Use the calculators below to calculate the surface area of several common shapes.
Please provide any two values below to calculate
The surface area of a solid is a measure of the total area that the surface of the object occupies. For 3D shapes, surface area is the sum of the areas of all faces or surfaces. Surface area is measured in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²).
A sphere is a perfectly round 3D shape where all points on the surface are equidistant from the center. The surface area of a sphere is calculated using the formula:
A = 4πr²
Where r is the radius
Example:
Find the surface area of a sphere with radius 5 meters.
A = 4 × π × 5² = 4 × π × 25 = 100π ≈ 314.16 m²
A cone is a 3D shape with a circular base and a single vertex. The surface area includes the base and the lateral (side) surface.
A = πr(r + s)
Where r is base radius, s is slant height = √(r² + h²)
A cube is a 3D shape with six equal square faces. The surface area is simply six times the area of one face.
A = 6a²
Where a is the edge length
A cylinder has two circular bases and a curved lateral surface. The surface area includes both bases and the lateral surface.
A = 2πr(r + h)
Where r is radius, h is height
A rectangular tank has six rectangular faces. The surface area is the sum of the areas of all six faces.
A = 2(lw + lh + wh)
Where l is length, w is width, h is height
A capsule is a cylinder with hemispherical ends. The surface area includes the curved surface of the cylinder and both hemispheres.
A = 2πr(2r + h)
Where r is radius, h is height of the cylindrical portion
A spherical cap is a portion of a sphere cut off by a plane. You need any two of: base radius (r), ball radius (R), or height (h).
A = 2πRh
Where R is ball radius, h is cap height
A conical frustum is a truncated cone with two parallel circular bases of different sizes.
A = π(r² + R² + (r + R)s)
Where r is top radius, R is bottom radius, s = √((R-r)² + h²)
An ellipsoid is a 3D shape that is a stretched or compressed sphere. The surface area calculation uses an approximation formula.
A ≈ 4π[(aᵖbᵖ + aᵖcᵖ + bᵖcᵖ)/3]^(1/p)
Where a, b, c are the three axes, p ≈ 1.6075
A square pyramid has a square base and four triangular faces meeting at a point (apex).
A = a² + 2as
Where a is base edge, s is slant height = √(h² + (a/2)²)
| Unit | meter² |
|---|---|
| m² | 1.000000e+0 |
| km² | 1.000000e+6 |
| hm² | 1.000000e+4 |
| dam² | 1.000000e+2 |
| dm² | 1.000000e-2 |
| cm² | 1.000000e-4 |
| mm² | 1.000000e-6 |
| μm² | 1.000000e-12 |
| nm² | 1.000000e-18 |
| ha | 1.000000e+4 |
| acre | 4.046860e+3 |
| mi² | 2.589988e+6 |
| yd² | 8.361270e-1 |
| ft² | 9.290300e-2 |
| in² | 6.451600e-4 |