The Surface Area Calculator calculates the total surface area of a 3D shape by adding up the area of every face and curved surface. For a cube that means 6 × side², for a cylinder the two circular ends plus the curved side (2πr² + 2πrh), and for a sphere 4πr².
Surface Area Calculator
Find the total surface area of common 3D shapes: cube, box, cylinder, sphere, cone, hemisphere, triangular prism and square pyramid.
Choose a shape — cube, rectangular prism (box), cylinder, sphere, cone, hemisphere, triangular prism or square pyramid — and enter its dimensions in any unit to get the surface area instantly.
Surface Area Formulas
The calculator uses a separate formula for each shape. Every formula adds together the areas of all the faces (flat or curved) that enclose the solid.
| Shape | Total surface area formula |
|---|---|
| Cube | A = 6a² |
| Rectangular prism (box) | A = 2(lw + lh + wh) |
| Cylinder | A = 2πr² + 2πrh = 2πr(r + h) |
| Sphere | A = 4πr² |
| Cone | A = πr² + πrs, where s = √(r² + h²) |
| Hemisphere (with flat base) | A = 2πr² + πr² = 3πr² |
| Triangular prism | A = 2B + (a + b + c) × L |
| Square pyramid | A = a² + 2as, where s = √(h² + (a/2)²) |
Where:
- A = total surface area
- a = side length (cube) or base side (pyramid); a, b, c = triangle sides (prism)
- l, w, h = length, width and height
- r = radius; s = slant height
- B = area of the triangular end of a prism; L = prism length
How the Calculation Works
Step 1: Break the solid into its surfaces — flat faces (squares, rectangles, triangles, circles) and curved surfaces (the side of a cylinder or cone, the skin of a sphere).
Step 2: Find the area of each surface. Flat faces use ordinary area formulas; curved surfaces use their own rules, such as 2πrh for the side of a cylinder or πrs for the side of a cone.
Step 3: Add all the surface areas together. The total is the surface area in square units (cm², m², in², ft²).
For cones and pyramids the calculator first works out the slant height from the vertical height with the Pythagorean theorem, because the sloping faces are measured along the slope, not straight up.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| a | Side length of a cube, or base side of a square pyramid | cm, m, in, ft… |
| l, w, h | Length, width and height of a box | cm, m, in, ft… |
| r | Radius (half the diameter) | cm, m, in, ft… |
| h | Vertical height (cylinder, cone, pyramid) | cm, m, in, ft… |
| s | Slant height, measured along the sloping face | cm, m, in, ft… |
| A | Total surface area | cm², m², in², ft²… |
You can enter each dimension in a different unit (for example, radius in mm and height in m). The calculator converts everything before calculating, and you can switch the result to any area unit.
Example Calculations
Cylinder
Given: radius = 3 cm, height = 10 cm
Formula: A = 2πr(r + h)
Calculation: A = 2 × 3.14159 × 3 × (3 + 10) = 2 × 3.14159 × 39
Result: A ≈ 245.04 cm²
Rectangular box
Given: length = 8 cm, width = 5 cm, height = 4 cm
Calculation: A = 2(8×5 + 8×4 + 5×4) = 2(40 + 32 + 20) = 2 × 92
Result: A = 184 cm²
Square pyramid
Given: base side = 6 cm, height = 4 cm
Slant height: s = √(4² + 3²) = √25 = 5 cm
Calculation: A = 6² + 2 × 6 × 5 = 36 + 60
Result: A = 96 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 cm² | 100 mm² |
| 1 m² | 10.7639 ft² |
| 1 ft² | 144 in² |
| 1 in² | 6.4516 cm² |
| 1 yd² | 9 ft² |
Because area is two-dimensional, conversion factors are squared: 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm².
Shape Properties
Solids with flat faces
Cubes, boxes, prisms and pyramids are polyhedra — every face is a flat polygon, so the surface area is simply the sum of polygon areas. A cube has 6 equal square faces; a box has 3 pairs of equal rectangles; a triangular prism has 2 triangles and 3 rectangles; a square pyramid has 1 square and 4 triangles.
Solids with curved surfaces
Cylinders, cones, spheres and hemispheres have curved surfaces. If you unroll the side of a cylinder it becomes a rectangle 2πr wide and h tall, which is why its curved area is 2πrh. A cone’s side unrolls into a sector of a circle with area πrs.
Dimensions Explained
Radius vs diameter
Every round shape here uses the radius. If you measured the diameter, divide it by 2 first.
Height vs slant height
Enter the vertical (perpendicular) height for cones and pyramids. The calculator converts it to slant height. If you only know the slant height, use the dedicated cone or pyramid surface area calculator, which accepts slant height directly.
Total vs lateral surface area
This calculator gives total surface area, including bases. Lateral surface area leaves out the top and bottom faces — use the Lateral Surface Area Calculator for that.
Frequently Asked Questions
How do you calculate surface area?
Find the area of each face or curved surface of the shape and add them together. For example, a cube with 5 cm sides has 6 faces of 25 cm² each, so its surface area is 150 cm².
What is the difference between surface area and volume?
Surface area measures the outside covering of a solid in square units (cm²). Volume measures the space inside it in cubic units (cm³). Use surface area for paint, wrapping or coating; use volume for capacity.
What units is surface area measured in?
Square units such as mm², cm², m², in², ft² or yd². If your dimensions are in centimeters, the surface area is in square centimeters.
Does surface area include the base?
Total surface area does. Lateral surface area excludes the bases. This calculator returns total surface area for every shape; the hemisphere result includes its flat circular base.
How do you find the surface area of a cylinder?
Use A = 2πr² + 2πrh: two circular ends plus the curved side. A cylinder with r = 3 cm and h = 10 cm has a surface area of about 245.04 cm².
How do you find the surface area of a sphere?
Multiply 4 × π × radius². A sphere with a 5 cm radius has a surface area of 4 × π × 25 ≈ 314.16 cm².
How do you find the surface area of an irregular 3D shape?
Split it into simpler solids, calculate the exposed surface of each part, and subtract any faces that are joined together and hidden. The Composite Figure Surface Area Calculator does this for common combinations.