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Area Calculator

Find how much surface a rectangle, square, circle, triangle, trapezoid, parallelogram or ellipse covers, in square meters, square feet and acres.

Level: Grades 6–7

  • Common Core standard 6.G.A.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
  • Common Core standard 7.G.B.4Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Printable worksheet

Area Calculator

Know the answer you need? Pick an input to work backward.

Inputs

Result

Area

120 ft²

The area is 120 ft².

In square meters
11.1484 m²
In acres
0.002755 ac
Perimeter
44 ft

See the step-by-step solution ↓

Step-by-step solution

  1. Multiply the length by the width. That counts how many unit squares cover the rectangle

    12×10=120 ft²

  2. To change to square meters, multiply by the size of 1 ft in meters, squared, because area has two directions

    120 ft²×0.30482=11.148365 m²

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much flat surface a shape covers, whether it's a floor, a wall, a garden bed or a plot of land. That amount is called area, and it's measured in square units, such as square feet. It's the number you need when buying flooring, paint, turf or fabric. Each common shape has its own short formula, and this calculator knows them all.

Choose a shape, pick the unit you measured in, and enter the sizes. You'll see the area in that unit squared. It's also changed to square meters, square feet and acres. Where a shape has an easy formula for its edge, you'll get the perimeter (distance around) or circumference too.

Where it's used

Why this math matters outside the classroom:

  • Flooring a room. A homeowner tiling a 12 ft by 15 ft kitchen multiplies the sides to get 180 square feet of floor.
  • Garden beds. A trapezoid-shaped bed with parallel sides of 8 ft and 12 ft, 5 ft apart, covers ½ × (8 + 12) × 5 = 50 square feet.
  • Round tablecloths. A round table 4 ft across has a top of π × 2², about 12.6 square feet, to cover.
  • Painting a gable. The triangular gable end of a shed, 10 ft wide and 4 ft tall, has ½ × 10 × 4 = 20 square feet to paint.
  • Land plots. A lot measuring 200 ft by 218 ft covers 43,600 square feet, almost exactly one acre of 43,560.

Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.G.A.1, 7.G.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Select the shape. For a triangle, choose base and height if you know the straight-up height. Choose three sides if you only know the side lengths.
  2. Select the unit your measurements are in, from millimeters to miles.
  3. Enter the sizes. Each one must be more than zero, and all must be in the same unit.
  4. Read the area and its conversions. Perimeter is shown for rectangles, squares, circles and three-side triangles.

What the inputs mean

Shape
The shape to measure. Odd shapes can often be split into rectangles and triangles, and their areas added together.
Measurement unit
The unit of every length you enter. The area comes out in the same unit, squared.
Bottom (longer parallel side)
The longer of the trapezoid's two parallel sides.
Top (shorter parallel side)
The shorter of the trapezoid's two parallel sides.
Height (perpendicular)
For triangles, parallelograms and trapezoids, use the straight-up height, measured at a right angle to the base. Don't use the length of a slanted side.
Semi-major axis (half the longest width)
Half the ellipse's longest width, measured from the center.
Semi-minor axis (half the shortest width)
Half the ellipse's shortest width, measured from the center.

Formula and method

Rectangle: A = length × width;  P = 2 × (length + width)
Square: A = side²;  P = 4 × side
Circle: A = π × r²;  C = 2 × π × r
Triangle (base, height): A = base × height ÷ 2
Triangle (three sides): s = (a + b + c) ÷ 2;  A = √(s × (s − a) × (s − b) × (s − c));  P = a + b + c
Trapezoid: A = (top + bottom) ÷ 2 × height
Parallelogram: A = base × height
Ellipse: A = π × semi-major × semi-minor
1 acre = 4,046.8564224 m² = 43,560 ft²

In the formulas, A is the area, P is the perimeter (the distance around), C is a circle's circumference and r is its radius (center to edge). π is about 3.14159, and a small ² means a number times itself. For the three-side triangle, a, b and c are the side lengths, s is half their total, and √ means square root.

The three-side triangle uses Heron's formula, which finds the area from the side lengths alone. The calculator works it out in a rearranged but equal form, with the sides sorted longest to shortest. That avoids rounding error for long, thin triangles. The sides must be able to make a triangle: each one shorter than the other two put together.

Converting area squares the length factor. 1 ft = 0.3048 m exactly, so 1 ft² = 0.09290304 m². Acres are found from square meters, using the exact size of the international acre.

An ellipse (oval) has no simple exact formula for its perimeter. The base-and-height triangle, trapezoid and parallelogram don't give enough information for one. So no perimeter is shown for those.

Worked example

A room measures 12 ft by 10 ft. How much floor area is that?

  1. Area: 12 × 10 = 120 ft².
  2. In square meters: 120 × 0.3048² = 120 × 0.09290304 = 11.1483648 m².
  3. In acres: 11.1483648 ÷ 4,046.8564224 ≈ 0.002755 ac.
  4. Perimeter: 2 × (12 + 10) = 44 ft.

Result: The floor is 120 square feet (about 11.15 m²), with a perimeter of 44 feet.

Understanding the result

Buy materials by area, then add a bit extra for cuts and waste. How much extra depends on the material and the layout.

Area grows faster than length. If you double every side of a shape, its area becomes four times as big.

Assumptions and limitations

  • All sizes are in the same unit and describe a perfect flat shape.
  • Heights are straight-up heights, at a right angle to the base.
  • US units use the international definitions (1 ft = 0.3048 m).
  • Curved surfaces, such as the walls of a round tank, and uneven outlines aren't handled directly. Split them into supported shapes where you can.
  • No perimeter is given for ellipses, base-and-height triangles, trapezoids or parallelograms.
  • Land measured with the US survey foot can differ very slightly from these results.

Frequently asked questions

How do I find the area of an L-shaped room?

Split it into two rectangles, work out each one, and add the results. For a shape with a piece cut out, work out the outer rectangle and take away the missing piece.

What if I only know the three sides of a triangle?

Choose “Triangle (three sides)”. It uses Heron's formula, so you don't need the height. A 3–4–5 triangle, for example, has an area of 6 square units.

Why do I get an error that the sides can't form a triangle?

Any two sides of a triangle together must be longer than the third. Sides of 1, 2 and 3 would lie flat in a straight line and enclose no area. So the calculator turns them away.

How many square feet are in an acre?

43,560 square feet, which is 4,046.8564224 square meters. A square acre is about 208.7 feet on each side.

How this calculator is checked

Method: Standard Euclidean area formulas; Heron's formula in its numerically stable sorted-side form; international foot and acre definitions for conversions. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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