Area Calculator

Say you are tiling a kitchen floor that measures 4 meters by 3 meters. The floor is a rectangle, so its area is length times width: 4 × 3 = 12 square meters (m²). Add about 10% for cuts and waste and you would buy roughly 13.2 m² of tile. That single calculation — turning two measurements into the space inside a shape — is what this area calculator does for seven of the most common shapes, and it shows the steps so you understand the result rather than just copying a number.

What is area?

Area is the amount of two-dimensional space enclosed by a flat shape. It is always measured in square units — square centimeters (cm²), square meters (m²), square feet (ft²), and so on — because you are effectively counting how many unit squares fit inside the shape. A region 3 units wide and 2 units tall holds 3 × 2 = 6 unit squares, hence 6 square units. Area is different from perimeter, which is the distance around the edge and is measured in plain length units.

The area formulas

Each shape has its own formula. The calculator applies the right one automatically once you pick the shape:

In these formulas L and W are length and width, s is a side, b is the base, h is the perpendicular height, r is the radius, a and b are the two parallel sides of a trapezoid or the two semi-axes of an ellipse, and π (pi) ≈ 3.14159.

How to use this area calculator

1. Pick a shape from the grid of buttons. The matching formula appears right below it.
2. Enter the dimensions the shape needs — for a rectangle that is length and width; for a circle just the radius.
3. Choose a unit from the dropdown. This is only a label, so make sure every measurement you typed is in that same unit.
4. Read the result. The large blue number is the area; where it applies, the perimeter or circumference appears beside it.
5. Check the steps. The step-by-step box shows the formula with your numbers plugged in, so you can verify or learn the method.

Who this calculator is for

• Students checking geometry homework and learning the formulas with worked steps.
• Teachers and tutors generating quick, correct examples for any of the seven shapes.
• DIY and home projects — flooring, paint, wallpaper, decking, turf, and garden beds.
• Trades and crafts — estimating material for a wall, a tabletop, or a fabric cut.
• Anyone who needs a fast, accurate square-footage or square-meter figure without doing the arithmetic by hand.

Worked example 1: a circular table top

You want to know the area of a round table with a radius of 0.6 m to estimate a glass cover. The circle formula is A = π × r². So A = π × 0.6² = π × 0.36 ≈ 1.131 m². The circumference (distance around the edge, useful for a trim) is C = 2 × π × r = 2 × π × 0.6 ≈ 3.770 m. If you only knew the diameter (1.2 m), you would halve it to get the radius first.

Worked example 2: a triangular garden bed

A triangular flower bed has a base of 5 ft and a perpendicular height of 3 ft. The triangle formula is A = ½ × b × h = ½ × 5 × 3 = 7.5 ft². The key word is perpendicular: the height must be measured straight from the base to the opposite point, not along a slanted side. Using a slant length instead is the most common triangle mistake.

Worked example 3: a trapezoidal deck

A deck is shaped like a trapezoid with parallel sides of 4 m and 6 m and a height between them of 3 m. Area = ½ × (a + b) × h = ½ × (4 + 6) × 3 = ½ × 10 × 3 = 15 m². Notice the formula simply averages the two parallel sides (4 and 6 average to 5) and multiplies by the height (5 × 3 = 15).

Quick area reference table

A handy summary of all seven shapes, what you need to measure, and the formula:

Key terms explained

• Base (b): the side a shape "sits on." For triangles and parallelograms it pairs with the perpendicular height.
• Height (h): the perpendicular (straight-up) distance from the base to the top — not a slanted edge.
• Radius (r): distance from a circle's center to its edge. Diameter = 2 × radius.
• Semi-axis: half of an ellipse's longest (major) or shortest (minor) diameter; a circle is an ellipse where both semi-axes are equal.
• π (pi): the ratio of a circle's circumference to its diameter, about 3.14159, an irrational constant.
• Square unit: the unit of area, written with a small "²", such as m² or ft².

Breaking complex shapes into simple ones

Most real-world shapes are not in the list, but they can be split into shapes that are. An L-shaped room divides into two rectangles — find each area and add them. A regular hexagon divides into six identical triangles, so a dedicated triangle calculator can solve each wedge if you only know the sides. A stadium / running-track shape is a rectangle with a half-circle on each end (a rectangle plus one full circle); the circle calculator gives you the round part directly. For a cut-out, like a window in a wall you are painting, calculate the big shape and subtract the small one. This "add and subtract" approach handles almost any flat layout.

Why the unit matters

Area scales with the square of length, which trips people up. If you double every dimension, the area becomes four times larger, not twice. That is also why unit conversions for area are not the same as for length: 1 m = 100 cm, but 1 m² = 10,000 cm² (because 100 × 100). Always convert all measurements to one length unit before calculating, and remember the answer is in that unit squared.

How this calculator compares to a single-shape tool

This page is a general-purpose tool that switches between seven shapes in one place — handy when you are estimating a mixed layout or checking homework across several shape types. If you are working exclusively with one shape and want extra outputs (such as a triangle's angles or a circle's circumference, diameter, and sector area), a dedicated tool digs deeper: the triangle calculator solves sides and angles, the circle calculator covers radius, diameter, area, and circumference together, and the perimeter calculator focuses on boundary length. Use this area calculator for speed and breadth, and a specialized one when you need every property of a single shape.

Tips for accurate results

• Measure twice; a small error in length is doubled in area for a square shape.
• For circles, measure the diameter across the widest point and halve it — it is easier than guessing the center for the radius.
• Always use the perpendicular height for triangles, trapezoids, and parallelograms.
• Keep extra decimal places during the calculation and round only the final answer.
• For materials, add a waste allowance (commonly 5–10%) on top of the calculated area.

Area vs perimeter vs volume

These three measurements describe completely different things, and mixing them up is the source of most everyday errors. The simplest way to keep them straight is by their units: a plain unit for distance, a squared unit for area, and a cubed unit for volume.

If you need the distance around a shape rather than the space inside it, use the perimeter calculator. When the project is three-dimensional — pouring concrete, filling a planter box, or sizing a tank — switch to the volume calculator instead. Area sits in the middle, and it is what almost every flooring, painting, and landscaping estimate starts from.

From area to square footage and material orders

The most common reason people calculate area is to buy something that covers a surface. The workflow is the same whether it is paint, tile, carpet, or sod. First, find the area in the unit the product is sold in (square feet in the US, square meters elsewhere). Second, divide that area by the coverage rating of the product — a gallon of paint covers roughly 350–400 ft², a box of tile lists its square footage on the label. Third, add a waste allowance (5% for a simple rectangular room, up to 15% for diagonal layouts or lots of cuts) and round up to whole packs. For example, a 12 ft × 15 ft room is 180 ft²; at one coat per 375 ft² per gallon you need about half a gallon (180 ÷ 375 ≈ 0.48), so you buy one gallon. For tile at 10 ft² per box plus 10% waste, 180 × 1.10 = 198 ft² ÷ 10 = 20 boxes. Getting the area right is the step that prevents both a second trip to the store and a pile of leftover material.

Converting between area units

Because area scales with the square of length, area conversions are not the same as length conversions — this catches almost everyone at least once. To convert an area unit, you square the length conversion factor. A few of the most useful conversions:

• 1 m² = 10,000 cm² (because 100 cm × 100 cm), and 1 m² ≈ 10.764 ft².
• 1 ft² = 144 in² (12 in × 12 in), and 1 yd² = 9 ft².
• 1 acre = 43,560 ft² ≈ 4,047 m², and 1 hectare = 10,000 m² ≈ 2.471 acres.
• 1 km² = 1,000,000 m² = 100 hectares.

The safe habit is to convert all of your length measurements into one unit before you calculate the area, then convert the final area only if you need a different unit at the end. That avoids the classic mistake of treating 1 m² as 100 cm². For other non-area conversions, a general unit converter handles length, weight, and temperature.

Related concepts

Area is the gateway to several other measurements. Perimeter and circumference measure the boundary instead of the inside. Surface area extends the idea to 3D solids — it is the total area of every face of a box, cylinder, or sphere. Volume measures the 3D space a solid contains (in cubic units). And ratios and proportions let you scale a shape up or down while keeping it the same form, which is where the square-scaling rule above comes in; the ratio calculator handles those scale factors, and finding a square's side from its area is exactly what a square root calculator does.

Sources

• National Institute of Standards and Technology (NIST) — SI units for area and unit definitions.
• NIST Handbook 44 / Special Publication 811 — Guide for the Use of the International System of Units (conversion factors).
• Standard Euclidean-geometry area formulas (rectangle, triangle, circle, trapezoid, parallelogram, ellipse), as taught in any geometry curriculum and tabulated in mathematical references.