Surface Area Calculator
Use the calculators below to calculate the surface area of several common shapes.
Ball Surface Area
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Cone Surface Area
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Cube Surface Area
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Cylindrical Tank Surface Area
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Rectangular Tank Surface Area
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Capsule Surface Area
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Cap Surface Area
Please provide any two values below to calculate.
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Conical Frustum Surface Area
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Ellipsoid Surface Area
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Square Pyramid Surface Area
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The surface area of any solid quantifies the total region covered by its outer skin. Detailed information about each shape can be found on the Volume Calculator and Area Calculator pages. Consequently, this tool concentrates on the formulas used to compute those surface areas. For deeper insight into each individual figure, consult the linked calculators.
Sphere
The surface area (SA) of a sphere can be calculated using the equation:
SA = 4πr2
where r is the radius
Xael is fiercely protective of her chocolate truffles. Whenever a box of Lindt sweets arrives, she immediately measures the surface area of each truffle so she can estimate how much she must lick to make them less tempting to anyone else. Each truffle has a radius of 0.325 inches.
SA = 4 × π × 0.3252 = 1.327 in2
Cone
To find a circular cone's surface area you add up the contributions of its separate parts. The "base SA" is the area of the circular base in a closed cone, while the lateral SA accounts for the sloping side that connects the base to the apex. Below are the formulas for each component and for the total surface area of a closed cone.
base SA = πr2
lateral SA = πr√r2 + h2
total SA = πr(r + √r2 + h2)
where r is the radius and h is the height
Athena has recently become fascinated by Southeast Asian traditions, especially the iconic conical "rice hat" worn in many countries. Determined to craft her own, she digs up her mother’s wedding gown from the back of the closet and calculates the amount of fabric needed for a hat with a 1‑foot radius and a 0.5‑foot height.
lateral SA = π × 0.4√0.42 + 0.52 = 0.805 ft2
Cube
The surface area of a cube can be calculated by summing the total areas of its six square faces:
SA = 6a2
where a is the edge length
Anne plans to surprise her younger brother with a Rubik’s Cube for his birthday, but she knows his attention span is short and he gets frustrated easily. She orders a custom black‑finished cube and the price is based on the surface area of a cube whose edges measure 4 inches.
SA = 6 × 42 = 96 in2
Cylindrical Tank
The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:
base SA = 2πr2
lateral SA = 2πrh
total SA = 2πr(r + h)
where r is the radius and h is the height
Jeremy prefers soaking in his massive cylindrical fish tank rather than taking a shower or bathtub. Curious whether his heated water loses heat faster than a standard tub, he needs to compute the tank’s surface area, which has a height of 5.5 feet and a radius of 3.5 feet.
total SA = 2π × 3.5(3.5 + 5.5) = 197.920 ft2
Rectangular Tank
The surface area of a rectangular tank is the sum of the area of each of its faces:
SA = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height
Banana, the senior heir of a long‑standing banana farm, wants to teach her spoiled sister Banana‑Bread a lesson in expectations. After Banana‑Bread begged all week for a new set of drawers for her Batman figures, Banana bought a lavish Barbie dollhouse stocked with tiny kitchen tools, an oven, aprons, and realistic rotting bananas. She packs the whole set into a rectangular box matching the desired drawer size—3 ft × 4 ft × 5 ft—and must calculate how much wrapping paper is required.
SA = (2 × 3 × 4) + (2 × 4 × 5) + (2 × 3 × 5) = 94 ft2
Capsule
The surface area of a capsule is obtained by merging the sphere’s surface formula with the lateral area of a cylinder. Note that the circular ends of the cylinder are excluded because they are not part of a capsule’s exterior. The combined surface area is computed as follows:
SA = 4πr2 + 2πrh
where r is the radius and h is the height
Horatio is developing a placebo that claims to sharpen individuality, critical thinking, and logical reasoning. Market tests show most people lack these traits and are eager to buy his product, which paradoxically reinforces the very qualities they wish to lose. He needs the surface area of each capsule so he can coat them in a heavy layer of sugar, appealing to sugar‑craving tongues, for his next “cure‑all” that promises to eliminate diabetes. Each capsule measures a radius r = 0.05 inches and a height h = 0.5 inches.
SA = 4π × 0.052 + 2π × 0.05 × 0.5 = 0.188 in2
Spherical Cap
The surface area of a spherical cap depends on the height of the segment. This calculator assumes a solid sphere and includes the base area when computing the total surface area, which is the sum of the base and the lateral area of the cap. When applying the tool to a hollow sphere, subtract the base’s contribution. By providing any two of the three parameters—height, cap radius, or base radius—the missing value can be derived using the formulas found on the Volume Calculator. The relevant surface‑area equations are listed below:
spherical cap SA = 2πRh
base SA = πr2
Total solid sphere SA = 2πRh + πr2
where R is the spherical cap radius, r is the base radius, and h is the height
Jennifer envies the globe her older brother Lawrence got for his birthday. Being only two‑thirds as old as him, she claims a one‑third share of his sphere. After putting her father's handsaw back in the shed, she works out the surface area of her hollow globe segment with a radius R of 0.80 ft and a height h of 0.53 ft, as illustrated below:
SA = 2π × 0.80 × 0.53 = 2.664 ft2
Conical Frustum
The surface area of a solid, right conical frustum is the sum of the areas of its two circular ends and that of its lateral face:
circular end SA = π(R2 + r2)
lateral SA = π(R+r)√(R-r)2 + h2
total SA = π(R2 + r2) + π(R+r)√(R-r)2 + h2
where R and r are the radii of the ends, h is the height
For his science‑fair exhibit, Paul is constructing a volcanic model shaped like a conical frustum. Disliking the destructive nature of real eruptions, he opts for a sealed frustum that never blows. Even if the judges aren't impressed, he still needs to compute the amount of material required to cover the outer surface, using a large radius R of 1 ft, a small radius r of 0.3 ft, and a height h of 1.5 ft:
total SA = π(12 + 0.32) + π(1 + 0.3) √(1 - 0.3)2 + 1.52 = 10.185 ft2
Ellipsoid
Unlike a cube, an ellipsoid lacks a straightforward exact formula for its surface area. The tool below applies an approximation that treats the ellipsoid as almost spherical:
SA ≈ 4π 1.6√(a1.6b1.6 + a1.6c1.6 + b1.6c1.6)/3
where a, b, and c are the axes of the ellipse
Coltaine loves to cook and just earned a ceramic knife in a competition. His meat‑loving family watches in dismay as he hones his slicing skills on a mountain of veggies. While his dad sighs at his untouched plate, he calculates the surface area of the zucchini slices, which are elliptical with axes measuring 0.1, 0.2, and 0.35 inches:
SA ≈ 4π 1.6√(0.11.60.21.6 + 0.11.60.351.6 + 0.21.60.351.6)/3 = 0.562 in2
Square Pyramid
A square pyramid’s total surface area consists of the base square plus the four triangular sides. With a height h and base edge a, you can determine this area using these formulas:
base SA = a2
lateral SA = 2a√(a/2)2 + h2
total SA = a2 + 2a√(a/2)2 + h2
Vonquayla’s class has just finished a replica of the Great Pyramid of Giza. Unsatisfied with its lack of awe, she plans to drape it in faux \"snow\" to recapture that majesty. She works out how much melted sugar is required to completely cover the model, which has a base edge a of 3 ft and a height h of 5 ft:
total SA = 32 + 2 × 3√(3/2)2 + 52 = 40.321 ft2
Unlike the Great Pyramid of Giza that has stood for thousands of years, its model, made of graham crackers and coated in sugar, lasted only a matter of days.
Common Area Units
| Unit | meter2 |
| kilometer2 | 1,000,000 |
| centimeter2 | 0.0001 |
| millimeter2 | 0.000001 |
| micrometer2 | 0.000000000001 |
| hectare | 10,000 |
| mile2 | 2,589,990 |
| yard2 | 0.83613 |
| foot2 | 0.092903 |
| inch2 | 0.00064516 |
| acre | 4,046.86 |