The following is a list of surface area calculators for several common shapes. Fill in the fields for the shape you need and click Calculate. Each dimension can use its own unit; when units differ, the surface area is shown in each unit used.
Provide any two of the three values below.
The surface area calculator on this page computes the surface area of ten common three-dimensional shapes: the sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, and square pyramid. Enter the required measurements for your shape, choose a unit of length, and click Calculate. The tool returns the total surface area — and, for shapes made of distinct faces, a breakdown of each part such as the base, lateral, and total areas. Because every dimension has its own unit selector, you can even mix units and see the result expressed in each unit you used.
Surface area is the total area of the outer boundary of a solid, measured in square units such as square meters, square feet, or square centimeters. It is a distinct and equally important measurement from volume: while volume tells you how much a shape holds, surface area tells you how much material covers or wraps it. Surface area calculations are essential for painting, coating, wrapping, heat transfer, material estimation, packaging, and countless engineering and manufacturing tasks.
Surface area is the sum of the areas of all the surfaces that bound a three-dimensional object. For a shape with flat faces, like a cube or a box, it is simply the total area of those faces added together. For a curved shape, like a sphere or a cone, calculus is used to derive a formula for the curved (lateral) surface. Surface area is always expressed in square units, because area is a two-dimensional quantity — even when it wraps around a three-dimensional object. This contrasts with volume, which is measured in cubic units.
A helpful way to picture surface area is to imagine unfolding or unwrapping the object into a flat pattern (a "net") and measuring the area of that flattened shape. The amount of wrapping paper needed to cover a gift, the paint needed to coat a tank, or the sheet metal needed to build a duct all depend on surface area.
Scroll to the shape that matches your object, fill in the labeled dimensions, and select a unit for each. The calculator converts your inputs as needed, applies the correct formula, and displays the surface area. For shapes with clearly separate faces — a cone's base and lateral surface, a cylinder's top, bottom, and side — the result shows each part separately along with the total, so you can see exactly where the area comes from. If you mix units, the calculator reports the surface area in each distinct unit you entered.
A sphere is a perfectly round solid where every surface point is the same distance r from the center. Its surface area is SA = 4 · π · r² — exactly four times the area of a circle of the same radius. Balls, bubbles, and planets are spheres.
A cone has a circular base of radius r and tapers to a point at height h. Its total surface area is the base plus the lateral (slanted) surface: SA = πr² + πr√(r² + h²), where √(r² + h²) is the slant height. Ice cream cones and funnels are familiar cones.
A cube has six identical square faces of edge length a, so its surface area is simply SA = 6 · a². Dice and boxes approximate cubes.
A cylinder has two circular ends of radius r and a curved side of height h. Its total surface area combines the two ends and the lateral surface: SA = 2πr² + 2πrh. Cans and pipes are everyday cylinders.
A rectangular tank (box or cuboid) with length l, width w, and height h has six rectangular faces in three matching pairs, giving SA = 2(lw + lh + wh). This is the standard formula for aquariums, boxes, and rooms.
A capsule is a cylinder of radius r and height h capped by a hemisphere on each end. The two hemispheres together form a full sphere, so its surface area is SA = 4πr² + 2πrh. Many pills and pressure vessels are capsules.
A spherical cap is the dome sliced from a sphere by a flat plane. Described by cap height h, base radius r, and sphere radius R (any two determine the third), its surface area is the flat circular base plus the curved cap: SA = πr² + 2πRh. Domes and contact lenses are spherical caps.
A conical frustum is a cone with its tip cut off, leaving a top radius r, a bottom radius R, and height h. Its surface area is the two circular ends plus the slanted band around it: SA = πr² + πR² + π(R+r)√((R−r)² + h²). Buckets and lampshades are frustums.
An ellipsoid is a stretched sphere with three semi-axes a, b, and c. Unlike the sphere, an ellipsoid has no simple exact surface-area formula, so the calculator uses a very accurate approximation (the Thomsen formula): SA ≈ 4π · [ ((ab)^1.6 + (ac)^1.6 + (bc)^1.6) / 3 ]^(1/1.6). Eggs and rugby balls are roughly ellipsoidal.
A square pyramid has a square base of edge a and four triangular faces meeting at an apex of height h. Its surface area is the base plus the four triangles: SA = a² + 2a√((a/2)² + h²), where √((a/2)² + h²) is the slant height of each face. The Egyptian pyramids are the classic example.
Surface area and volume answer different questions about the same object. Volume measures how much space a shape occupies or how much it can hold, in cubic units. Surface area measures how much material covers its outside, in square units. When you scale an object up, these two quantities grow at different rates: volume increases with the cube of size while surface area increases only with the square. This is the famous square-cube law, and it has profound consequences. It explains why small creatures lose heat quickly (lots of surface area relative to volume), why large storage tanks are more efficient than small ones, and why cells stay microscopic to keep enough surface for nutrients to pass through. The ratio of surface area to volume is one of the most important quantities in biology and engineering.
Surface area is a practical, everyday quantity. In painting and coating, it determines how much paint, primer, or sealant a project needs. In construction and manufacturing, it sets the amount of sheet metal, fabric, or material to cut. In packaging, it drives how much cardboard or wrapping is required and affects shipping costs. In heating and cooling, heat transfer through a wall, radiator, or heat sink is proportional to surface area — which is why radiators have fins and why heat sinks are ribbed. In chemistry, reaction rates depend heavily on the exposed surface area of the reactants, so powders react faster than solid lumps. Even in cooking, surface area affects how quickly food browns and cooks.
For shapes like cones, cylinders, frustums, and pyramids, it is useful to distinguish the lateral surface area from the total surface area. The lateral surface area is just the curved or slanted side of the shape, excluding the flat top and bottom. The total surface area adds those flat faces back in. This distinction matters in practice: a label wrapped around a can covers only the lateral surface, while paint on a closed tank covers the total surface. That is why this calculator reports the base, top, and lateral areas separately in addition to the total — so you can pick exactly the figure your task requires.
Imagine you need to paint the outside of a cylindrical water tank that is 3 meters in radius and 4 meters tall, and you want to know how much surface the paint must cover. Using the cylinder calculator, the two circular ends each contribute πr² ≈ 28.27 square meters, and the curved side (the lateral surface) contributes 2πrh ≈ 75.40 square meters, for a total of about 131.95 square meters. If the tank sits on the ground and you only paint the top and sides, you would use the top area plus the lateral area and skip the bottom — roughly 103.67 square meters. Multiplying by the number of coats and dividing by the coverage rate on your paint can (often listed in square meters or square feet per liter or gallon) tells you how much paint to buy. This is exactly why the calculator breaks the result into separate faces: real projects rarely cover every surface, and seeing each part lets you add only the ones that matter.
One of the most useful quantities you can derive from surface area is the surface-area-to-volume ratio, found by dividing a shape's surface area by its volume. Because surface area grows with the square of size while volume grows with the cube, small objects have a much higher ratio than large ones. This single idea explains a startling range of phenomena. Crushed ice melts faster than a single block because breaking it up multiplies the exposed surface. Small mammals eat more relative to their size because they lose body heat quickly through their proportionally large skin area. Engineers design radiators, filters, and catalytic converters with intricate folded or porous surfaces precisely to maximize this ratio and speed up heat or chemical exchange. Whenever transfer across a boundary matters — heat, moisture, nutrients, or reactants — the surface-area-to-volume ratio is the number that governs how fast it happens, and pairing this calculator with a volume calculation lets you compute it directly.
You can enter each dimension in miles, yards, feet, inches, kilometers, meters, centimeters, millimeters, micrometers, nanometers, or angstroms. The surface area is returned in the square of the unit you select, and if you mix units the result is shown in each unit used.
Surface area measures the total area of the outside of a shape, in square units, and tells you how much material covers it. Volume measures the space inside, in cubic units, and tells you how much it holds. Both are computed from the same dimensions but answer different questions.
Unlike the sphere, an ellipsoid has no simple exact closed-form surface-area formula — the exact expression involves elliptic integrals. The calculator uses the Thomsen approximation, which is accurate to a fraction of a percent for typical ellipsoids and is the standard practical formula.
Lateral surface area is the area of the curved or slanted sides of a shape, not counting the flat top and bottom faces. For a cylinder it is the label area (2πrh); for a cone it is the slanted cone side. Total surface area adds the flat faces to the lateral area.
Start with the total surface area from the appropriate formula, then subtract the area of any missing face. For an open-top cylinder, subtract one circular end (πr²); for a box without a lid, subtract the top rectangle. The calculator shows each face separately to make this easy.
Not directly, but you can approximate it by dividing the object into the standard shapes offered here, computing each, and adding the exposed surfaces while subtracting any areas where the pieces join. For very irregular shapes, specialized 3D scanning or numerical methods are used.
This Surface Area Calculator is provided for educational and informational purposes. Results are computed with standard geometric formulas (and, for the ellipsoid, a high-accuracy approximation) and displayed to high precision; round them as appropriate for your application. For engineering, construction, or other critical work, always verify measurements and calculations independently.