Surface Area Calculator
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Total surface area:
Isometric reference drawing (approximate proportions) and its unfolded net.
Lateral surface area:
Area of the bases:
Slant height (s):
Calculation:
With this surface area calculator you pick a solid (cylinder, cone, sphere, hemisphere, cube, rectangular prism, square pyramid or triangular prism), enter its dimensions and get the total area, the lateral area and the area of the bases. It also draws the solid and, for the ones that can be unfolded, its net with the side faces in blue (lateral) and the bases in orange.
Below you will find the formulas, worked examples and the most common questions.
How to use the surface area calculator
Step 1: Pick the Solid from the list. The input boxes, the drawing and the net change with your choice.
Step 2: If you like, pick a length unit so the results come with their unit (for example cm²).
Step 3: Enter the dimensions. A decimal point or comma both work, for example 2.5 or 2,5. For the triangular prism you enter the three sides of the triangular base and the length of the prism.
Step 4: Click Calculate or press Enter. You get the total area, the lateral area, the area of the bases (and the slant height for the cone and the pyramid), and the Calculation box shows every step.
Surface area formulas
The lateral area is the sum of the faces that are not bases. The total area is the lateral area plus the bases. It is measured in square units (cm², m², ft²):
| Solid | Lateral area | Total area |
|---|---|---|
| Cube | 4a² | 6a² |
| Rectangular prism | 2c(a + b) | 2(ab + ac + bc) |
| Cylinder | 2πrh | 2πr(r + h) |
| Cone | πrs, with s = √(r² + h²) | πr(r + s) |
| Sphere | 4πr² (the whole surface) | 4πr² |
| Hemisphere | 2πr² | 3πr² |
| Square pyramid | 2as, with s = √(h² + (a/2)²) | a² + 2as |
| Triangular prism | (a + b + c) × L | 2 × triangle area + (a + b + c) × L |
In the cone, s is the slant height (the sloping side) and in the pyramid, s is the height of each triangular face. Both come from the Pythagorean theorem.
Surface area examples
Example 1: A cube with edge 4
A cube has six equal square faces. Four are lateral faces and two are the bases (top and bottom):
A (lateral) = 4a² = 4 × 4² = 64 cm²
A (total) = 6a² = 6 × 4² = 96 cm²
The total surface area is 96 cm² and the lateral area is 64 cm².
Example 2: A can (cylinder)
A cylinder has radius 3 cm and height 5 cm. The lateral surface is a rectangle of length 2πr and height h, and the bases are two circles:
A (lateral) = 2πrh = 2 × π × 3 × 5 ≈ 94.25 cm²
A (total) = 2πr(r + h) = 2 × π × 3 × (3 + 5) ≈ 150.8 cm²
The can needs 150.8 cm² of material, of which 94.25 cm² is the side label.
Example 3: A cone
A cone has radius 3 cm and height 4 cm. First the slant height s, the hypotenuse of the triangle formed by the radius and the height:
s = √(r² + h²) = √(9 + 16) = 5 cm
A (lateral) = πrs = π × 3 × 5 ≈ 47.12 cm²
A (total) = πr(r + s) = π × 3 × (3 + 5) ≈ 75.4 cm²
The slant height is 5 cm and the total surface area is 75.4 cm².
Example 4: A rectangular prism
A box is 4 cm long, 3 cm wide and 5 cm tall:
A (lateral) = 2c(a + b) = 2 × 5 × (4 + 3) = 70 cm²
A (total) = 2(ab + ac + bc) = 2 × (12 + 20 + 15) = 94 cm²
It takes 94 cm² of cardboard to cover it completely.
Frequently asked questions
What is the difference between lateral area and total area?
The lateral area counts only the side faces. The total area adds the bases too. For the cylinder with radius 3 and height 5, the lateral area is 94.25 and the total is 150.8.
What is the net of a solid?
It is the flat shape you get when you cut the solid open and lay it out on a plane. A cylinder opens into a rectangle and two circles; a cone opens into a circular sector and a circle. It shows where each term of the formula comes from.
How do you find the slant height of a cone?
With the Pythagorean theorem: s = √(r² + h²). With radius 3 and height 4, s = 5.
Why does a sphere have no lateral area?
It has no bases or flat faces: its whole surface is a single curved surface of area 4πr². That is why the calculator shows only the total area.
What units does the area come in?
The length unit squared: if you measure in cm, the result comes out in cm². Convert every measurement to the same unit before calculating.
Learn more
- Surface area of a cube
- Surface area of a cylinder
- Surface area of a rectangular prism
- Surface area of a triangular prism
- Area and volume of a sphere
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- Volume Calculator
- Area and Perimeter Calculator
- Circle Calculator (Area and Circumference)
- Triangle Calculator
- Pythagorean Theorem Calculator
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