📐 Area Calculator (Shapes)
By ToolNimba Math Team · Updated 2026-06-19
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) 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.
When to use it
- Working out how much flooring, carpet, turf or tile you need to cover a room or yard.
- Checking geometry homework for the area of rectangles, triangles, circles and trapezoids.
- Estimating how much paint, fabric or material a surface will require before you buy.
- Comparing the size of two plots, screens or panels that have different shapes.
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.
- 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.
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
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 |
Common square-unit 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 |
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.
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.
- 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.
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.
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.