Area Calculator
Find the area of eight common 2D shapes, with the formula and the substituted numbers shown for every result.
Details
Area of the rectangle
15
in square units
This works out the area of any common flat shape: rectangle, square, triangle, parallelogram, trapezoid, rhombus or circle.
Pick the shape, enter its measurements, and it returns the area in square units along with the formula used.
What area measures
Area is how much flat space a shape covers, measured in square units: square feet, square metres, square inches.
A square unit is literally a square one unit wide. An area of 96 square feet means 96 one-foot squares would cover it exactly.
Most of the formulas come from the same place. A rectangle is length × width, and nearly every other shape is a rectangle that has been halved, tilted or averaged, which is why they look related once you see it.
Draw a rectangle around any triangle using its base and height, and the triangle takes up exactly half of it, whatever shape the triangle is.
What to enter
- Shape
- The fields change to match: a rectangle needs two sides, a triangle needs a base and height, a trapezoid needs both parallel sides.
- Height
- For triangles and parallelograms this is the perpendicular height, straight up from the base, not the sloping side.
- Units
- Use one unit throughout. Mixing feet and inches in a single shape is the most common cause of a wrong answer.
The formulas, and where each comes from
- Rectangle
- length × width. Everything else is built from this.
- Square
- side × side. A rectangle with equal sides.
- Triangle
- ½ × base × height. Exactly half the rectangle around it.
- Parallelogram
- base × height. A rectangle pushed sideways, which does not change the area.
- Trapezoid
- ½ × (a + b) × height. The average of the two parallel sides, times the height.
- Circle
- π × radius². The one that is not built from a rectangle.
What this assumes
Shapes are regular and flat. An irregular plot needs splitting into pieces that are each a recognisable shape.
Height means perpendicular height. Using a slanted side instead overstates the area.
How to calculate the area of a shape
Identify the shape, use the matching formula, and keep every measurement in the same unit.
- base
- Any side you choose to measure from
- height
- The perpendicular distance from that base to the opposite point
Convert your units first. Get everything into feet, or everything into inches, before multiplying.
Find the perpendicular height. For triangles and parallelograms, measure straight up from the base at a right angle, not along the slope.
Apply the formula. The answer comes out in square units automatically, because you multiplied two lengths.
Split irregular shapes. An L-shaped room is two rectangles. Work out each and add them.
See a worked example: an L-shaped room, 12×8 with a 4×5 alcove
- Main area
- 12 ft × 8 ft
- Alcove
- 4 ft × 5 ft
Main rectangle: 12 × 8 = 96 sq ft.
Alcove: 4 × 5 = 20 sq ft.
Total: 96 + 20 = 116 sq ft.
Splitting into rectangles works for almost any awkward floor plan, and it is far more reliable than trying to find one clever formula.
116 square feet
Frequently asked questions
Area is the space inside, in square units. [Perimeter](/math/perimeter-calculator) is the distance around the edge, in ordinary units.
Area is what you need for flooring, paint or turf. Perimeter is what you need for fencing, skirting or edging.
Because any triangle fits exactly half of the rectangle drawn around its base and height.
It holds for every triangle, not just right-angled ones. Leaning the top point sideways does not change the area at all, as long as the height stays the same.
The perpendicular height: straight up from the base at a right angle, to the opposite corner.
On a slanted triangle that line sits inside the shape rather than along an edge, and using a sloping side instead always gives an answer that is too large.
Break it into pieces you recognise. Most rooms and plots divide neatly into two or three rectangles.
For curved or genuinely irregular boundaries, split it into strips of roughly equal width, treat each as a rectangle, and add them. More strips gives a better estimate.
Because area depends on two measurements at once. Doubling both length and width multiplies the area by 2 × 2 = 4.
This is why a 16-inch pizza has far more than twice the pizza of a 12-inch one, and why pricing by diameter is so misleading.
Problems people actually run into
Using a slanted side as the height
On a leaning triangle or parallelogram, the sloping side is longer than the perpendicular height. Using it inflates the area, sometimes considerably.
The height always meets the base at a right angle. On a strongly slanted shape that line may fall outside the figure entirely, which is correct even though it looks wrong.
Mixing units within one shape
Measuring a room as 12 feet by 90 inches and multiplying straight through gives an answer that is meaningless.
Convert first: 90 inches is 7.5 feet, so the area is 90 square feet. Order flooring off the unconverted figure and the mistake becomes expensive.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026