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Area Calculator

The area of a square, rectangle, triangle, trapezoid, parallelogram, circle or ellipse — with the formula worked through and, for round shapes, the answer in terms of π.

Choose a shape and enter its measurements to see its area.

Exact calculation. Given your inputs, this is the answer — no estimation involved.

How this calculator works

Area is the amount of flat surface a shape covers, measured in square units: square inches, square feet, square meters. Each shape has its own formula, and the calculator shows it with your numbers substituted, step by step.

Straight-sided shapes come down to multiplying a length by a width. A rectangle is length times width. A parallelogram is base times height, where the height is measured straight up from the base, not along the slanted side. A triangle is half of that, because two copies of any triangle make a parallelogram, and a trapezoid averages its two parallel sides before multiplying by the height.

Round shapes use π. A circle’s area is π times the radius squared, so the radius matters twice as much as you might expect: doubling it makes the circle four times as big. If you know the diameter instead, the calculator halves it for you. The answer is given both as a decimal and in terms of π, such as 25π, because that is how many teachers ask for it.

Units are labels. The formula is the same in inches or meters; the area comes out in the square of whichever unit you chose.

The formula

Exactly what happens to your numbers, step by step.

Square and rectangle
```
A = s²          A = l × w
```
Parallelogram and triangle
```
A = b × h       A = ½ × b × h
```
h is the height at right angles to the base.
Trapezoid
```
A = ½ × (a + b) × h
```
a and b are the two parallel sides.
Circle
```
A = π r²        C = 2π r
```
r is the radius, half the diameter.
Ellipse
```
A = π × a × b
```
a and b are the two semi-axes, half the longest and shortest widths.

A worked example

A round tabletop 12 inches across.

What you enter

Shape: Circle
Diameter: 12 in

Step by step

Radius: r = 12 ÷ 2 = 6 in
Area: A = π × 6² = 36π
As a decimal: 36π ≈ 113.0973 in²
Circumference: C = 2π × 6 = 12π ≈ 37.6991 in

Area 36π, about 113.0973 square inches

A common slip is to square the diameter instead of the radius, which gives an answer four times too big: π × 12² is 144π, not 36π.

Area questions, worked out

Common homework and project questions, each solved with the same formula the calculator uses.

1.What is the area of a circle with a radius of 5?
1. A = π r² = π × 5² = 25π ≈ 78.5398
25π, or about 78.5398 square units.
2.What is the area of a circle with a diameter of 12 inches?
1. r = d ÷ 2 = 12 ÷ 2 = 6 in
2. A = π r² = π × 6² = 36π ≈ 113.0973 in²
36π, or about 113.0973 square inches.
3.What is the area of a triangle with a base of 10 and a height of 6?
1. A = ½ × b × h = ½ × 10 × 6 = 30
30 square units.
4.What is the area of a trapezoid with bases of 6 and 10 and a height of 4?
1. A = ½ × (a + b) × h = ½ × (6 + 10) × 4 = 32
32 square units.
5.How many square feet is a 12 by 15 foot room?
1. A = l × w = 12 × 15 = 180 ft²
180 square feet.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

Measurements are of a flat shape; for curved surfaces such as a dome, area works differently.
Heights are perpendicular to the base. A slanted side is not the height.
π is used to full precision; decimals are shown to four places.

What this cannot tell you

It handles one shape at a time. For an L-shaped room or several shapes added together, the square footage calculator adds them up.
A parallelogram’s or trapezoid’s perimeter needs the slanted sides, which these inputs do not include, so only the area is given. An ellipse’s perimeter has no exact formula and is not estimated.
For a triangle where you know the three sides rather than the base and height, use the triangle calculator.

Questions people ask

How do you find the area of a circle?

Square the radius and multiply by π. For a radius of 5, that is π × 25 = 25π, about 78.5398. If you have the diameter, halve it first: squaring the diameter by mistake gives an answer four times too big.

What is the difference between area and perimeter?

Area is the surface inside a shape, in square units. Perimeter is the distance around its edge, in plain units. A 12 by 15 foot room has an area of 180 square feet and a perimeter of 54 feet: carpet is bought by area, baseboard by perimeter.

How do I find the area of an irregular shape?

Split it into shapes you can measure, such as rectangles, triangles and half-circles, find each area, and add them up. An L-shaped room is two rectangles. The square footage calculator does the adding for several shapes at once.

What does "in terms of π" mean?

It means leaving π as a symbol instead of multiplying it out. A circle with a radius of 5 has an area of 25π exactly, which is about 78.5398. The π form is exact; the decimal is rounded, which is why many teachers ask for the π form.

Sources and review

This calculator uses standard arithmetic with no external rules or published rates, so there is nothing to cite beyond the formulas shown above.

Methodology version 1.0.0 · Last reviewed October 5, 2026

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 5). Area Calculator (Methodology version 1.0.0). https://chalkcalculator.com/area-calculator/

Link to it from your site

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