Surface Area Calculator
Set to a rectangular prism 5 cm long, 4 cm wide and 3 cm high, the surface area calculator gives 94 cm²: two faces of 20, two of 15 and two of 12. Pick another shape to get its surface area the same way.
Total surface area
- Total surface area A = 2(lw + lh + wh) = 2(5×4 + 5×3 + 4×3).
- 94 cm²
- Volume Volume units are the measurement unit cubed: in centimeters the answer is in cubic centimeters.
- 60 cm³
- Formula Volume counts unit cubes. A box l by w by h holds l × w cubes in each layer and h layers. Every other formula in this calculator is this one, rearranged or taken to a limit.
- V = l × w × h = 5 × 4 × 3 = 60
- Measurements used
- l = 5 cm, w = 4 cm, h = 3 cm
- Lateral area (four walls) Perimeter of the base times the height: 2(l + w)h. The walls of a room, without floor or ceiling.
- 54 cm²
- In liters 1 liter is 1,000 cubic centimeters, the volume of a 10 cm cube.
- 0.06 L
- In US gallons A US gallon is defined as exactly 231 cubic inches, 3.785411784 liters. An imperial gallon is about 20% larger.
- 0.01585032 gal
- In other cubic units Cubic conversions cube the length factor: a yard is 3 feet, so a cubic yard is 27 cubic feet.
- 0.00006 m³ = 0.00211888 ft³ = 0.000078477 yd³
| Every length times | Volume | Surface area |
|---|---|---|
| 0.5 | 7.5 cm³ (×0.125) | 23.5 cm² (×0.25) |
| 1 | 60 cm³ (×1) | 94 cm² (×1) |
| 2 | 480 cm³ (×8) | 376 cm² (×4) |
| 3 | 1,620 cm³ (×27) | 846 cm² (×9) |
| 10 | 60,000 cm³ (×1,000) | 9,400 cm² (×100) |
- Volume scales with the cube of length and surface area with the square. Double every measurement and the volume goes up 8 times while the surface only goes up 4. That is why large animals keep heat better and why small ice cubes melt faster.
How the Volume Calculator works
Surface area is the total area of every face of a solid: the amount of paper to wrap it, paint to cover it or sheet metal to make it. It is measured in square units, so centimeters in give square centimeters out. Each shape has its own formula for surface area, and each comes from unfolding the solid flat into a net and adding up the pieces.
Rectangular prism. The formula for the surface area of a rectangular prism is A = 2(lw + lh + wh), because a box has three pairs of matching faces. For 5 by 4 by 3 cm that is 2(20 + 15 + 12) = 94 cm². The four side walls alone, the lateral area, are the perimeter of the base times the height: 2(5 + 4) × 3 = 54 cm². A cube is the case where every edge is equal, so A = 6s², and a 5 cm cube has 6 × 25 = 150 cm².
Sphere and hemisphere. A sphere's surface is A = 4πr². For a radius of 5 cm that is 100π, about 314.16 cm². A hemisphere is half the curved surface plus the flat circle it was cut along, 2πr² + πr² = 3πr², which is 75π, about 235.62 cm², for the same radius.
Cone. The base is a circle, πr², and the sloping side unrolls into a sector of a circle with area πrs, where s is the slant height √(r² + h²). For a radius of 3 and a height of 4 the slant is 5, and A = 9π + 15π = 24π, about 75.40 square units. The calculator works out the slant from the vertical height.
Pyramid. The base plus four triangles. A square pyramid with a 6 by 6 base and a height of 4 has a slant height of 5 on each face, so each triangle is ½ × 6 × 5 = 15, and A = 36 + 60 = 96 square units. With a rectangular base the two pairs of triangles have different slant heights, and the calculator finds both.
Triangular prism. Two triangles and three rectangles. For an isosceles triangle with base 6 and height 4, the two sloping sides are 5 each, and with a length of 10 the area is 2 × 12 + (6 + 5 + 5) × 10 = 184 square units.
A cylinder is two circles and a rolled-up rectangle, 2πr² + 2πrh, and its total and lateral areas have their own page among the variants below. Capsules, ellipsoids and frustums are also among the shapes; an ellipsoid's surface has no elementary formula and is computed from elliptic integrals.
Scaling. Surface area grows with the square of the size. Double every length and the area goes up 4 times while the volume goes up 8 times. That is why big objects have less surface for their volume than small ones, and the table under the result shows both at several scales.
Volume Calculator FAQ
What is the formula for surface area?
It depends on the shape. A rectangular prism is 2(lw + lh + wh), a cube 6s², a sphere 4πr², a cone πr² + πrs with s the slant height, and a cylinder 2πr² + 2πrh. Each is the sum of the areas of the solid's faces.
How do you find the surface area of a rectangular prism?
Add the areas of the three different faces and double the total: A = 2(lw + lh + wh). A box 5 by 4 by 3 has 2(20 + 15 + 12) = 94 square units.
What is the difference between surface area and lateral area?
Lateral area leaves out the top and bottom: only the sides. For a 5 by 4 by 3 box the lateral area is 54 and the total surface area is 94, the difference being the two 20-unit ends.
What units is surface area in?
Square units: square centimeters, square inches, square feet. Volume is in cubic units. Converting square units squares the factor, so 1 square foot is 144 square inches.
More from the Volume Calculator
- Cubic feet calculator
- Cubic yard calculator
- Triangular prism calculator
- Pipe volume calculator
- Volume of a cylinder calculator
- Volume of a cone calculator
- Volume of a sphere calculator
- Volume of a cube calculator
- Volume of a pyramid calculator
- Surface area of a cylinder calculator