Optionally type a unit label (such as cm or m) so the result is shown in square units.
- Press Calculate area to see the area, the formula used, and the full working.
- For an irregular shape, split it into simple parts, calculate each one, then add (or subtract any cut-outs).
Formula & method
Worked examples
Find the area of a rectangle that is 8 m long and 5 m wide.
- Use Area = l x w for a rectangle.
- Area = 8 x 5
- Area = 40
Result: Area = 40 m²
Find the area of a triangle with base 10 cm and height 4 cm.
- Use Area = 0.5 x b x h for a triangle.
- Area = 0.5 x 10 x 4
- Area = 0.5 x 40 = 20
Result: Area = 20 cm²
Find the area of a circle with radius 7 in.
- Use Area = pi x r² for a circle.
- r² = 7 x 7 = 49
- Area = 3.14159 x 49 = 153.938
Result: Area ≈ 153.94 in²
Find the area of a trapezoid with parallel sides 6 and 10 and height 5.
- Use Area = 0.5 x (a + b) x h for a trapezoid.
- a + b = 6 + 10 = 16
- Area = 0.5 x 16 x 5 = 40
Result: Area = 40 square units
Find the floor area of an L-shaped room made of a 4 m x 3 m rectangle plus a 2 m x 2 m rectangle.
- Split the L-shape into two rectangles.
- First rectangle: 4 x 3 = 12 m².
- Second rectangle: 2 x 2 = 4 m².
- Add the parts: 12 + 4 = 16 m².
Result: Area = 16 m²
How much flooring covers a 5 m x 4 m room if each box holds 2 m² and you allow 10 percent waste?
- Find the room area: 5 x 4 = 20 m².
- Add 10 percent waste: 20 x 1.10 = 22 m².
- Divide by box coverage: 22 / 2 = 11 boxes.
Result: Buy 11 boxes (22 m² including waste)
Area formula for each supported shape
| Shape | Inputs needed | Area formula |
|---|---|---|
| Rectangle | length l, width w | l x w |
| Square | side s | s x s = s² |
| Triangle | base b, height h | 0.5 x b x h |
| Circle | radius r | pi x r² |
| Trapezoid | parallel sides a and b, height h | 0.5 x (a + b) x h |
| Parallelogram | base b, height h | b x h |
Formulas for other shapes you can build from the basics
| Shape | Inputs needed | Area formula |
|---|---|---|
| Semicircle | radius r | 0.5 x pi x r² |
| Ellipse | semi-axes a and b | pi x a x b |
| Sector | radius r, angle in degrees | (angle / 360) x pi x r² |
| Rhombus | diagonals d1 and d2 | 0.5 x d1 x d2 |
| Regular hexagon | side s | 2.598 x s² |
| Right triangle | two legs a and b | 0.5 x a x b |
Common square-unit and land conversions
| From | To | Multiply by |
|---|---|---|
| 1 m² | cm² | 10,000 |
| 1 m² | ft² | 10.7639 |
| 1 ft² | in² | 144 |
| 1 ft² | m² | 0.092903 |
| 1 km² | m² | 1,000,000 |
| 1 acre | ft² | 43,560 |
| 1 hectare | m² | 10,000 |
| 1 acre | hectares | 0.404686 |
Common mistakes to avoid
- Using a slanted side instead of the perpendicular height. For triangles, parallelograms and trapezoids the h in the formula is the straight-up height, measured at a right angle to the base, not the length of a sloping edge. Using the slanted side overstates the area.
- Using the diameter instead of the radius for a circle. The circle formula uses the radius, which is half the diameter. If you have the diameter, divide it by two first. Plugging the diameter straight into pi x r² gives four times the true area.
- Forgetting the 0.5 in the triangle and trapezoid formulas. A triangle is half of the rectangle that would surround it, so the area is 0.5 x b x h. Leaving out the half doubles the answer. The trapezoid formula also begins with 0.5.
- Mixing units within one shape. All lengths for a single shape must share the same unit. Multiplying a length in meters by a width in centimeters gives a meaningless result, so convert everything to one unit first.
- Forgetting a waste allowance on material estimates. Flooring, tile and turf need cuts around edges, so the area you calculate is the bare minimum. Add roughly 5 to 10 percent extra (more for diagonal or patterned layouts) so you do not run short mid-job.
- Confusing area with perimeter. Perimeter is the distance around a shape in plain length units, while area is the surface inside it in square units. Reaching for the perimeter formula when you need area, or vice versa, gives an answer in the wrong kind of unit.
Glossary
- Area
- The amount of flat surface a shape covers, measured in square units such as cm² or m².
- Base
- The side of a triangle, parallelogram or trapezoid that the perpendicular height is measured against.
- Height
- The perpendicular (straight-up) distance from the base to the opposite point or side, not a slanted edge.
- Radius
- The distance from the center of a circle to its edge. It is half the diameter.
- Diameter
- The distance straight across a circle through its center. It is twice the radius.
- Parallel sides
- The two sides of a trapezoid that never meet, labelled a and b in the area formula.
- Square unit
- The unit of area, such as the square meter (m²), formed by squaring a unit of length.
- Perimeter
- The total distance around the outside edge of a shape, measured in plain length units rather than square units.
Frequently asked questions
How do I calculate the area of a rectangle?
Multiply the length by the width: Area = l x w. For example, a rectangle 8 units long and 5 units wide has an area of 8 x 5 = 40 square units. A square is the special case where the length and width are equal, so its area is the side squared.
What is the formula for the area of a triangle?
The area of a triangle is 0.5 x base x height, where the height is measured at a right angle to the base. A triangle with a base of 10 and a height of 4 has an area of 0.5 x 10 x 4 = 20 square units. This works for any triangle, not just right triangles.
How do I find the area of a circle?
Use Area = pi x r², where r is the radius and pi is about 3.14159. Square the radius first, then multiply by pi. A circle with a radius of 7 has an area of about 3.14159 x 49 = 153.94 square units. If you only know the diameter, halve it to get the radius.
What is the area of a trapezoid?
Add the two parallel sides, multiply by the height, then halve it: Area = 0.5 x (a + b) x h. With parallel sides of 6 and 10 and a height of 5, the area is 0.5 x 16 x 5 = 40 square units. The height is the perpendicular gap between the parallel sides.
How do I calculate the area of an irregular shape?
Break the irregular shape into simple shapes you recognize, such as rectangles, triangles and parts of circles. Calculate the area of each piece, then add them together for the total. If part of the shape is cut out, like a pillar or pond, work out that area and subtract it.
How do I work out square footage for a room?
For a rectangular room, multiply the length by the width in feet to get the area in square feet. A 12 ft by 10 ft room is 120 square feet. For an L-shaped or irregular room, split it into rectangles, find each area, and add them. Add 5 to 10 percent extra for material waste.
How many square feet are in an acre?
One acre is 43,560 square feet. To convert square feet to acres, divide by 43,560; to go the other way, multiply acres by 43,560. For metric land area, one hectare is 10,000 square meters, and one acre is about 0.405 hectares.
Why is area measured in square units?
Area counts how many unit squares fit inside a shape, so the unit is a square. If you measure lengths in meters the area is in square meters (m²); in centimeters it is square centimeters (cm²). Always keep the lengths in one unit so the squared result is consistent.
What is the difference between area and perimeter?
Perimeter is the total distance around the outside of a shape, measured in plain length units. Area is the surface inside the outline, measured in square units. A shape can have a large perimeter but a small area, or the other way around, so they answer different questions.
If I double the size of a shape, does the area double?
No. Area grows with the square of the size, so doubling every length makes the area four times larger, and tripling the lengths makes it nine times larger. That is why a room twice as long and twice as wide needs four times as much flooring, not twice as much.