Area Calculator
Area of 14 shapes, room square footage, Pythagoras and slope. Runs in your browser.
About this area calculator
This area calculator finds the area of 14 common shapes, from rectangles and triangles to sectors, rings and regular polygons, and converts the answer into every everyday unit from square inches to acres. A labelled diagram shows exactly which measurement goes where.
It also has a room square footage calculator for flooring, tile, carpet and paint jobs, with feet-and-inches input, cut-outs, a waste allowance and a cost estimate. Two smaller helpers solve right triangles with the Pythagorean theorem and work out the slope, angle and grade between two points.
Each result shows the formula with your own numbers in it, so you can check the work or copy it into homework.
Features
14 shapes with diagrams
Rectangle, square, three kinds of triangle (base and height, three sides, two sides and an angle), circle, semicircle, sector, ellipse, trapezoid, parallelogram, rhombus or kite, regular polygon and ring.
Perimeter and extras
Most shapes also give the perimeter or circumference, plus useful extras: diagonals, a triangle's angles and height, arc length, and a polygon's apothem and interior angle.
Every area unit at once
Enter lengths in mm, cm, m, km, inches, feet, yards or miles. The area is shown in your chosen unit and in all ten common area units, each with a copy button.
Room square footage with feet and inches
Type 12' 6" or 12ft 6in directly. Add as many rectangles as your floor plan needs and tick the minus box for areas you won't cover.
Waste and cost
Add an overage percentage for cuts and breakage, enter a price per square foot, meter or yard, and see how much to buy and roughly what it costs.
Pythagorean and slope helpers
Leave any side of a right triangle blank to solve it, with both acute angles. Enter two points to get the slope, angle, percent grade, distance and line equation.
How to use the area calculator
- 1Pick a shape, or the room, Pythagorean or slope helper.
- 2Enter the measurements and the unit they are in.
- 3Read the area, perimeter and conversions into every common unit.
When to use it
Buying flooring
The sample floor plan, a living room, bedroom and hallway minus a kitchen island, comes to 411 sq ft. With 10% waste you buy about 452 sq ft, roughly $2,034 at $4.50 a square foot.
Garden and lawn
A round flower bed with a 4 ft radius is about 50.3 sq ft. Use the ring shape for a path around a tree, or the sector for a corner bed.
Homework
Each result shows the formula and the substituted values, such as A = (6 + 10) ÷ 2 × 4 = 32 for a trapezoid. For fraction measurements like 5 3/8 in, the fraction calculator turns them into decimals first.
Ramps and roofs
A wheelchair ramp at 1:12 has a slope of 0.0833, a grade of 8.33% and an angle of about 4.76°. The Slope tab shows all three at once.
How do you calculate square footage?
Measure the length and width in feet and multiply them. A room 12 ft by 10 ft is 120 square feet. If a measurement has inches, turn the inches into a fraction of a foot first: 6 inches is 0.5 ft, so 18' 6" is 18.5 ft. The room calculator does this conversion for you.
Most rooms aren't perfect rectangles. Split an L-shaped room into two rectangles, measure each, and add them. Subtract anything you won't cover, like a kitchen island or a fireplace hearth. Measure wall to wall at floor level, because skirting boards and trim can hide a few inches.
What are the area formulas for common shapes?
These are the formulas the calculator uses. Every one of them works in any unit, as long as all lengths are in the same unit.
- Rectangle: A = length × width
- Triangle: A = ½ × base × height
- Triangle from three sides (Heron's formula): A = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) ÷ 2
- Circle: A = π × r²
- Sector: A = (θ ÷ 360) × π × r²
- Ellipse: A = π × a × b, with a and b the semi-axes
- Trapezoid: A = (a + b) ÷ 2 × h
- Rhombus or kite: A = p × q ÷ 2, with p and q the diagonals
- Regular polygon: A = n × s² ÷ (4 × tan(180° ÷ n))
How do I convert square feet to square meters?
Multiply square feet by 0.09290304, or divide by about 10.764. So 120 sq ft is 11.15 m². The factor is the square of 0.3048, the exact number of meters in a foot. Squaring is the step people miss: since 1 ft = 12 in, 1 sq ft = 144 sq in, not 12.
For land, an acre is exactly 43,560 square feet, or about 4,046.86 m², and a hectare is 10,000 m², about 2.471 acres. The table under each result lists all of these, and the unit converter handles other area units and lengths.
How does the Pythagorean theorem work?
In a right triangle, the squares of the two shorter sides add up to the square of the longest side: a² + b² = c². With legs of 3 and 4, c = √(9 + 16) = √25 = 5. With a hypotenuse of 13 and one leg of 12, the other leg is √(169 − 144) = 5.
Builders use this to check that a corner is square. Mark 3 ft along one wall and 4 ft along the other. If the diagonal between the marks is exactly 5 ft, the corner is 90°. For bigger rooms, 6-8-10 or 9-12-15 give a more accurate check.
Why use Mavros
| Mavros | Typical upload sites | |
|---|---|---|
| Shapes | 14 shapes, three ways to do a triangle | 6 or 7 shapes |
| Diagrams | Labelled with your own measurements | Static image |
| Units | 8 length units in, 10 area units out at once | One output unit |
| Rooms | Feet and inches, multiple rectangles, cut-outs, waste and cost | One rectangle |
| Extras | Perimeter, angles, Pythagorean and slope helpers | Area only |
| Privacy | Runs in your browser | Ad-heavy pages |
Tips
- Measure each room twice, and round up to the nearest inch rather than down. Running short of flooring costs more than a few spare tiles.
- Diagonal and herringbone layouts waste more material than straight ones. Many installers allow 15% or more, so ask your supplier.
- For a circle, measure the diameter across the widest point and halve it to get the radius.
- Painting walls? Treat each wall as a rectangle of width × ceiling height, and tick the minus box for doors and windows.
- Budgeting for a bigger project such as a renovation loan? The mortgage calculator shows what the monthly payments look like.
Questions
How do I calculate the area of a room?
Multiply the length by the width. For an irregular room, split it into rectangles, work out each one and add them together. The room tab does this and subtracts any cut-outs you mark.
How many square feet is a 12 by 12 room?
144 square feet, which is about 13.38 square meters. If you're buying flooring, add 5% to 10% for waste, so plan on about 152 to 159 square feet.
How do you find the area of a triangle without the height?
Use Heron's formula with the three side lengths. A triangle with sides 5, 6 and 7 has s = 9 and area √(9 × 4 × 3 × 2) = √216, about 14.70.
What is the formula for the area of a circle?
A = π × r², where r is the radius. A circle with a 5 m radius has an area of about 78.54 m². If you know the diameter, halve it first.
How many square feet are in an acre?
An acre is exactly 43,560 square feet, which is about 4,046.86 square meters, or 0.4047 hectares. A square acre is roughly 208.7 feet on each side.
How do I convert square meters to square feet?
Multiply by about 10.764. So 50 m² is roughly 538.2 sq ft. The exact factor is 1 ÷ 0.09290304, because a foot is exactly 0.3048 m.
What is the area of a trapezoid?
Add the two parallel sides, divide by 2, and multiply by the height. With sides of 6 and 10 and a height of 4, the area is (6 + 10) ÷ 2 × 4 = 32.
How do I work out a slope as a percentage?
Divide the rise by the run and multiply by 100. A rise of 1 over a run of 12 is 8.33%. The Slope tab also gives the angle, which is arctan(rise ÷ run).