Surface Area Calculator

Surface area is the total area of all the faces or curved surfaces of a solid, so you add up the areas of its parts. For a box, find the area of each rectangle and add all six. For a cylinder, add the two circles, 2πr², and the side that unrolls into a rectangle, 2πrh. Choose the shape above, enter the lengths in one unit, and the calculator adds the parts for you.

SA is short for surface area, often written S. Pick the solid, then use its formula: 6a² for a cube, 2(lw + lh + wh) for a box, 2πr(r + h) for a cylinder, 4πr² for a sphere. The calculator applies these and also gives the side or lateral area, the flat bases, the volume and the surface area to volume ratio.

It depends on the solid. Cube: 6a². Rectangular prism: 2(lw + lh + wh). Cylinder: 2πr² + 2πrh. Cone: πr² + πrs, with slant height s = √(r² + h²). Sphere: 4πr². Hemisphere: 3πr². Square pyramid: a² + 2as, with s = √(h² + (a/2)²). The formula box under the calculator lists all ten shapes, including the triangular prism, capsule and spherical cap.

Use S = 4πr², where r is the radius. For a radius of 3 inches that is 4 × π × 9 = 113.10 square inches. If you know the diameter d, use S = πd². The surface of a sphere is exactly four times the area of its largest circle, πr². Choose "Sphere" above to try your own radius.

Divide the surface area by 6 and take the square root: a = √(S / 6). A cube with a surface area of 150 square inches has edges of √25 = 5 inches, and 96 square inches gives √16 = 4 inches. If you only know the area of one face, the side is the square root of that area.

Divide the surface area by 4π and take the square root: r = √(S / 4π). A sphere with a surface area of 100 square meters has r = √(100 / 12.566) = 2.82 meters. You can check the answer by entering that radius under "Sphere" and comparing the surface area.

It is 2πr² + 2πrh = 2π × 4 + 2π × 4 = 16π, about 50.27 square inches. Of that, 25.13 is the two circular ends and 25.13 is the curved side. Choose "Cylinder", enter 2 for the radius and 2 for the height, and keep inches as the unit.

Treat the house as a box plus a roof. The four walls are 2 × height × (length + width), minus the windows and doors. A 30 by 20 foot house with 10-foot walls has 2 × 10 × (30 + 20) = 1,000 square feet of wall, which is the side area of a rectangular prism. A pitched roof is larger than the floor plan: for a 6/12 pitch multiply the footprint by √(6² + 12²) / 12 = 1.118, so 600 square feet becomes about 671.

Lateral (side) surface area counts only the sides, not the flat bases. Total surface area adds the bases. For a cylinder with radius 3 and height 8, the side is 2πrh = 150.80 and each base is πr² = 28.27, so the total is 150.80 + 56.55 = 207.35. Use lateral area for a label around a can or paint on the walls of a room, and total area for wrapping the whole object.

Add the base circle πr² and the side πrs, where s is the slant height √(r² + h²). For r = 3 and h = 4 the slant height is 5, so S = 9π + 15π = 24π, about 75.40. Enter the height measured straight up from the base. If you know the slant height instead, use it for s directly in the formula.

Add the two triangular ends and the three rectangular sides: S = 2T + (a + b + c) × L, where T is the area of the triangle and L the length of the prism. For a 3-4-5 triangle and a length of 10, T = 6, so S = 12 + 12 × 10 = 132. The calculator finds T from the three sides with Heron’s formula and rejects sides that cannot form a triangle.

It is the surface area divided by the volume, so it shows how much surface there is for each unit of volume. For a sphere it equals 3 / r, so a radius of 3 gives a ratio of 1 and a radius of 10 gives 0.3. Smaller objects have a larger ratio, which is why small pieces dissolve, cool or react faster than a large piece of the same material.

Use the cylinder with the pipe’s outer radius and its length, and read the side area, 2πrh. That is the outside surface for paint or insulation. For a 10-foot pipe with an outer radius of 2 inches, choose inches, enter a height of 120 and a radius of 2: 2π × 2 × 120 = 1,507.96 square inches, or 10.47 square feet. For the inside surface use the inner radius.

The curved surface of a hemisphere is 2πr², half of the sphere. A solid hemisphere also has a flat circular face of πr², so the total is 3πr². The calculator shows both parts: the curved one as the side area and the flat one as the base area. For a bowl without its top, the surface you want is the side area, 2πr².

A capsule is a cylinder with a hemisphere on each end. Its surface is 4πr² + 2πrL, where L is the length of the straight middle. A spherical cap is the piece of a sphere cut off by a plane. With sphere radius R and cap height h, the curved surface is 2πRh and the flat circle is πh(2R − h).

Add the surface areas of the parts and leave out the faces that are joined, on both parts. A cylinder with a cone on top, for example, has the cylinder’s side and bottom plus the cone’s side; the circle where they meet is hidden on both. Use the side area and base area results of each piece to build the sum.

Enter the lengths in feet and the result is in square feet. If you use another unit, the calculator also converts the total surface area to square feet and square meters. Convert before you square: 12 inches make 1 foot, but 144 square inches make 1 square foot. A square foot is exactly 0.09290304 square meters.

Square units of length: square inches (in²), square feet (ft²), square yards, square centimeters or square meters (m²). The SI unit is the square meter. Volume uses cubic units, and the ratio of surface area to volume uses 1 over a length, such as 1/in. The foot is defined as exactly 0.3048 meters, which fixes all the conversions on this page.