Surface Area Calculator

This surface area calculator finds the total surface area and lateral surface area of six common solids: cube, rectangular prism, sphere, cylinder, cone, and triangular prism. It works as a surface area of a cube calculator, a surface area of a sphere calculator, a surface area of a cylinder calculator, and everything in between, all from the same tool. Pick a shape, type in the dimensions, and the answer updates as fast as you change the numbers.

1. Select a shape from the buttons: Cube, Rectangular Prism, Sphere, Cylinder, Cone, or Triangular Prism. The input fields swap to match the shape you pick, so you never have to guess which dimensions are needed.
2. Enter the dimensions in any consistent unit. Use radius (not diameter) for spheres, cylinders, and cones. For a rectangular prism enter length, width, and height. For a triangular prism enter the three triangle side lengths plus the prism length.
3. Read the total surface area in the primary result panel. This is the full outer skin of the solid, including every face, base, and top. Useful for paint, wrapping paper, sheet metal, and any coating that has to cover the entire object.
4. Check the lateral surface area in the secondary panel. This excludes the top and bottom bases. It is what you want when calculating a label that wraps only the curved side of a can, or siding that covers only the walls of a building.
5. Inspect the formula shown below the numbers. The calculator substitutes your actual inputs into the equation so you can copy the worked steps straight into homework or a report.

Units stay consistent: enter centimeters and the area comes back in square centimeters, enter inches and you get square inches. If your measurements are mixed, convert them to one unit before you type them in. To learn how to calculate surface area by hand for each shape, the Formulas section below shows every equation with a worked example in real numbers.

Every solid has its own surface area formula, but they all follow the same idea: add up the area of every face. Below is the reference card for how to calculate surface area for the most common shapes, each with a worked example using real numbers. Area always has squared units (cm², m², in²), never plain length units.

Cube (side s)

SA = 6s²

A cube has 6 identical square faces, each of area s².

Example: cube with side s = 4 cm
SA = 6 × 4² = 6 × 16 = 96 cm²

Rectangular Prism / Box (length l, width w, height h)

SA = 2(lw + lh + wh)

Three pairs of identical faces: top+bottom, front+back, left+right.

Example: box with l = 6 in, w = 4 in, h = 3 in
SA = 2(6×4 + 6×3 + 4×3)
   = 2(24 + 18 + 12)
   = 2 × 54
   = 108 in²

Sphere (radius r)

SA = 4πr²

A sphere has no lateral/base distinction: the whole surface is one piece.

Example: sphere with r = 5 cm
SA = 4 × π × 5²
   = 4 × π × 25
   = 100π
   ≈ 314.16 cm²

Cylinder (radius r, height h)

SA = 2πr² + 2πrh = 2πr(r + h)

Two circular bases (2πr²) plus the curved side (2πrh, the lateral area).
Lateral surface area alone = 2πrh, which is what you use for a label
that wraps only the side of a can.

Example: cylinder with r = 3 m, h = 7 m
Lateral SA = 2π × 3 × 7 = 42π ≈ 131.95 m²
Total SA   = 2π × 3 × (3 + 7) = 60π ≈ 188.50 m²

Cone (radius r, height h, slant ℓ)

Slant height ℓ = √(r² + h²)
SA = πr² + πrℓ = πr(r + ℓ)

The base (πr²) plus the curved lateral surface (πrℓ). The slant comes
from the Pythagorean theorem on the right triangle formed by r and h.

Example: cone with r = 3 in, h = 4 in
ℓ = √(3² + 4²) = √25 = 5 in
SA = π × 3 × (3 + 5) = 24π ≈ 75.40 in²

Pyramid (square base, side s, slant height ℓ)

SA = s² + 2s × ℓ

The square base (s²) plus 4 triangular sides, each of area (s × ℓ)/2.
Slant height ℓ here is measured up the middle of a triangular face
(not the lateral edge). If you only have the pyramid's vertical
height h, use ℓ = √(h² + (s/2)²).

Example: pyramid with s = 6 m and slant height ℓ = 5 m
SA = 6² + 2 × 6 × 5
   = 36 + 60
   = 96 m²

Triangular Prism (triangle base area A, perimeter p, length l)

SA = 2A + p × l

Two triangular end caps (2A) plus three rectangular sides whose
combined area is the perimeter times the prism length.

If you only know the three triangle side lengths, use Heron's formula
for A: s = (a + b + c)/2, A = √[s(s−a)(s−b)(s−c)].

Example: prism with 3-4-5 triangle ends and length l = 10 cm
Triangle area A = (3 × 4)/2 = 6 cm² (or Heron's: s=6, A=√36=6)
Perimeter p = 3 + 4 + 5 = 12 cm
SA = 2 × 6 + 12 × 10 = 12 + 120 = 132 cm²

Quick Reference: Surface Area at Common Sizes

How fast surface area grows with size, for the three most common solids. All values in square units.

Notice the pattern: every time the size doubles, surface area quadruples, because area scales with the square of length. Going from a side of 5 to a side of 10 multiplies surface area by 4, not 2. This is the same reason a child loses heat much faster than an adult, and why scaling up a recipe pan changes the cooking time.

Surface area is not just a geometry exercise. It decides how much paint you buy, how fast a house loses heat in winter, how much cardboard a package uses, and why a polar bear is shaped the way it is. Here is how the total surface area calculator above connects to problems you actually run into.

Real-World Uses: From Paint Coverage to Gift Wrap

Once you know the surface area of an object, most practical calculations are a single division or multiplication.

• Paint coverage. Gallons needed = surface area ÷ coverage per gallon. A typical latex wall paint covers 350 ft² per gallon on smooth drywall. A room with 400 ft² of wall takes 400 ÷ 350 ≈ 1.15 gallons for one coat, so 2 gallons for two coats. Rough surfaces like stucco or fresh drywall drop coverage to 200 ft² per gallon.
• Heat loss through walls. Heat loss is proportional to wall surface area: Q = (A × ΔT) ÷ R, where A is surface area, ΔT is the indoor-outdoor temperature difference, and R is the R-value of the wall. Double the wall area, double the heat bill.
• Packaging and cardboard. A cardboard box uses material equal to its surface area plus a few inches of overlap for flaps. Shipping-cost models frequently use dimensional weight too, but the raw material cost scales with SA.
• Gift wrap. Add about 20% to the surface area for overlap and folds. A box that is 12 × 9 × 4 inches has SA = 2(108 + 48 + 36) = 384 in². You want about 460 in² of wrapping paper, which is a 23 × 20 sheet.
• Land-use mapping. Solar panel output depends on the surface area exposed to the sun, not the footprint of the building. A tilted roof has more surface area than the ground it shadows.
• Aquarium glass. An aquarium open at the top uses lateral surface area plus one base: for a 24 × 12 × 16 inch tank, glass = 24 × 12 + 2(24 × 16) + 2(12 × 16) = 288 + 768 + 384 = 1,440 in². That is the minimum pane stock before trimming.

Why Planets Are Round: Spheres Minimize Surface Area

Of all shapes with a given volume, the sphere has the smallest possible surface area. This is why soap bubbles, planets, and water droplets in free fall all pull themselves into spheres: surface tension and gravity both want to minimize exposed area. For the same volume, a cube has about 24% more surface area than a sphere, and a thin pancake shape can have ten times more.

This is also why small animals lose heat faster. A mouse and an elephant are both roughly the same shape, but the mouse has far more surface area per gram of body than the elephant. More area means more radiator, which is why small mammals eat almost constantly just to stay warm.

The Surface-Area-to-Volume Ratio

SA-to-volume ratio (SA/V) is one of the most useful numbers in biology, chemistry, and engineering. As an object gets larger, its volume grows faster than its surface area, so SA/V goes down. As it shrinks, SA/V goes up. For a cube of side s, SA/V = 6/s.

Why this matters: cells stay small because nutrients enter through the membrane (area) but are used throughout the cell (volume). A cell that gets too big cannot import nutrients fast enough. Crushed ice melts faster than a single block of the same mass because crushing it multiplies the exposed surface area without changing the volume. Your hands and feet feel cold first because they have a much higher SA/V than your torso, so they shed heat at a greater rate.

Common Traps When Calculating Surface Area

Most wrong answers on a surface area problem come from the same few mistakes. Watch for these.

• Missing a face. An open-top box has 5 faces, not 6. An aquarium with a glass bottom and 4 glass walls but no lid uses 2(lh + wh) + lw, not 2(lw + lh + wh). Always count how many faces the real object actually has.
• Using diameter where radius is required. A ball is advertised as 10 inches. That is the diameter. For surface area use r = 5, not r = 10. SA = 4π(5)² ≈ 314, not 4π(10)² ≈ 1,257.
• Mixing units. If one dimension is in centimeters and another is in meters, convert before you multiply. 30 cm × 2 m is not 60, it is 30 × 200 = 6,000 cm² or 0.30 × 2 = 0.60 m².
• Writing the answer with length units. Surface area is always squared units. A cube of side 4 cm has SA = 96 cm², not 96 cm. Points are deducted in class exactly for this.
• Confusing slant height with vertical height. For a cone, the formula uses the slant ℓ, not the straight-up height h. A cone with r = 6 and h = 8 has slant 10, so SA = π × 6 × (6 + 10) = 96π, not π × 6 × (6 + 8) = 84π.
• Assuming lateral equals total. A cylindrical label that only wraps the side uses 2πrh. A full paint job on the same cylinder needs 2πrh + 2πr². On a short wide can, the bases can be more than half the total surface area, so the difference is not small.