Surface area is the total area of all the faces or curved surfaces that wrap a solid. You need it when you paint a tank, wrap a box, order sheet metal or insulation, or estimate how fast something will heat up or cool down. This calculator supports 13 solids and itemizes the answer, so you can see the side area and each base separately and leave out any face you do not need.
How to use the surface area calculator
- Choose a Shape: cube, rectangular prism, sphere, hemisphere, cylinder, cone, conical frustum, capsule, square pyramid, pyramid frustum, triangular prism, tube or ellipsoid.
- Enter the dimensions shown for that shape.
- Pick the Units.
- Read the total surface area, then the breakdown: lateral or side area, the area of each base or face, the volume and useful extras like slant height. The steps list the formula with your numbers and a diagram labels the dimensions.
Surface area formulas
| Shape | Total surface area |
|---|---|
| Cube (edge a) | 6a² |
| Rectangular prism (l, w, h) | 2(lw + lh + wh) |
| Sphere (r) | 4πr² |
| Hemisphere (r) | 3πr² (curved part 2πr²) |
| Cylinder (r, h) | 2πr² + 2πrh |
| Cone (r, h) | πr² + πrs, with s = √(r² + h²) |
| Conical frustum (R, r, h) | πR² + πr² + π(R + r)s, with s = √((R − r)² + h²) |
| Capsule (r, cylinder length a) | 4πr² + 2πra |
| Square pyramid (a, h) | a² + 2as, with s = √(h² + (a ⁄ 2)²) |
| Pyramid frustum (n sides, edges a, b) | A₁ + A₂ + n(a + b)s ⁄ 2 |
| Triangular prism (sides a, b, c, length L) | 2B + (a + b + c)L |
| Tube (R, r, L) | 2π(R + r)L + 2π(R² − r²) |
| Ellipsoid (a, b, c) | ≈ 4π((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ) ⁄ 3)^(1 ⁄ p), p = 1.6075 |
Worked example: painting a water tank
A vertical cylindrical tank is 8 ft across and 10 ft tall. It sits on a pad, so the bottom will not be painted.
Choose Cylinder and enter r = 4 and h = 10 in feet.
- Side: 2π × 4 × 10 ≈ 251.33 ft².
- Each round end: π × 4² ≈ 50.27 ft²; the total for both ends and the side is 351.86 ft².
- Painted area: side plus top = 251.33 + 50.27 ≈ 301.59 ft².
- At 350 ft² per gallon, one coat takes about 0.86 gallon, so buy two gallons for two coats.
A box of 3 × 2 × 1.5 ft works the same way: 2(6 + 4.5 + 3) = 27 ft², of which the four sides are 15 ft² and the top and bottom 6 ft² each.
Lateral, total and partial areas
Count only the surfaces you need
Real jobs rarely use the textbook total. An open bucket needs the side and one base; a pipe sleeve needs only the outside of a tube; a roof needs a pyramid’s sloping faces but not its base. Because the results list each part, you can add exactly the pieces that apply.
Slant height is not height
Cones and pyramids use the slant height s, measured along the surface, for their side area, while volume uses the vertical height h. Mixing them up undercounts the material. The calculator derives s from h for you and shows it in the results.
Surface area and scale
Doubling every dimension multiplies surface area by 4 but volume by 8, so large objects have less surface for each unit of volume. That ratio governs heat loss, evaporation, rusting and coating costs. Among all shapes with the same volume, the sphere has the smallest surface: a 1,000 cm³ cube has 600 cm² of surface, a sphere holding the same 1,000 cm³ only about 483.6 cm².
Related tools
For capacity in liters and gallons use the volume calculator, and for paint quantities across walls and rooms see the paint calculator. All formulas for these solids are collected on the 3D shape formulas page.
Frequently asked questions
What is the difference between lateral area and total surface area?
Lateral area covers only the sides of a solid, leaving out its bases. Total surface area adds the bases. For an open-topped can you would use the lateral area plus one base, which the itemized results make easy to add up.
What units is surface area measured in?
Square units, the square of whatever length unit you enter. Lengths in feet give square feet; lengths in centimeters give square centimeters. To convert, multiply by the square of the length factor, so 1 ft² = 144 in².
Why is the ellipsoid result marked approximate?
An ellipsoid with three different axes has no surface-area formula built from ordinary functions. The calculator uses Knud Thomsen's approximation, which stays within about 1.1% of the exact value for any proportions.
How do I use surface area to estimate paint?
Add up only the faces you will paint, then divide by the coverage on the can, often around 350 to 400 square feet per gallon for one coat. Multiply by the number of coats and add a little for waste.
Which shape has the least surface area for its volume?
The sphere. A 1,000 cm³ cube has 600 cm² of surface, while a sphere of the same volume has about 483.6 cm². That is why bubbles and droplets are round and why compact shapes lose heat more slowly.