CalcDuck

Area Calculator

Area Calculator

Shape
Area
40
Units
Results are in square units. Enter any consistent unit (all in cm, all in feet, etc.) and the area will be in that unit squared.

Area measures the space inside a two-dimensional shape, in square units. A rectangle 8 units long and 5 units wide has an area of 8 × 5 = 40 square units, while a circle of radius 7 has an area of π × 7² ≈ 153.94 square units.

Tip: “Copy with settings” shares a link that opens this calculator with your numbers already filled in.

How this calculator works

Pick a shape and enter its dimensions to get its area using the standard geometric formula for that shape. The rectangle, triangle, and trapezoid formulas work with any consistent unit of length; the circle formula uses the exact value of π available to JavaScript's floating-point math rather than a rounded approximation like 3.14.

Area is always expressed in square units because it measures a two-dimensional region: if your side lengths are in centimeters, the area comes out in square centimeters (cm²); in inches, it comes out in square inches (in²), and so on. The calculator does not convert between units, so keep every input in the same unit.

How do you calculate area?

Rectangle: Area = length × widthCircle: Area = π × radius²Triangle: Area = ½ × base × heightTrapezoid: Area = ½ × (a + b) × height, where a and b are the two parallel sides

Worked example: a trapezoid with parallel sides 3 and 5, height 4

  1. Add the parallel sides: 3 + 5 = 8.
  2. Take half of that sum: 8 ÷ 2 = 4.
  3. Multiply by the height: 4 × 4 = 16 square units.

Frequently asked questions

Why does a triangle's area use ½?

A triangle is exactly half of a parallelogram with the same base and height. If you place two identical triangles together along one side, they form a parallelogram of area base × height, so a single triangle is half of that.

Which side is the 'height' for a triangle?

It is the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. For a right triangle, the two legs can serve as base and height directly.

How accurate is the circle area?

This calculator uses JavaScript's built-in Math.PI, which carries about 15-16 significant digits of π, far more precision than the 3.14 or 3.14159 approximations used in most classroom problems.

Can I use a trapezoid formula for a rectangle?

Yes. A rectangle is a trapezoid where both parallel sides are equal, so a = b makes the trapezoid formula reduce to ½ × (a + a) × height = a × height, the same as the rectangle formula.

What is the difference between area and perimeter?

Area measures the two-dimensional space enclosed by a shape, in square units, while perimeter measures the distance around its boundary, in linear units. An 8-by-5 rectangle has an area of 8 × 5 = 40 square units, but a perimeter of 2 × (8 + 5) = 26 units — the two measure fundamentally different things, so they are never interchangeable even for the same shape.

Sources

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