Surface Area Calculator
Calculate the surface area and volume of 3D shapes including cubes, spheres, cylinders, cones, pyramids, and prisms.
Results
Surface Area
94.0000
Square units
Select Shape & Dimensions
Calculation
Formula
SA = 2(lw + lh + wh)
Total Surface Area
94.0000
square units
Volume
60.0000
cubic units
Area Breakdown
Surface Area Formulas
Cube
SA = 6s²
V = s³
Rectangular Prism
SA = 2(lw + lh + wh)
V = lwh
Sphere
SA = 4πr²
V = (4/3)πr³
Cylinder
SA = 2πr² + 2πrh
V = πr²h
Cone
SA = πr² + πrl
V = (1/3)πr²h
Square Pyramid
SA = b² + 2bl
V = (1/3)b²h
Where: s = side, l = length, w = width, h = height, r = radius, b = base, l (in cone/pyramid) = slant height
Practical Applications
Painting & Coating
Calculate how much paint or coating is needed to cover an object. Paint coverage is usually given in m²/liter.
Packaging
Determine material needed for wrapping or boxing products. Minimize packaging costs by optimizing surface area.
Heat Transfer
Heat loss/gain is proportional to surface area. Important for HVAC calculations and insulation planning.
Results
Surface Area
94.0000
Square units
?How Do You Calculate Surface Area?
Surface area is the total area covering a 3D object. Cube: 6*s^2. Sphere: 4*pi*r^2. Cylinder: 2*pi*r^2 + 2*pi*r*h (two circles + curved surface). Cone: pi*r^2 + pi*r*l (base + lateral). Rectangular prism: 2(lw + lh + wh). Surface area is measured in square units.
What is Surface Area?
Surface area is the total area of all surfaces (faces) of a three-dimensional object. It measures how much material would be needed to cover the outside of a solid shape. Surface area calculations are essential in manufacturing, construction, packaging, heat transfer, and many engineering applications.
Key Facts About Surface Area
- Cube surface area = 6 * side^2 (6 equal square faces)
- Sphere surface area = 4 * pi * r^2
- Cylinder = 2*pi*r^2 + 2*pi*r*h (2 circles + lateral)
- Cone = pi*r^2 + pi*r*l (l = slant height)
- Rectangular prism = 2(lw + lh + wh)
- Lateral surface area excludes bases
- Total surface area includes all faces and bases
- Surface area is always in square units (cm^2, m^2, etc.)
Quick Answer
Surface area is the total area covering a 3D object. Cube: 6*s^2. Sphere: 4*pi*r^2. Cylinder: 2*pi*r^2 + 2*pi*r*h (two circles + curved surface). Cone: pi*r^2 + pi*r*l (base + lateral). Rectangular prism: 2(lw + lh + wh). Surface area is measured in square units.
Frequently Asked Questions
Surface area is the total area of all the surfaces (faces) of a 3D object. Imagine wrapping the object in paper - surface area is the amount of paper needed. It's measured in square units (cm², m², ft², etc.).
A cube has 6 identical square faces. Surface area = 6s², where s is the side length. For example, a cube with 3cm sides has surface area = 6 × 3² = 6 × 9 = 54 cm².
Surface area measures the total outer covering of a 3D shape (in square units). Volume measures the space inside the shape (in cubic units). Surface area is like the wrapping paper, volume is like the gift inside.
Lateral surface area is the area of just the sides of a 3D shape, excluding the top and bottom (bases). For a cylinder, it's the curved surface only (2πrh). For a prism, it's all the rectangular faces.
The surface area of a sphere is SA = 4πr², where r is the radius. This equals exactly 4 times the area of a circle with the same radius. For Earth (r ≈ 6,371 km), SA ≈ 510 million km².
Last updated: 2025-01-15
Results
Surface Area
94.0000
Square units