gizmobench

Area Calculator

Pick a shape, type its sides in millimetres, centimetres, metres, inches or feet, and read the area with the formula it came from. Ten flat shapes from rectangle to sector, five solids for surface area, and every answer listed in six more units at once, so a room measured in feet still comes out in square metres.

l = 12 cmw = 8 cm
Rectangle · l × w96cm²9,600 mm² · 0.0096 m² · 14.88 in²
Flat
Solid, surface area
Length (cm)
Width (cm)
Unit

Length times width. Any two sides that meet at a corner.

  • The workingarea, in cm²
    12 × 8 = 96
  • Square millimetresmm²
    9,600
  • Square metresm²
    0.0096
  • Square inchesin²
    14.8800297601
  • Square feetft²
    0.10333354
  • Square yardsyd²
    0.0114815044445
  • Acresac
    0.00000237221166208
The formula is on the stage, and the working is the first row. Every answer here is one textbook formula with your numbers put in, printed so you can check it: a circle is π r², a three-sided triangle is Heron's formula, a regular polygon is n s² / (4 tan(π/n)). The solids give surface area for a closed shape, both ends of a cylinder and the base of a cone included. Conversions use exact definitions, so a square foot is 0.09290304 m² and 43,560 of them make an acre.

Common questions

Do I enter the radius or the diameter of a circle?
Either. The circle, sphere, cylinder and cone each take a radius by default, and a switch beside the field turns it into a diameter. The diameter is halved before it goes into the formula, and the formula line says so: it reads π r², r = d/2. A radius of 5 and a diameter of 10 are the same circle and give the same 78.5398.
How does the three-sided triangle work without a height?
By Heron's formula. Half the perimeter is s = (a + b + c) / 2, and the area is the square root of s(s − a)(s − b)(s − c). Sides of 3, 4 and 5 give 6. If the two shorter sides do not add up to more than the longest, the sides cannot meet to form a triangle, and the page says so instead of printing zero or a blank.
Which units can I use, and how does the conversion work?
Type the sides in millimetres, centimetres, metres, inches or feet. The area comes out in that unit squared, and the list under it converts the same area to six more units: square millimetres, centimetres, metres, kilometres, inches, feet and yards, acres and hectares between them. The conversions use the exact definitions, so a square foot is exactly 0.09290304 square metres and exactly 144 square inches.
What is the difference between area and surface area?
A flat shape has one area: the space inside its outline. A solid has a surface area: the total area of every face wrapped around it. The five solids here (cube, box, sphere, cylinder, cone) give that total for a closed shape, ends and base included. A cylinder of radius 2 and height 5 has a surface of 2 π r (r + h), which is 87.96, both circular ends counted.
How is the regular polygon worked out?
From the number of sides and the length of one side, with the formula n s² / (4 tan(π/n)). A regular polygon has every side the same length and every corner the same angle, so a hexagon of side 2 is 10.3923 and four sides of 5 give exactly the square's 25. The number of sides has to be a whole number of at least 3.
How many decimal places does the answer have?
The headline shows six significant figures and the rows under it show twelve. The arithmetic itself runs at the precision of ordinary double-precision numbers, about 16 significant figures, and π is the same constant every calculator uses, so a formula that comes out whole, like 12 × 8, prints exactly 96.

Every area is computed from the formula shown, exact to the precision of the numbers you type, and conversions use exact unit definitions. Measurements from the real world carry their own error.