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Free surface area calculator for cube, sphere, cylinder, cone & rectangular prism. Calculate surface area and volume instantly with step-by-step solutions.
Calculate surface area & volume of 3D shapes - Cube, Sphere, Cylinder, Cone, Rectangular Prism
Surface area is the total area of all the outer surfaces of a three-dimensional object. It measures how much area the surface of the object occupies, expressed in square units (cm², m², in², ft²). Unlike volume which measures the space inside, surface area measures the outside covering.
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Enter Dimensions: Input the required measurements for your selected shape
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Formula: SA = 6a²
Where: a = side length
Example: If side = 5 cm, SA = 6 × 5² = 150 cm²
Formula: SA = 2(lw + lh + wh)
Where: l = length, w = width, h = height
Example: If l=5, w=3, h=4 cm, SA = 2(15+20+12) = 94 cm²
Formula: SA = 4πr²
Where: r = radius
Example: If radius = 7 cm, SA = 4 × π × 49 = 615.75 cm²
Formula: SA = 2πr(r + h)
Where: r = radius, h = height
Example: If r=3, h=10 cm, SA = 2π × 3 × 13 = 245.04 cm²
Formula: SA = πr(r + l)
Where: r = radius, l = slant height = √(r² + h²)
Example: If r=4, h=3 cm, l=5, SA = π × 4 × 9 = 113.10 cm²
Cylinder LSA: 2πrh (curved surface only)
Cylinder TSA: 2πr(r + h) (includes bases)
Our calculator shows Total Surface Area
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Surface area is the total area of all outer surfaces of a three-dimensional object, measured in square units (cm², m², in², ft²). It represents the amount of material needed to cover the object completely.
To calculate cube surface area, use the formula SA = 6a² where 'a' is the side length. Since a cube has 6 equal square faces, multiply the area of one face (a²) by 6. For example, if the side is 5 cm, SA = 6 × 5² = 150 cm².
The surface area of a sphere is calculated using SA = 4πr² where r is the radius. For example, if radius = 7 cm, SA = 4 × π × 7² = 615.75 cm². This formula calculates the total curved surface area of the sphere.
Cylinder surface area is calculated using SA = 2πr(r + h) where r is radius and h is height. This formula includes both circular bases and the curved surface. For example, if r = 3 cm and h = 10 cm, SA = 2π × 3 × 13 = 245.04 cm².
Surface area measures the total area of all outer surfaces in square units (cm², m²), while volume measures the space inside a 3D object in cubic units (cm³, m³). Surface area is a 2D measurement of the exterior, while volume is a 3D measurement of interior capacity.
Calculate surface area for cube, rectangular prism, sphere, cylinder, and cone
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| Aspect | Surface Area | Volume |
|---|---|---|
| Definition | Total area of outer surfaces | Space inside the 3D object |
| Units | Square units (cm², m², in²) | Cubic units (cm³, m³, in³) |
| Dimension | 2D measurement | 3D measurement |
| Cube Formula | 6a² | a³ |
| Sphere Formula | 4πr² | (4/3)πr³ |
| Use Cases | Painting, wrapping, coating | Capacity, filling, storage |