How to use
- Choose a shape, such as Rectangle, Triangle (base and height), Triangle (three sides) or Circle.
- Choose the unit your sides are in, such as meters or feet, and enter each side. For a circle sector the angle is in degrees.
- Read the area. It is shown in the square of your unit and in the other area units below. The formula used is shown above the result.
- For a room or plot made of several shapes, press Add another part and pick a shape for each. Mark a part as a hole to subtract it, and the total is the floor minus the holes.
- To buy flooring, tile or paint, enter an allowance for waste in percent. The page then shows how much to buy next to the net area.
Examples
L-shaped room: a 5 m by 4 m part plus a 2 m by 3 m part
→ 26 m²20 + 6. Each part is a rectangle, and the two are added.
A 10 m by 10 m floor with a round hole of radius 2 m, marked as a hole
→ about 87.43 m²100 − π × 2² = 100 − 12.566.
20 m² of floor with 10 percent waste
→ 22 m² to buy20 × 1.10. The allowance depends on the material and the layout; the page only does the multiplication.
Rectangle 5 m by 4 m
→ 20 m²length × width.
Circle with a radius of 2 m
→ 12.566371 m²π × 2² = 12.5664.
Triangle with sides 3, 4 and 5
→ 6Heron's formula; this is the right triangle, whose area is 3 × 4 ÷ 2.
Rectangle 10 ft by 20 ft
→ 200 ft² = 18.58 m²A foot is exactly 0.3048 m, so a square foot is 0.09290304 m².
How it works
The area is computed from the formula of the shape, written out under the form, in the unit you chose. The conversions to other area units are done with the js-quantities library, which keeps the exact definitions of the units (the foot is exactly 0.3048 m, the acre is exactly 4,046.8564224 m²).
The triangle from three sides uses Kahan’s arrangement of Heron’s formula, with the sides sorted, which does not lose digits on needle-like triangles where the plain formula does. Sides that are zero, missing or negative, an inner radius that is not smaller than the outer, an angle over 360 degrees and sides that cannot meet are refused. The formulas and conversions are covered by tests, and the page is checked in a real browser.
Sources
- Kahan: Miscalculating area and angles of a needle-like triangle
- NIST Special Publication 811: guide for the use of the SI, conversion factors
- Wikipedia: Area
Frequently asked questions
- How is the area of a triangle found from its three sides?
- With Heron's formula: with s half the sum of the sides, the area is the square root of s × (s − a) × (s − b) × (s − c). The page computes it in a form that stays accurate for long thin triangles, and it says so when the three sides cannot make a triangle.
- What is the difference between a circle and a sector?
- A sector is a slice of a circle, like a slice of a pie, given by the radius and the angle at the centre in degrees. Its area is the circle's area times angle ÷ 360.
- How do I find the area of an irregular or L-shaped room?
- Press Add another part for each rectangle or triangle the room splits into and the page adds them. For a room with a part cut out, such as a pillar or a stairwell, add the whole shape and then add the cut-out as a part marked as a hole, and the page subtracts it.
- How much flooring or tile should I buy?
- Enter the waste allowance in percent and the page shows the net area and the area to buy, which is the net area times one plus the allowance. How much waste to allow depends on the material, the pattern and the shape of the room, so check the maker's advice; the page does not know it.
- Can I enter the sides in different units?
- All sides share one unit. Convert one first, for example with the unit converter, or enter every side in the smaller unit.
- Is anything sent to a server?
- No. The sides stay in your browser.
Related tools
Guides
Version history
- 1.1.1 — Draws each shape with its sides named next to the inputs, and an empty extra part no longer hides the total.
- 1.1.0 — Adds parts: a room or plot made of several shapes can be added up, with holes taken away, and an allowance for waste shows how much to buy.
- 1.0.2 — The Korean page now also shows the area in pyeong, right below square meters, and its title and description mention it.
- 1.0.1 — Clarifies the search title with the tool's main task and whether it is free or runs online.
- 1.0.0 — First release.