Calculate the area of any shape instantly — rectangles, triangles, circles, trapezoids, and more. Enter your measurements and get results with step-by-step formulas. Free online area calculator.
A rectangle is a quadrilateral with four right angles. It is one of the simplest shapes, and calculating its area only requires that its length and width are known. When the length and width of a rectangle are equal, the shape is a special case called a square.
A farmer's rectangular plot: 220 ft × 99 ft = 21,780 sq ft (half an acre). Despite having cows and measuring in feet (defined as 0.3048 meters in 1959), the farmer struggles to sell his land to foreign investors who expect more square feet for their money.
There are many equations for calculating the area of a triangle. This calculator uses Heron's formula (sometimes called Hero's formula), referring to Hero of Alexandria, a Greek mathematician considered by some to be the greatest experimenter of ancient times.
After selling his land, the farmer builds a triangular pool for his triangle-obsessed 7-year-old daughter. An equilateral triangle with 77 ft sides: s = 115.5, area = √(115.5 × 38.5³) = 2,567.33 sq ft. The pool has edges for "laps" while the daughter presides as queen.
A trapezoid is a simple convex quadrilateral that has at least one pair of parallel sides (bases). The other two sides are called legs. The height is the perpendicular distance between the bases.
Now 9, the daughter needs a BMX ramp using only triangles and the number 9. The farmer builds a trapezoidal ramp face: height 9 ft, bottom base 29.528 ft (9 m), top base 9 ft. Area = (9 + 29.528)/2 × 9 = 173.376 sq ft.
A circle is a simple closed shape formed by the set of all points in a plane that are a given distance (radius) from a given center point. Values in a circle are related through the mathematical constant π.
At 15, the daughter creates a crop circle with outer radius 15 ft: area = π × 15² = 706.858 sq ft. The crop circle attracts "cereologists" and alien investigators, causing significant crop damage.
A sector of a circle is a proportion of the circle enclosed by two radii and an arc. The area is the entire circle area multiplied by the ratio of the known angle to 360° (or 2π radians).
A raccoon eats 180° of a 16-inch radius blackberry pie. Each person gets 60°: area = 60°/360° × π × 16² = 134.041 in². Each gets one-third less pie, reminding the daughter of the Alamo and Davy Crockett's coonskin hat.
An ellipse is the generalized form of a circle. The semi-major axis (a) is the longest radius, and the semi-minor axis (b) is the shortest. When both are equal, the ellipse becomes a circle.
After college rejection, the 18-year-old builds an elliptical Earth orbit model: semi-major 20 ft, semi-minor 18 ft. Area = π × 18 × 20 = 1,130.97 sq ft. She gazes at the sun, her passion burning but distant.
A parallelogram is a simple quadrilateral with two pairs of parallel sides. Rectangles, rhombuses, and squares are all special cases. Area uses base and height (perpendicular distance between bases).
A massive octahedral diamond asteroid lands on the farm. Measuring a rhomboidal face: 20 ft × 18 ft = 360 sq ft. She sells the diamond to a wealthy collector, abandoning her convictions for lavish indulgence.
| Unit | Area in m² |
|---|---|
| square meter | SI Unit |
| hectare | 10,000 |
| square kilometre (km²) | 1,000,000 |
| square foot | 0.0929 |
| square yard | 0.8361 |
| acre | 4,046.9 (43,560 square feet) |
| square mile | 2,589,988 (640 acres) |
So you need to find the area of something. Maybe it's a room you're painting, a garden you're planting, or a math problem you're stuck on. Whatever it is, our area calculator has your back.
Here's the thing about area - it's just the amount of space inside a shape. Think of it like this: if you had a tiny paint roller and wanted to color in the whole shape, area tells you how much paint you'd need. Simple, right?
Our calculator handles all the common shapes: squares, rectangles, circles, triangles, trapezoids, parallelograms, ellipses, and sectors. Whatever shape you're working with, we've got you covered.
Using this thing is dead simple. Here's what you do:
Say you've got a rectangular room that's 12 feet long and 10 feet wide. Pick "rectangle" from the menu, type in 12 for length and 10 for width, and you'll get 120 square feet. That's how much flooring you'd need. Simple as that.
Each shape has its own formula, but they're all based on the same idea: how much space is inside.
The simplest of all. Multiply length by width. That's it.
Area = length × width
Uses the special number pi (π ≈ 3.14). Square the radius and multiply by pi.
Area = π × radius²
If you only know the diameter, divide it by 2 to get the radius first.
A triangle is half of a rectangle. So take half the base times height.
Area = ½ × base × height
Make sure the height is perpendicular to the base, not the slanted side.
Has two parallel sides of different lengths. Average them and multiply by height.
Area = ½ × (base₁ + base₂) × height
Like a pushed-over rectangle. Base times perpendicular height.
Area = base × height
Use the straight-up height, not the slanted side length.
A squished circle. Uses two radii: one for width, one for height.
Area = π × radius₁ × radius₂
A slice of a circle. Needs the angle and radius.
Area = (θ / 360°) × π × radius²
You might be thinking, "When am I ever gonna use this?" More often than you'd think.
Painting a room? You need wall area to buy paint. One gallon covers ~350-400 sq ft. Flooring? Carpet, tile, hardwood all sold by area. Don't overbuy or underbuy.
Planting grass seed or spreading mulch? Know your garden's area first. A typical mulch bag covers about 2 cubic feet spread 3 inches deep — but you need square footage first.
Building a model? Making a poster? Teachers and bosses love when you can explain your material estimates. Area calculations make you look like a pro.
Here's where most people mess up. Don't worry, it happens to everyone.
Mistake #1: Mixing Up Units
If length is in feet and width is in inches, you'll get a wrong answer. Always convert everything to the same unit first.
Mistake #2: Forgetting Square Units
Area is always in square units — square feet, square meters, square inches. If your answer just says "feet," something's off.
Mistake #3: Using the Wrong Measurement
For triangles, use perpendicular height, not the slanted side. For circles, use radius, not diameter (unless you divide by 2).
Mistake #4: Not Accounting for Waste
When buying materials, add 10-15% extra for waste. Cuts, mistakes, weird corners — they all eat up material. Better to have a little left over than run out.
Got a shape that doesn't fit any of the standard ones? Like an L-shaped room or a weird garden bed? Here's the trick: break it down.
Divide into smaller shapes
Calculate each one separately
Add (or subtract) the results
An L-shaped room is just two rectangles. A circular garden with a rectangular path through it? That's the circle's area minus the rectangle's area.
For really irregular shapes, use the grid method. Draw a grid where each square represents a known area (like 1 square foot). Count the full squares, estimate the partial ones, and add them up.
🧮 Use the calculator for complex shapes
Calculate each piece separately, write down the results, then add them up. Our calculator makes this fast.
📐 Convert units properly
Need square feet but measured in meters? 1 square meter = 10.76 square feet. Always convert before calculating.
🔍 Do a sanity check
If your room is 10×10 feet, the area should be about 100 sq ft. If you get 1,000, something's wrong.
The word "area" comes from Latin and means "a vacant piece of level ground." Makes sense when you think about it.
Ancient Egyptians used area calculations after the Nile flooded every year — they'd lose boundary markers and have to remeasure farmland. That's over 4,000 years ago.
The largest country by area is Russia at about 6.6 million square miles. The smallest is Vatican City at about 0.17 square miles. That's area at the extremes.
Area is the space inside a shape. Perimeter is the distance around the outside. Think of a fence around a yard — the fence length is the perimeter, the grass inside is the area.
Break it down into smaller shapes. An L-shaped room is two rectangles. A circle with a triangle cut out is the circle's area minus the triangle's area. For really weird shapes, use the grid method on graph paper.
Divide the diameter by 2 to get the radius, then use π × radius². So if your diameter is 10 feet, radius is 5 feet, and area is about 78.5 square feet.
½ × base × height. The base can be any side, but the height must be perpendicular to that base. Don't use the slanted side length unless it's actually the height.
Multiply the room's perimeter by the ceiling height to get total wall area. Subtract doors and windows. One gallon covers ~350-400 sq ft. Divide wall area by 350 to get gallons needed.
Add the two parallel sides, divide by 2 to average them, then multiply by height. Formula: ½ × (base₁ + base₂) × height. Height must be perpendicular to the bases.
Multiply base × perpendicular height. It's like a rectangle, but measure the height straight up from the base, not along the slanted side.
Measure length × width in feet. Add 10% extra for waste. A 12×10 room needs 120 + 12 = 132 square feet of flooring.