This surface area calculator computes the surface area of geometric shapes, including sphere, cone, cylinder, torus, capsule, cube, rectangular prism and conical frustum. Formulas are provided below. Use it to calculate the total outer area of 3D objects quickly and accurately. Select a shape, enter dimensions, and get step-by-step results instantly.
Calculation Steps
Surface Area Formulas for Common Shapes
Below are the standard surface area formulas for common 3D shapes. These help you quickly reference each equation before using the calculators.
- Sphere:
4πr²— where r is the radius. - Cylinder:
2πr(h + r)— r is radius, h is height. - Cone:
πr(l + r)— r is radius, l is slant height. - Torus:
4π²Rr— R is major radius, r is minor radius. - Capsule:
2πr(2r + h)— r is radius, h is cylindrical height. - Conical Frustum:
π(r + R)l + πr² + πR²— r is top radius, R is base radius, l is slant height. - Rectangular Prism:
2(lw + lh + wh)— l = length, w = width, h = height. - Cube:
6a²— a is the side length.
Surface Area Calculators
Surface Area of Sphere Calculator
Surface Area of Cylinder Calculator
Surface Area of Cone Calculator
Surface Area of Torus Calculator
Surface Area of Capsule Calculator
Surface Area of Conical Frustum Calculator
Surface Area of Rectangular Prism Calculator
Surface Area of Cube Calculator
Multiple-shape use case: Estimating area across cones, cylinders, and flat boards? Use the surface area calculator for the full object, and switch to the area calculator when you only need cross-sections — like circles, rectangles, or trapezoids — for base layouts or material cutouts.
Formula for Sphere
The surface area of a sphere is calculated using A = 4 × π × r², where r is the radius from the center to the surface. This formula is used to measure the external area of round objects. For example, a sphere with radius 5 cm yields A = 4 × π × 5² = 4 × π × 25 ≈ 314.16 cm² using the sphere surface area calculator.
Formula for Cone
The surface area of a cone is A = π × r × (r + l), where r is the radius and l is the slant height. This includes the circular base and the curved side surface. Using the cone calculator with r = 4 in and l = 7 in, we get A = π × 4 × (4 + 7) = π × 4 × 11 ≈ 138.23 in².
Formula for Cylinder
The surface area of a cylinder is A = 2 × π × r × (r + h), where r is the radius and h is the height. This covers both circular ends and the side surface. For a cylinder with r = 3 m and h = 10 m, the calculator gives A = 2 × π × 3 × (3 + 10) = 2 × π × 3 × 13 ≈ 245.04 m².
Formula for Torus
The surface area of a torus is A = 4 × π² × R × r, where R is the major radius and r is the minor radius. This is used for doughnut-shaped 3D objects. With R = 6 cm and r = 2 cm, the torus calculator shows A = 4 × π² × 6 × 2 ≈ 474.98 cm².
Formula for Capsule
The surface area of a capsule is A = 2 × π × r × (2r + h), where r is the radius and h is the cylindrical height between the hemispherical ends. For r = 2 m and h = 5 m, the capsule area calculator computes A = 2 × π × 2 × (4 + 5) = 2 × π × 2 × 9 ≈ 113.10 m².
Formula for Conical Frustum
The surface area of a conical frustum is A = π × (r₁ + r₂) × √[(r₁ - r₂)² + h²] + π × r₁² + π × r₂², where r₁ and r₂ are the radii of the two ends and h is the height. This is useful for truncated cones like buckets or lampshades. For r₁ = 5 cm, r₂ = 3 cm, and h = 10 cm, the calculator gives approximately A ≈ 471.24 cm².
Frequently Asked Questions
What is surface area?
Surface area is the total area covering the outer surface of a three-dimensional object.
What's the difference between surface area and volume?
Surface area measures the outside covering, while volume measures the space inside an object.
Can I use these calculators for school or construction?
Yes. They're helpful for students, teachers, engineers, and builders to estimate surface coverage.