Area Calculator
Work out the area of seven common shapes without hunting for the right formula first. Pick a shape, choose your unit, enter the dimensions, and you get the answer along with the arithmetic that produced it. Circles, triangles, trapezoids, parallelograms, and ovals are all covered, not just rectangles.
Every dimension has to be in this same unit.
Formula
A = width × height
Your area will appear here
Choose a shape, set your unit, fill in the dimensions, then calculate.
Quick Answer
Area is the space inside a shape, measured in square units. Rectangle: width × height. Square: side². Triangle: ½ × base × height. Circle: π × radius². Trapezoid: ((base₁ + base₂) ÷ 2) × height. Parallelogram: base × height. Ellipse: π × a × b, using the two semi-axes. Every dimension has to be in the same unit, and the height in a triangle, trapezoid, or parallelogram is the perpendicular height, never the slanted side.
How It Works: Formula & Variables
Seven shapes, seven formulas. All of them take lengths in one unit and give back an area in square units of that same unit.
- Rectangle
- A = width × height
- Square
- A = side²
- A square is a rectangle with both sides equal, so it uses the same rule.
- Triangle
- A = ½ × base × height
- The height is the perpendicular drop from the opposite corner onto the base you picked.
- Circle
- A = π × radius²
- Trapezoid
- A = ((base₁ + base₂) ÷ 2) × height
- The two bases are the parallel sides. The height is the perpendicular distance between them.
- Parallelogram
- A = base × height
- Perpendicular height again, not the sloped edge.
- Ellipse
- A = π × a × b
- a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest). Set a and b equal and you get πr² back, which is why the circle is really a special case of the ellipse.
Pricing a floor rather than measuring one? Our Square Footage / Flooring Cost Calculator handles waste allowance, box counts, and cost per square foot across multiple rectangular rooms. This page stays on the geometry.
Worked Examples
Example 1: Circle with a 5 m radius
Square the radius first, then multiply by pi. 5² is 25, and π × 25 = 78.5398…, which rounds to 78.54 m². Had you measured the full 10 m across instead, halve it to get the radius before squaring. Squaring the diameter by mistake would give you four times too much.
Example 2: Ellipse with semi-axes of 5 m and 3 m
Multiply the two semi-axes together and then by pi. 5 × 3 = 15, and π × 15 = 47.1238…, so about 47.12 m². This oval measures 10 m across at its widest and 6 m at its narrowest. Plugging those full widths straight into the formula would report four times the real area.
Example 3: Trapezoid with bases of 8 and 4, height 5
Average the two parallel sides, then multiply by the height. (8 + 4) ÷ 2 = 6, and 6 × 5 = 30 square units. Averaging the bases is what makes this work: a trapezoid covers the same space as a rectangle whose width is the mean of its two parallel sides.
Key Concepts
Square units, always: Area answers arrive in square units because you multiplied two lengths together. Meters times meters gives m². That also means unit conversions for area are the square of the length conversion, so 1 ft = 0.3048 m but 1 sq ft = 0.0929 m².
Perpendicular height is the whole game: Triangles, parallelograms, and trapezoids all rely on a height measured at a right angle to the base. On a leaning shape that height sits shorter than the sloped side, sometimes a lot shorter. Picture dropping a plumb line from the top corner and measure that.
Semi-axes, not full axes: The ellipse formula wants half of each axis. Since a and b are both halved, using full measurements inflates the answer by a factor of four rather than two, which is easy to miss because the number still looks plausible.
Break awkward shapes into simple ones: An L-shaped room is two rectangles. A gable wall is a rectangle with a triangle on top. Splitting a shape, calculating each piece, then adding the results handles most real rooms without any new formulas.
This tool measures, it does not price: There are no cost fields, waste percentages, or box counts here on purpose. If you need those, the Square Footage / Flooring Cost Calculator takes rectangular rooms through to a budget.
Common Mistakes
Using the slanted side as the height: The single most common error with triangles, parallelograms, and trapezoids. The sloped edge is longer than the true perpendicular height, so the area comes out too big. Measure straight across, at a right angle to the base.
Feeding full axes into the ellipse formula: a and b are semi-axes, meaning half the full width in each direction. Halve your measurements before multiplying, or use the axis toggle in the calculator and let it do the halving.
Mixing units in one calculation: Centimeters for one side and meters for another gives a number with no meaning. Convert everything to a single unit first. This bites hardest when you measure small features in inches and room dimensions in feet.
Squaring the diameter instead of the radius: A circle's formula needs the radius. Using the diameter without halving it first quadruples the answer, and the result rarely looks obviously wrong.
Converting area with the length factor: Multiplying square feet by 0.3048 instead of 0.0929 is a common slip. Area conversions square the length factor.
Frequently Asked Questions
Area is the amount of space inside a shape, so it is always measured in square units like m² or ft². Perimeter is the distance around the outside of it, measured in plain units like meters or feet. A 4 by 6 meter room has an area of 24 m² and a perimeter of 20 m. Paint and flooring go by area; skirting board and fencing go by perimeter.
Multiply pi by the radius squared, so A = π × r². The radius runs from the center to the edge, which is half the diameter. A circle with a 5 m radius covers π × 25, about 78.54 m². If you measured all the way across the circle instead, switch the calculator to diameter and it halves the figure for you before squaring it.
Multiply pi by both semi-axes: A = π × a × b, where a is half the longest width and b is half the shortest. An oval measuring 10 m by 6 m across has semi-axes of 5 and 3, so the area is π × 15, roughly 47.12 m². When a and b are equal you are back to a circle and the formula gives you πr² again.
The perpendicular height that meets your chosen base at a right angle, not the slanted side. On a leaning parallelogram the sloped edge is longer than the true height, and using it will overstate the area every time. Same rule for a triangle: measure straight down from the opposite corner to the base line, extending the base beyond the shape if you have to.
Square units of whatever you measured in. Feed the calculator meters and you get m²; feed it feet and you get ft². The one rule that matters is consistency. Mixing centimeters for one side and meters for another produces a number that means nothing, so convert everything first and then calculate.
Divide by 10.7639, since one square meter holds that many square feet. A 300 sq ft room works out to about 27.87 m². Going the other way, multiply square meters by 10.7639. Note that the conversion factor for area is the square of the length factor, which catches people out: 1 ft is 0.3048 m, but 1 sq ft is 0.0929 m².
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