Area Calculator
Area of a rectangle, circle, triangle, trapezoid, ellipse, sector, rhombus or regular polygon, converted to square feet, square metres, acres and hectares.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Area Calculator?
Area is the amount of flat surface a shape covers, measured in square units. This area calculator handles the shapes that come up in school, at home and on site: rectangle, square, circle, triangle from base and height, triangle from three sides, trapezoid, parallelogram, ellipse, circle sector, rhombus and any regular polygon. Pick the shape, choose the unit your tape measure uses, and the answer appears as you type.
Every result is converted at once into square millimetres, centimetres, metres and kilometres, square inches, feet, yards and miles, acres and hectares, so you do not need a second tool to turn a lawn measured in feet into acres or a plot in metres into hectares. A labelled sketch shows which measurement goes in which box, and the working panel prints the formula with your numbers substituted.
Perimeter is shown where the inputs are enough to find it. For an ellipse the perimeter has no simple exact formula, so the calculator uses Ramanujan's approximation, which is far more precise than any tape measurement for ordinary ellipses and stays within 0.04% even for extremely flat ones.
- Eleven shapes, including Heron's three-side triangle and regular polygons
- Eight length units and ten area units, including acres and hectares
- Perimeter where it can be determined, with Ramanujan's ellipse approximation
- Labelled shape sketches and the substituted formula
- Copy and shareable links
How to use the Area Calculator
- Choose the shape from the list. The sketch updates to show which lengths it needs.
- Choose the length unit you measured in, such as feet or metres.
- Enter each measurement. A sector also needs its central angle in degrees, and a regular polygon needs its number of sides.
- Read the area and perimeter, then use "Show area in" to pick the unit you want on top, or read any unit from the table.
- Copy the results or share a link that reopens the same shape and numbers.
Worked examples
Floor of a bedroom
Input
Rectangle, 12 ft by 8 ft
Output
96 ft², 8.91869 m², 0.00220386 acres; perimeter 40 ft
Length times width. Multiplying 96 by 0.09290304 gives the square metres used on flooring sold by the square metre.
A field in hectares and acres
Input
Rectangle, 200 m by 150 m
Output
30,000 m² = 3 hectares = 7.41316 acres
Hectares are a straight division by 10,000. Acres divide by 4,046.8564224.
A hexagonal patio
Input
Regular polygon, 6 sides of 2 m
Output
10.3923 m²; perimeter 12 m
A regular hexagon is six equilateral triangles of side 2, each √3 m², giving 6√3 = 10.3923 m².
A pizza slice
Input
Sector, radius 3 in, angle 120°
Output
9.42478 in²; perimeter 12.2832 in
A third of a circle of radius 3, which is 3π. The perimeter adds the 6.283 in arc to two 3 in radii.
Background and insight
The conversions rest on exact definitions. Since the 1959 international yard and pound agreement the inch is exactly 2.54 cm, so a square foot is exactly 0.09290304 m². An international acre is 43,560 square feet, or 4,046.8564224 m², and a hectare is a 100 m by 100 m square, 10,000 m². One hectare is therefore about 2.471 acres. NIST retired the older US survey foot at the end of 2022; acreage based on it differs from the international acre by about four parts per million, far below the accuracy of any tape measurement.
Several formulas are the same idea in disguise. A parallelogram is a rectangle with one end sliced off and moved to the other side, so it keeps base × height. A triangle is half of such a parallelogram. A trapezoid is the average of its two parallel sides times the height. A regular polygon with n sides of length s splits into n identical triangles meeting at the centre, which leads to n·s² / (4·tan(180°/n)). As n grows the polygon approaches a circle, and the formula approaches πr².
Heron's formula for a triangle from three sides needs no angle or height at all, which makes it the practical choice when you can measure the edges of a triangular bed or plot but not its height.
Common use cases
Flooring, paint and turf
Get the area of each room or lawn section in the unit the product is sold in, then add a waste allowance.
Land and property
Convert a lot measured in feet or metres into acres or hectares for listings, tax forms or planning applications.
School geometry
Check answers for circles, trapezoids and sectors, with the substituted formula shown for each step.
Material estimates
Work out the surface of a circular table top, an elliptical rug or a hexagonal tile before ordering.
Tips and limitations
- Use the perpendicular height for triangles, parallelograms and trapezoids, not the slanted side.
- Break an L-shaped or irregular room into rectangles and add the areas.
- Squared units do not convert like lengths: 1 m is 3.28 ft, but 1 m² is 10.76 ft².
- For an ellipse enter the semi-axes (half the full width and half the full length).
- Half an inch of measuring error on each side of a 12 ft by 8 ft room shifts the area by close to 1%, so round the final figure accordingly.
Frequently asked questions
How do you calculate the area of a shape?
Each shape has its own formula: length × width for a rectangle, πr² for a circle, ½ × base × height for a triangle and ½ × (a + b) × h for a trapezoid. Measure in one unit, apply the formula, and the result is in that unit squared.
How many square feet are in an acre?
An acre is 43,560 square feet, or about 4,046.86 square metres. A square plot of one acre is roughly 208.7 ft on each side.
How do I convert square metres to square feet?
Multiply by 10.7639. The factor is (1 / 0.3048)², because a foot is exactly 0.3048 m and both dimensions convert. 50 m² is 538.2 ft².
What is the difference between a hectare and an acre?
A hectare is 10,000 m², a square 100 m on a side. An acre is 43,560 ft² or 4,046.86 m². One hectare equals about 2.471 acres, and one acre about 0.4047 hectares.
How do I find the area of a trapezoid?
Add the two parallel sides, halve the sum, and multiply by the perpendicular height between them. Parallel sides of 6 and 10 with a height of 6 give ½ × 16 × 6 = 48.
How do I calculate the area of an irregular room?
Divide the floor into rectangles and triangles that do not overlap, find each area here in the same unit, and add them. For a bay window or curved wall, a sector or half circle is usually close enough.
Is there an in-depth guide to the Area Calculator?
Yes. “Area and Volume Formulas, and Why They Work” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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