Area Calculator

Area is the amount of surface a shape covers, measured in square units — and it is the number behind paint quantities, flooring orders, seed coverage, and land prices. This calculator handles eight shapes, then converts the result between square metres, square feet, square centimetres, and square inches automatically.

The Eight Shapes and Their Formulas

| Shape | Inputs | Formula | | --- | --- | --- | | Rectangle | length, width | $A = l \times w$ | | Square | side | $A = s^2$ | | Circle | radius | $A = \pi r^2$ | | Triangle | base, height | $A = \tfrac{1}{2} b h$ | | Trapezoid | both parallel sides, height | $A = \tfrac{1}{2}(a + b) h$ | | Ellipse | semi-axis a, semi-axis b | $A = \pi a b$ | | Parallelogram | base, height | $A = b \times h$ | | Sector | radius, angle in degrees | $A = \frac{\theta}{360} \pi r^2$ |

Two inputs cause most errors in practice. A triangle's or parallelogram's height is the perpendicular distance, not the slanted side — use the slant and you overstate the area. And an ellipse takes semi-axes (half the full width and half the full height), because the formula $\pi a b$ is the circle formula generalized: set $a = b = r$ and it collapses back to $\pi r^2$.

Worked Examples

• Room (rectangle): 4 m × 3 m = 12 m² — which the converter also reports as 129.17 ft², the number a flooring supplier working in imperial will quote against.
• Circular rug: radius 5 m → $\pi \times 25$ = 78.54 m². Note the radius, not the diameter: a 10 m wide rug has radius 5.
• Garden bed (trapezoid): parallel sides 8 m and 12 m, 5 m apart → $\tfrac{1}{2}(8 + 12) \times 5$ = 50 m² of soil and mulch to order.
• Pizza slice (sector): radius 10 cm, angle 90° → $\tfrac{90}{360} \pi \times 100$ = 78.54 cm² — exactly a quarter of the whole pizza, as it should be.
• Oval patio (ellipse): semi-axes 4 m and 3 m → $\pi \times 4 \times 3$ = 37.70 m².

Units and Conversions

Enter dimensions in metres, centimetres, feet, inches, or yards — one unit per calculation, applied to every dimension. The engine converts through square metres (1 ft² = 0.092903 m², 1 in² = 0.00064516 m², 1 yd² = 0.836127 m²). For land units, which this tool does not output directly: acres = square feet ÷ 43,560 and hectares = square metres ÷ 10,000.

The single most common area mistake is mixing units mid-problem — a room measured as 12 ft by 3.5 m has no area until both sides share a unit. Convert lengths first, then multiply; converting the final area with a linear factor (using 3.28 instead of 10.76 for m² → ft²) is the runner-up error.

Irregular Shapes and Real-World Use

Real rooms are rarely one clean shape. Split the floor plan into rectangles and triangles, calculate each piece, and add them; subtract cut-outs (a hearth, an island) the same way. Then apply the project logic on top: flooring and tile need a waste allowance on the area (the tile calculator handles that), paint needs wall area minus openings (the paint calculator), and land listings deserve a skeptical re-measure — advertised square footage sometimes includes garages, wall thickness, or unfinished space depending on local convention.

Limitations

Formulas assume flat, Euclidean surfaces and exact inputs; measured dimensions carry their own error, which squaring amplifies — a 2% error in a circle's radius becomes a 4% error in its area. Three-dimensional coverage (domes, slopes, curved roofs) needs surface-area methods beyond these eight shapes.

Frequently Asked Questions

How do I get acres or hectares from the result?

Take the converted figure and divide: acres = ft² ÷ 43,560; hectares = m² ÷ 10,000. A 50 m² garden bed, for instance, is 0.005 hectares.

Why does the sector angle cap at 360 degrees?

A sector is a slice of one circle, so its angle runs from just above 0° to a full 360° (the whole circle, where the formula returns $\pi r^2$). Angles beyond that describe more than one disc and have no single-sector area.

Is square footage the same as area?

Yes — "square footage" is simply area expressed in square feet, the convention in US real estate. This calculator reports it alongside metric units so listings and metric measurements can be compared directly.