Area is the flat space inside a shape, measured in square units. Rectangle: length × width. Triangle: ½ × base × height. Circle: π × radius². A 12 ft × 15 ft room is 180 sq ft (about 16.72 m²). Pick a shape above, enter lengths in one unit, and the result is that unit squared.
Students, DIYers, and planners use it for rooms, plots, and simple geometry checks. Keep both lengths in the same unit so the squared result stays meaningful.
Area Formulas for Common Shapes
| Shape | Formula | What to measure | Example | Area |
|---|---|---|---|---|
| Rectangle | A = l × w | Length and width | 12 × 15 | 180 |
| Square | A = s² | One side (enter it as both A and B) | 9 × 9 | 81 |
| Triangle | A = ½ × b × h | Base and the height at right angles to it | b 8, h 5 | 20 |
| Circle | A = π × r² | Radius (half the diameter) | r 5 | 78.5398 |
| Trapezoid | A = ½ × (b₁ + b₂) × h | Both parallel sides and the height | 10, 6, h 4 | 32 |
Results are in square units of whatever you measured: feet in, square feet out. Multiply an area by a depth or height to get volume; the volume calculator handles boxes, cylinders, cones and spheres. The calculator rounds to four decimal places.
For circles, see also the circle calculator.
Worked example
Shape rectangle, side A = 10, side B = 5. Area = 50.
| Input | Value |
|---|---|
| Shape | Rectangle |
| Side A | 10 |
| Side B | 5 |
| Area | 50 |
How to use the fields
- Shape selects which formula runs.
- Side A is base, first length, or radius for circles.
- Side B is the second length (rectangle), the height (triangle) or the second parallel side (trapezoid, which also uses the height field).
Unit tips
If you measure in feet, area is square feet. If you need square meters, convert lengths first or convert the area after. Mixing feet and inches without conversion is a common flooring estimate error.
Square Feet, Square Meters and Square Yards
The calculator does not convert units. Convert the final area with these exact factors.
| From | To | Multiply by | Example: 180 sq ft room |
|---|---|---|---|
| Square feet | Square meters | 0.09290304 | 16.72 m² |
| Square meters | Square feet | 10.7639 | – |
| Square feet | Square yards | ÷ 9 | 20 sq yd |
| Square inches | Square centimeters | 6.4516 | – |
| Square feet | Acres | ÷ 43,560 | 0.0041 acre |
| Square meters | Hectares | ÷ 10,000 | 0.0017 ha |
Squaring a length also squares its conversion factor. 1 m = 100 cm, so 1 m² = 10,000 cm², not 100.
Lot example: a 100 ft × 150 ft lot is 15,000 sq ft, which is about 0.344 acres or 1,393.5 m². One acre is exactly 43,560 sq ft (about 4,046.86 m²), and one hectare is 10,000 m² (about 2.471 acres).
Need to convert lengths first? Use the unit converter.
Practical uses
Estimate paint coverage, turf, or tile needs after you know area, then add waste percent outside this tool. For irregular rooms, split the floor into rectangles and sum areas from repeated runs.
Common mistakes
- Using diameter in the circle field that expects radius
- Mixing units between a and b
- Treating trapezoid inputs as something other than the plugin’s a, b convention
- Forgetting that triangle needs base and height, not two slanted sides alone
For circles, radius is half the diameter. A round rug labeled 10 feet across has radius 5, so area is pi * 5 * 5, not pi * 10 * 10. That single mistake is common in DIY shopping.
Trapezoid: enter the two parallel sides as A and B and the perpendicular height in the height field; area = ½ × (A + B) × height.
Classroom check
Compare a rectangle 10 by 5 against a triangle with the same base and height: the triangle should be half, or 25. A circle with radius 10 should be about 314.16. Those quick checks confirm you selected the right shape mode.
Compound shapes
Real rooms rarely match one rectangle. Split L shaped floors into two rectangles, compute each area, then add. For a circular patio with a rectangular walkway, compute each piece separately and sum. This calculator handles one shape per run, so keep a notepad total beside the browser.
When only a diameter is known for a circle, divide by two before entering radius. Entering diameter as if it were radius inflates area by a factor of four.
Worked example: L-shaped room
A 20 ft × 12 ft room with an 8 ft × 6 ft corner notch splits into two rectangles: 12 × 12 = 144 sq ft and 8 × 6 = 48 sq ft (the remaining strip). Run the calculator once for each and add them: 144 + 48 = 192 sq ft (about 17.84 m²).
For flooring totals across several rooms, the square footage calculator multiplies length × width × number of rooms.
Material estimating extras
- Add waste percent after you know clean area.
- Confirm whether product coverage uses the same units you measured.
- Remeasure twice on long walls; small length errors square into larger area errors.
- For paint, area is wall area, not floor area, unless you are coating a floor.
Accurate area is the foundation; coverage rates and waste finish the shopping list.
Landscaping quotes sometimes mix square feet and square yards. Divide square feet by 9 for square yards after you compute area in feet.
Walls and ceilings
Floor area does not equal wall paint area. Measure wall length times height for each wall, subtract large openings if you want a tighter estimate, then sum. Ceilings are usually length times width like a rectangle run on this calculator.
Write each surface area down before you buy materials so a single forgotten wall does not leave you short mid project.
For outdoor paving, add edge cuts and breakage waste after the clean area is known. The calculator gives the geometric area; suppliers still expect a waste allowance on top.
Recheck long diagonal measurements when a room is out of square so rectangle assumptions do not hide missing square footage.
Limitations
Results are flat shape areas only. They do not compute surface area of cylinders or spheres, and they do not convert units. Use them for clean 2D geometry first passes.
For related percent checks while you plan materials, try the percentage calculator.